1.1
1. 2.
3.
1.2
1.2.1
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How to use this Notebook
Run the cells to get a birds eye view of whats going on.
Interact with the code to better understand how it worksadd cells, plot values, change parameters, etc.
Complete exercises.
Principle Component AnalysisIntroduction
Principle Component Analysis
lab 3 final
October 24, 2019
1 APS1070
PCAProject 3 Project 3 is structured a bit differently than Projects 1 and 2here, all the code for the tutorial part is given. Youre encouraged to read closely, adjust and experiment to make sure you fully understand what the code is doing. Once you have a firm grasp of PCA, you should be in great shape for the exercises at the end. Note that all 12.5 marks for this project are attributed to the exercises. The tutorial is not marked.
Please fill out the following:
As you get deeper in the world of data science, youll learn that in practice its very uncommon to work with datasets that are 2 or 3 dimensional, and so can be plotted directly. Were now going to look at dimensionality reduction : a category of unsupervised algorithms which attempt to collapse highdimensional datasets into a lowdimensional space.
As suggested above, one reason to do this is to aid visualization. However, thats far from the only reason dimensionality reduction is useful! These techniques also allow us to filter noise, extract useful features, and accomplish much more.
Lets dive into PCA with the Iris dataset.
1.2.2 PCAOverview
1. Standardize the data.
2. Obtain the Eigenvectors and Eigenvalues from the Covariance matrix or Correlation matrix, or perform Singular Vector Decomposition.
3. Sort eigenvalues in descending order and choose the k eigenvectors that correspond to the k largest eigenvalues where k is the number of dimensions of the new feature subspace. k is less than original dimensionality.
4. Construct the projection matrix W from the selected k eigenvectors.
5. Transform the original dataset X via W to obtain a kdimensional feature subspace Y.
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1.3 PCAIris dataset
Whats that flower?
1.3.1 Intro
For the following tutorial, we will be working with the famous Iris dataset that has been deposited on the UCI machine learning repository https:archive.ics.uci.edumldatasetsIris.
The iris dataset contains measurements for 150 iris flowers from three different species.
The three classes in the Iris dataset are: 1. Irissetosa n50 1. Irisversicolor n50 1. Irisvirginica n50
And the four features of in Iris dataset are: 1. sepal length in cm 1. sepal width in cm 1. petal length in cm 1. petal width in cm
In 0: import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
In 0: dfpd.readcsvfilepathorbufferhttps:raw.githubusercontent.comaps10702019datasetsmas
headerNone,
Out0:
145
146
147
148
149
sepal len 6.7 6.3 6.5 6.2 5.9
sepal wid 3.0 2.5 3.0 3.4 3.0
petal len 5.2
5.0
5.2
5.4
5.1
petal wid class 2.3 Irisvirginica 1.9 Irisvirginica 2.0 Irisvirginica 2.3 Irisvirginica 1.8 Irisvirginica
sep,
df.columnssepallen, sepalwid, petallen, petalwid, class
df.tail
In 0:split data table into data X and class labels y Xdf.iloc:,0:4.values
ydf.iloc:,4.values
In 0: labelssety
labels
Out0: Irissetosa, Irisversicolor, Irisvirginica
1.3.2 Exploratory Data Analysis
Lets explore a bit.
In 0: fig, axesplt.subplots2, 2, figsize12,12
noOfColsX.shape1
iterate over each column feature, and plot in separate subplot.
for col in rangenoOfCols:
plot data for different labels for choosen column feature. for label in labels:
axes.flatcol.histXylabel, col, alpha0.5, labellabel
axes.flatcol.legendlocupper right
axes.flatcol.setxlabeldf.columnscol, ylabelcount 2
As one can see, no feature can on its own predict the class of the flower.
1.3.3 Standardizing Data
Since PCA yields a feature subspace that maximizes the variance along the axes, it makes sense to standardize the data, especially, if it was measured on different scales.
Although, all features in the Iris dataset were measured in centimeters, let us continue with the trans formation of the data onto unit scale mean0 and variance1, which is a requirement for the optimal performance of many machine learning algorithms.
In 0: XstdStandardScaler.fittransformX
In 0: X:, 0.mean, Xstd:, 0.mean
Out0: 5.843333333333334, 4.736951571734001e16
In 0: X:, 0.var, Xstd:, 0.var
Out0: 0.6811222222222223, 1.0
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1.3.4 EigendecompositionComputing Eigenvectors and Eigenvalues
The eigenvectors and eigenvalues of a covariance or correlation matrix represent the core of a PCA: The eigenvectors principal components determine the directions of the new feature space, and the eigenvalues determine their magnitude. In other words, the eigenvalues explain the variance of the data along the new feature axes.
Methods to perform PCA: 1. The classic approach to PCA is to perform the eigendecomposition on the covariance matrix , which is a dd matrix where each element represents the covariance between two features. 2. But, most PCA implementations perform a Singular Vector Decomposition SVD to improve the computational efficiency.
Using Covariance Matrix
In 0: n, mXstd.shape
Compute covariance matrix
Cnp.dotXstd.T, Xstdn1or Cnp.covXstd.T
Eigen decomposition
eigenValues, eigenVectorsnp.linalg.eigC
eigenVectors, eigenValues
Out0: array 0.52237162, 0.37231836, 0.72101681,0.26199559,
0.26335492, 0.92555649,0.24203288, 0.12413481,
0.58125401, 0.02109478,0.14089226, 0.80115427,
0.56561105, 0.06541577,0.6338014 ,0.52354627,
array2.93035378, 0.92740362, 0.14834223, 0.02074601
Using Singular Vector Decomposition
In 0: eigenVectors, s, vnp.linalg.svdXstd.T
eigenVectors
Out0: array0.52237162, 0.37231836,0.72101681,0.26199559,
0.26335492, 0.92555649, 0.24203288, 0.12413481,
0.58125401, 0.02109478, 0.14089226, 0.80115427,
0.56561105, 0.06541577, 0.6338014 ,0.52354627
In 0: n, mXstd.shape
eigenValuess2n1
eigenValues
Out0: array2.93035378, 0.92740362, 0.14834223, 0.02074601
Are the eigenVectors and the eigenValues returned by both the methods the same?
Sort based on eigenValues Decreasing order of eigenValues. It was not needed in this case as eigenValues were already in decreasing order.
In 0: argseigenValues.argsort
eigenValueseigenValuesargs
eigenVectorseigenVectors:, args
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1.3.5 Explained Variance
In 0: eigValSumsumeigenValues
expVareigVeigValSum100 for eigV in eigenValues
cumExpVarnp.cumsumexpVar
cumExpVar
Out0: array 72.77045209,95.80097536,99.48480732, 100.
In 0: plt.barrange4, expVar, labelExplained Variance
plt.plotcumExpVar, ro, labelCumulative Explained Variance
plt.legend
plt.show
How many eigenValues are needed to explain more than 95 of variance?
1.3.6 Pro jections
Since only 2 eigenVectors are enough to explain more than 95 of variance, well create the projection matrix using the first 2 eigenVectors.
In 0: COUNT2
WeigenVectors:, 0:COUNT
W
Out0: array0.52237162, 0.37231836,
0.26335492, 0.92555649,
0.58125401, 0.02109478,
0.56561105, 0.06541577
In 0: projXnp.dotXstd, W
X.shape, projX.shape
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Out0: 150, 4, 150, 2
In 0: for label in labels:
plt.plotprojXylabel, 0, projXylabel, 1, o, labellabel
plt.legendlocupper right
What has PCA helped us achieve here?
1. Visualization: easier visualization of all 3 classes
2. Classification: a flower of unknown class can be plotted here, and then classified visually or using
algorithms such as KNNs
We have used PCA on numerical data. But can it used on Image data?
1.4 Eigenfaces
Lets face the Eigen.
1.4.1 Intro
Eigenfaces is the name given to a set of eigenvectors when they are used in the computer vision problem of human face recognition. The approach of using eigenfaces for recognition was developed by Sirovich and Kirby 1987 and used by Matthew Turk and Alex Pentland in face classification.
Eigenfaces refers to an appearancebased approach to face recognition that seeks to capture the variation in a collection of face images and use this information to encode and compare images of individual faces in a holistic as opposed to a partsbased or featurebased manner.
The motivation of Eigenfaces is twofold:
1. Extract the relevant facial information, which may or may not be directly related to human intuition of face features such as the eyes, nose, and lips. One way to do so is to capture the statistical variation between face images.
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2. Represent face images efficiently. To reduce the computation and space complexity, each face image can be represented using a small number of parameters.
Images are downloaded from Labeled Faces in the Wild.
In 0: !pip install wget
Requirement already satisfied: wget in usrlocallibpython3.6distpackages 3.2
In 0: import os
import numpy as np
from PIL import Image
import matplotlib.pyplot as plt
import wget
import math
In 0:Download and unzip dataset.
filenamewget.downloadhttps:github.comaps10702019datasetsrawmasterlfwa.tgz, lfwa !tar xvzf filename
lfwAaron Eckhart
lfwAaron EckhartAaron Eckhart 0001.jpg
lfwAaron Guiel
lfwAaron GuielAaron Guiel 0001.jpg
lfwAaron Patterson
lfwAaron PattersonAaron Patterson 0001.jpg lfwAaron Peirsol
lfwAaron PeirsolAaron Peirsol 0001.jpg
lfwAaron PeirsolAaron Peirsol 0002.jpg
lfwAaron PeirsolAaron Peirsol 0003.jpg
lfwAaron PeirsolAaron Peirsol 0004.jpg
lfwAaron Pena
lfwAaron PenaAaron Pena 0001.jpg
lfwAaron Sorkin
lfwAaron SorkinAaron Sorkin 0001.jpg
lfwAaron SorkinAaron Sorkin 0002.jpg
lfwAaron Tippin
lfwAaron TippinAaron Tippin 0001.jpg
lfwAbba Eban
lfwAbba EbanAbba Eban 0001.jpg
lfwAbbas Kiarostami
lfwAbbas KiarostamiAbbas Kiarostami 0001.jpg lfwAbdel Aziz AlHakim
lfwAbdel Aziz AlHakimAbdel Aziz AlHakim 0001.jpg lfwAbdel Madi Shabneh
lfwAbdel Madi ShabnehAbdel Madi Shabneh 0001.jpg lfwAbdel Nasser Assidi
lfwAbdel Nasser AssidiAbdel Nasser Assidi 0001.jpg lfwAbdel Nasser AssidiAbdel Nasser Assidi 0002.jpg lfwAbdoulaye Wade
lfwAbdoulaye WadeAbdoulaye Wade 0001.jpg lfwAbdoulaye WadeAbdoulaye Wade 0002.jpg lfwAbdoulaye WadeAbdoulaye Wade 0003.jpg lfwAbdoulaye WadeAbdoulaye Wade 0004.jpg lfwAbdulaziz Kamilov
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lfwAbdulaziz KamilovAbdulaziz Kamilov 0001.jpg lfwAbdullah
lfwAbdullahAbdullah 0001.jpg lfwAbdullahAbdullah 0002.jpg lfwAbdullahAbdullah 0003.jpg lfwAbdullahAbdullah 0004.jpg
lfwAbdullah Ahmad Badawi
lfwAbdullah Ahmad BadawiAbdullah Ahmad Badawi 0001.jpg
lfwAbdullah alAttiyah
lfwAbdullah alAttiyahAbdullah alAttiyah 0001.jpg
lfwAbdullah alAttiyahAbdullah alAttiyah 0002.jpg
lfwAbdullah alAttiyahAbdullah alAttiyah 0003.jpg
lfwAbdullah Gul
lfwAbdullah GulAbdullah Gul 0001.jpg
lfwAbdullah GulAbdullah Gul 0002.jpg
lfwAbdullah GulAbdullah Gul 0003.jpg
lfwAbdullah GulAbdullah Gul 0004.jpg
lfwAbdullah GulAbdullah Gul 0005.jpg
lfwAbdullah GulAbdullah Gul 0006.jpg
lfwAbdullah GulAbdullah Gul 0007.jpg
lfwAbdullah GulAbdullah Gul 0008.jpg
lfwAbdullah GulAbdullah Gul 0009.jpg
lfwAbdullah GulAbdullah Gul 0010.jpg
lfwAbdullah GulAbdullah Gul 0011.jpg
lfwAbdullah GulAbdullah Gul 0012.jpg
lfwAbdullah GulAbdullah Gul 0013.jpg
lfwAbdullah GulAbdullah Gul 0014.jpg
lfwAbdullah GulAbdullah Gul 0015.jpg
lfwAbdullah GulAbdullah Gul 0016.jpg
lfwAbdullah GulAbdullah Gul 0017.jpg
lfwAbdullah GulAbdullah Gul 0018.jpg
lfwAbdullah GulAbdullah Gul 0019.jpg
lfwAbdullah Nasseef
lfwAbdullah NasseefAbdullah Nasseef 0001.jpg
lfwAbdullatif Sener
lfwAbdullatif SenerAbdullatif Sener 0001.jpg
lfwAbdullatif SenerAbdullatif Sener 0002.jpg
lfwAbdul Majeed Shobokshi
lfwAbdul Majeed ShobokshiAbdul Majeed Shobokshi 0001.jpg
lfwAbdul Rahman
lfwAbdul RahmanAbdul Rahman 0001.jpg
lfwAbel Aguilar
lfwAbel AguilarAbel Aguilar 0001.jpg
lfwAbel Pacheco
lfwAbel PachecoAbel Pacheco 0001.jpg
lfwAbel PachecoAbel Pacheco 0002.jpg
lfwAbel PachecoAbel Pacheco 0003.jpg
lfwAbel PachecoAbel Pacheco 0004.jpg
lfwAbid Hamid Mahmud AlTikriti
lfwAbid Hamid Mahmud AlTikritiAbid Hamid Mahmud AlTikriti 0001.jpg lfwAbid Hamid Mahmud AlTikritiAbid Hamid Mahmud AlTikriti 0002.jpg lfwAbid Hamid Mahmud AlTikritiAbid Hamid Mahmud AlTikriti 0003.jpg lfwAbner Martinez
lfwAbner MartinezAbner Martinez 0001.jpg
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lfwAbraham Foxman
lfwAbraham FoxmanAbraham Foxman 0001.jpg
lfwAby HarEven
lfwAby HarEvenAby HarEven 0001.jpg
lfwAdam Ant
lfwAdam AntAdam Ant 0001.jpg
lfwAdam Freier
lfwAdam FreierAdam Freier 0001.jpg
lfwAdam Herbert
lfwAdam HerbertAdam Herbert 0001.jpg
lfwAdam Kennedy
lfwAdam KennedyAdam Kennedy 0001.jpg
lfwAdam Mair
lfwAdam MairAdam Mair 0001.jpg
lfwAdam Rich
lfwAdam RichAdam Rich 0001.jpg
lfwAdam Sandler
lfwAdam SandlerAdam Sandler 0001.jpg
lfwAdam SandlerAdam Sandler 0002.jpg
lfwAdam SandlerAdam Sandler 0003.jpg
lfwAdam SandlerAdam Sandler 0004.jpg
lfwAdam Scott
lfwAdam ScottAdam Scott 0001.jpg
lfwAdam ScottAdam Scott 0002.jpg
lfwAdel AlJubeir
lfwAdel AlJubeirAdel AlJubeir 0001.jpg
lfwAdel AlJubeirAdel AlJubeir 0002.jpg
lfwAdel AlJubeirAdel AlJubeir 0003.jpg
lfwAdelina Avila
lfwAdelina AvilaAdelina Avila 0001.jpg
lfwAdisai Bodharamik
lfwAdisai BodharamikAdisai Bodharamik 0001.jpg lfwAdolfo Aguilar Zinser
lfwAdolfo Aguilar ZinserAdolfo Aguilar Zinser 0001.jpg lfwAdolfo Aguilar ZinserAdolfo Aguilar Zinser 0002.jpg lfwAdolfo Aguilar ZinserAdolfo Aguilar Zinser 0003.jpg lfwAdolfo Rodriguez Saa
lfwAdolfo Rodriguez SaaAdolfo Rodriguez Saa 0001.jpg lfwAdolfo Rodriguez SaaAdolfo Rodriguez Saa 0002.jpg lfwAdoor Gopalakarishnan
lfwAdoor GopalakarishnanAdoor Gopalakarishnan 0001.jpg lfwAdriana Lima
lfwAdriana LimaAdriana Lima 0001.jpg
lfwAdrian Annus
lfwAdrian AnnusAdrian Annus 0001.jpg
lfwAdriana Perez Navarro
lfwAdriana Perez NavarroAdriana Perez Navarro 0001.jpg lfwAdrian Fernandez
lfwAdrian FernandezAdrian Fernandez 0001.jpg lfwAdrian McPherson
lfwAdrian McPhersonAdrian McPherson 0001.jpg lfwAdrian McPhersonAdrian McPherson 0002.jpg lfwAdrian Murrell
lfwAdrian MurrellAdrian Murrell 0001.jpg
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lfwAdrian Nastase
lfwAdrian NastaseAdrian Nastase 0001.jpg lfwAdrian NastaseAdrian Nastase 0002.jpg lfwAdrianna Zuzic
lfwAdrianna ZuzicAdrianna Zuzic 0001.jpg lfwAdrien Brody
lfwAdrien BrodyAdrien Brody 0001.jpg
lfwAdrien BrodyAdrien Brody 0002.jpg
lfwAdrien BrodyAdrien Brody 0003.jpg
lfwAdrien BrodyAdrien Brody 0004.jpg
lfwAdrien BrodyAdrien Brody 0005.jpg
lfwAdrien BrodyAdrien Brody 0006.jpg
lfwAdrien BrodyAdrien Brody 0007.jpg
lfwAdrien BrodyAdrien Brody 0008.jpg
lfwAdrien BrodyAdrien Brody 0009.jpg
lfwAdrien BrodyAdrien Brody 0010.jpg
lfwAdrien BrodyAdrien Brody 0011.jpg
lfwAdrien BrodyAdrien Brody 0012.jpg
lfwAfton Smith
lfwAfton SmithAfton Smith 0001.jpg
lfwAgbani Darego
lfwAgbani DaregoAgbani Darego 0001.jpg
lfwAgnelo Queiroz
lfwAgnelo QueirozAgnelo Queiroz 0001.jpg lfwAgnes Bruckner
lfwAgnes BrucknerAgnes Bruckner 0001.jpg lfwAhmad Jbarah
lfwAhmad JbarahAhmad Jbarah 0001.jpg
lfwAhmad Masood
lfwAhmad MasoodAhmad Masood 0001.jpg
lfwAhmad MasoodAhmad Masood 0002.jpg
lfwAhmed Ahmed
lfwAhmed AhmedAhmed Ahmed 0001.jpg
lfwAhmed Chalabi
lfwAhmed ChalabiAhmed Chalabi 0001.jpg
lfwAhmed ChalabiAhmed Chalabi 0002.jpg
lfwAhmed ChalabiAhmed Chalabi 0003.jpg
lfwAhmed ChalabiAhmed Chalabi 0004.jpg
lfwAhmed ChalabiAhmed Chalabi 0005.jpg
lfwAhmed Ghazi
lfwAhmed GhaziAhmed Ghazi 0001.jpg
lfwAhmed Ibrahim Bilal
lfwAhmed Ibrahim BilalAhmed Ibrahim Bilal 0001.jpg lfwAhmed Lopez
lfwAhmed LopezAhmed Lopez 0001.jpg
lfwAhmed Qureia
lfwAhmed QureiaAhmed Qureia 0001.jpg
lfwAhmet Demir
lfwAhmet DemirAhmet Demir 0001.jpg
lfwAhmet Necdet Sezer
lfwAhmet Necdet SezerAhmet Necdet Sezer 0001.jpg lfwAhmet Necdet SezerAhmet Necdet Sezer 0002.jpg lfwAicha El Ouafi
lfwAicha El OuafiAicha El Ouafi 0001.jpg
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lfwAicha El OuafiAicha El Ouafi 0002.jpg lfwAicha El OuafiAicha El Ouafi 0003.jpg lfwAidan Quinn
lfwAidan QuinnAidan Quinn 0001.jpg lfwAileen Riggin Soule
lfwAileen Riggin SouleAileen Riggin Soule 0001.jpg lfwAin Seppik
lfwAin SeppikAin Seppik 0001.jpg
lfwAinsworth Dyer
lfwAinsworth DyerAinsworth Dyer 0001.jpg lfwAishwarya Rai
lfwAishwarya RaiAishwarya Rai 0001.jpg lfwAi Sugiyama
lfwAi SugiyamaAi Sugiyama 0001.jpg lfwAi SugiyamaAi Sugiyama 0002.jpg lfwAi SugiyamaAi Sugiyama 0003.jpg lfwAi SugiyamaAi Sugiyama 0004.jpg lfwAi SugiyamaAi Sugiyama 0005.jpg lfwAitor Gonzalez
lfwAitor GonzalezAitor Gonzalez 0001.jpg lfwAitor GonzalezAitor Gonzalez 0002.jpg lfwAiysha Smith
lfwAiysha SmithAiysha Smith 0001.jpg lfwAJ Cook
lfwAJ CookAJ Cook 0001.jpg
lfwAjit Agarkar
lfwAjit AgarkarAjit Agarkar 0001.jpg
lfwAJ Lamas
lfwAJ LamasAJ Lamas 0001.jpg
lfwAkbar Al Baker
lfwAkbar Al BakerAkbar Al Baker 0001.jpg
lfwAkbar Hashemi Rafsanjani
lfwAkbar Hashemi RafsanjaniAkbar Hashemi Rafsanjani 0001.jpg lfwAkbar Hashemi RafsanjaniAkbar Hashemi Rafsanjani 0002.jpg lfwAkbar Hashemi RafsanjaniAkbar Hashemi Rafsanjani 0003.jpg lfwAkhmed Zakayev
lfwAkhmed ZakayevAkhmed Zakayev 0001.jpg
lfwAkhmed ZakayevAkhmed Zakayev 0002.jpg
lfwAkhmed ZakayevAkhmed Zakayev 0003.jpg
lfwAkiko Morigami
lfwAkiko MorigamiAkiko Morigami 0001.jpg
lfwAkmal Taher
lfwAkmal TaherAkmal Taher 0001.jpg
lfwAlain Cervantes
lfwAlain CervantesAlain Cervantes 0001.jpg
lfwAlain Ducasse
lfwAlain DucasseAlain Ducasse 0001.jpg
lfwAlan Ball
lfwAlan BallAlan Ball 0001.jpg
lfwAlan BallAlan Ball 0002.jpg
lfwAlan Dershowitz
lfwAlan DershowitzAlan Dershowitz 0001.jpg
lfwAlan Dreher
lfwAlan DreherAlan Dreher 0001.jpg
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lfwAlan Greenspan
lfwAlan GreenspanAlan Greenspan 0001.jpg
lfwAlan GreenspanAlan Greenspan 0002.jpg
lfwAlan GreenspanAlan Greenspan 0003.jpg
lfwAlan GreenspanAlan Greenspan 0004.jpg
lfwAlan GreenspanAlan Greenspan 0005.jpg
lfwAlan Greer
lfwAlan GreerAlan Greer 0001.jpg
lfwAlanis Morissette
lfwAlanis MorissetteAlanis Morissette 0001.jpg lfwAlan Jackson
lfwAlan JacksonAlan Jackson 0001.jpg
lfwAlan Mulally
lfwAlan MulallyAlan Mulally 0001.jpg
lfwAlan MulallyAlan Mulally 0002.jpg
lfwAlanna Ubach
lfwAlanna UbachAlanna Ubach 0001.jpg
lfwAlan Stonecipher
lfwAlan StonecipherAlan Stonecipher 0001.jpg lfwAlan Tang Kwongwing
lfwAlan Tang KwongwingAlan Tang Kwongwing 0001.jpg lfwAlan Trammell
lfwAlan TrammellAlan Trammell 0001.jpg
lfwAlan Zemaitis
lfwAlan ZemaitisAlan Zemaitis 0001.jpg
lfwAlastair Campbell
lfwAlastair CampbellAlastair Campbell 0001.jpg lfwAlastair CampbellAlastair Campbell 0002.jpg lfwAlastair CampbellAlastair Campbell 0003.jpg lfwAlastair CampbellAlastair Campbell 0004.jpg lfwAlastair CampbellAlastair Campbell 0005.jpg lfwAlastair Johnston
lfwAlastair JohnstonAlastair Johnston 0001.jpg lfwAlbaro Recoba
lfwAlbaro RecobaAlbaro Recoba 0001.jpg
lfwAlberta Lee
lfwAlberta LeeAlberta Lee 0001.jpg
lfwAlbert Brooks
lfwAlbert BrooksAlbert Brooks 0001.jpg
lfwAlbert Costa
lfwAlbert CostaAlbert Costa 0001.jpg
lfwAlbert CostaAlbert Costa 0002.jpg
lfwAlbert CostaAlbert Costa 0003.jpg
lfwAlbert CostaAlbert Costa 0004.jpg
lfwAlbert CostaAlbert Costa 0005.jpg
lfwAlbert CostaAlbert Costa 0006.jpg
lfwAlbert Montanes
lfwAlbert MontanesAlbert Montanes 0001.jpg lfwAlberto Acosta
lfwAlberto AcostaAlberto Acosta 0001.jpg lfwAlberto Fujimori
lfwAlberto FujimoriAlberto Fujimori 0001.jpg lfwAlberto FujimoriAlberto Fujimori 0002.jpg lfwAlberto Gonzales
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lfwAlberto GonzalesAlberto Gonzales 0001.jpg lfwAlberto Ruiz Gallardon
lfwAlberto Ruiz GallardonAlberto Ruiz Gallardon 0001.jpg lfwAlberto Ruiz GallardonAlberto Ruiz Gallardon 0002.jpg lfwAlberto Sordi
lfwAlberto SordiAlberto Sordi 0001.jpg lfwAlbert Pujols
lfwAlbert PujolsAlbert Pujols 0001.jpg lfwAlbrecht Mentz
lfwAlbrecht MentzAlbrecht Mentz 0001.jpg lfwAlbrecht MentzAlbrecht Mentz 0002.jpg lfwAl Cardenas
lfwAl CardenasAl Cardenas 0001.jpg lfwAl Davis
lfwAl DavisAl Davis 0001.jpg
lfwAl DavisAl Davis 0002.jpg lfwAldo Paredes
lfwAldo ParedesAldo Paredes 0001.jpg lfwAldo ParedesAldo Paredes 0002.jpg lfwAlec Baldwin
lfwAlec BaldwinAlec Baldwin 0001.jpg lfwAlec BaldwinAlec Baldwin 0002.jpg lfwAlec BaldwinAlec Baldwin 0003.jpg lfwAlec BaldwinAlec Baldwin 0004.jpg lfwAlecos Markides
lfwAlecos MarkidesAlecos Markides 0001.jpg lfwAlejandro Atchugarry
lfwAlejandro AtchugarryAlejandro Atchugarry 0001.jpg lfwAlejandro AtchugarryAlejandro Atchugarry 0002.jpg lfwAlejandro Avila
lfwAlejandro AvilaAlejandro Avila 0001.jpg lfwAlejandro AvilaAlejandro Avila 0002.jpg lfwAlejandro AvilaAlejandro Avila 0003.jpg lfwAlejandro Fernandez
lfwAlejandro FernandezAlejandro Fernandez 0001.jpg
lfwAlejandro Gonzalez Inarritu
lfwAlejandro Gonzalez InarrituAlejandro Gonzalez Inarritu 0001.jpg lfwAlejandro Lembo
lfwAlejandro LemboAlejandro Lembo 0001.jpg
lfwAlejandro Lerner
lfwAlejandro LernerAlejandro Lerner 0001.jpg
lfwAlejandro Lopez
lfwAlejandro LopezAlejandro Lopez 0001.jpg
lfwAlejandro Toledo
lfwAlejandro ToledoAlejandro Toledo 0001.jpg
lfwAlejandro ToledoAlejandro Toledo 0002.jpg
lfwAlejandro ToledoAlejandro Toledo 0003.jpg
lfwAlejandro ToledoAlejandro Toledo 0004.jpg
lfwAlejandro ToledoAlejandro Toledo 0005.jpg
lfwAlejandro ToledoAlejandro Toledo 0006.jpg
lfwAlejandro ToledoAlejandro Toledo 0007.jpg
lfwAlejandro ToledoAlejandro Toledo 0008.jpg
lfwAlejandro ToledoAlejandro Toledo 0009.jpg
lfwAlejandro ToledoAlejandro Toledo 0010.jpg
13
lfwAlejandro ToledoAlejandro Toledo 0011.jpg lfwAlejandro ToledoAlejandro Toledo 0012.jpg lfwAlejandro ToledoAlejandro Toledo 0013.jpg lfwAlejandro ToledoAlejandro Toledo 0014.jpg lfwAlejandro ToledoAlejandro Toledo 0015.jpg lfwAlejandro ToledoAlejandro Toledo 0016.jpg lfwAlejandro ToledoAlejandro Toledo 0017.jpg lfwAlejandro ToledoAlejandro Toledo 0018.jpg lfwAlejandro ToledoAlejandro Toledo 0019.jpg lfwAlejandro ToledoAlejandro Toledo 0020.jpg lfwAlejandro ToledoAlejandro Toledo 0021.jpg lfwAlejandro ToledoAlejandro Toledo 0022.jpg lfwAlejandro ToledoAlejandro Toledo 0023.jpg lfwAlejandro ToledoAlejandro Toledo 0024.jpg lfwAlejandro ToledoAlejandro Toledo 0025.jpg lfwAlejandro ToledoAlejandro Toledo 0026.jpg lfwAlejandro ToledoAlejandro Toledo 0027.jpg lfwAlejandro ToledoAlejandro Toledo 0028.jpg lfwAlejandro ToledoAlejandro Toledo 0029.jpg lfwAlejandro ToledoAlejandro Toledo 0030.jpg lfwAlejandro ToledoAlejandro Toledo 0031.jpg lfwAlejandro ToledoAlejandro Toledo 0032.jpg lfwAlejandro ToledoAlejandro Toledo 0033.jpg lfwAlejandro ToledoAlejandro Toledo 0034.jpg lfwAlejandro ToledoAlejandro Toledo 0035.jpg lfwAlejandro ToledoAlejandro Toledo 0036.jpg lfwAlejandro ToledoAlejandro Toledo 0037.jpg lfwAlejandro ToledoAlejandro Toledo 0038.jpg lfwAlejandro ToledoAlejandro Toledo 0039.jpg lfwAleksander Kwasniewski
lfwAleksander KwasniewskiAleksander Kwasniewski 0001.jpg lfwAleksander KwasniewskiAleksander Kwasniewski 0002.jpg lfwAleksander KwasniewskiAleksander Kwasniewski 0003.jpg lfwAleksander KwasniewskiAleksander Kwasniewski 0004.jpg lfwAleksander Voloshin
lfwAleksander VoloshinAleksander Voloshin 0001.jpg lfwAlek Wek
lfwAlek WekAlek Wek 0001.jpg
lfwAlessandra Cerna
lfwAlessandra CernaAlessandra Cerna 0001.jpg lfwAlessandro Nesta
lfwAlessandro NestaAlessandro Nesta 0001.jpg lfwAlexa Loren
lfwAlexa LorenAlexa Loren 0001.jpg lfwAlexander Downer
lfwAlexander DownerAlexander Downer 0001.jpg lfwAlexander DownerAlexander Downer 0002.jpg lfwAlexander DownerAlexander Downer 0003.jpg lfwAlexander DownerAlexander Downer 0004.jpg lfwAlexander Losyukov
lfwAlexander LosyukovAlexander Losyukov 0001.jpg lfwAlexander LosyukovAlexander Losyukov 0002.jpg lfwAlexander LosyukovAlexander Losyukov 0003.jpg lfwAlexander LosyukovAlexander Losyukov 0004.jpg
14
lfwAlexander Lukashenko
lfwAlexander LukashenkoAlexander Lukashenko 0001.jpg lfwAlexander Payne
lfwAlexander PayneAlexander Payne 0001.jpg
lfwAlexander Rumyantsev
lfwAlexander RumyantsevAlexander Rumyantsev 0001.jpg lfwAlexander RumyantsevAlexander Rumyantsev 0002.jpg lfwAlexandra Jackson
lfwAlexandra JacksonAlexandra Jackson 0001.jpg lfwAlexandra Pelosi
lfwAlexandra PelosiAlexandra Pelosi 0001.jpg lfwAlexandra Rozovskaya
lfwAlexandra RozovskayaAlexandra Rozovskaya 0001.jpg lfwAlexandra Spann
lfwAlexandra SpannAlexandra Spann 0001.jpg
lfwAlexandra Stevenson
lfwAlexandra StevensonAlexandra Stevenson 0001.jpg lfwAlexandra StevensonAlexandra Stevenson 0002.jpg lfwAlexandra StevensonAlexandra Stevenson 0003.jpg lfwAlexandra Vodjanikova
lfwAlexandra VodjanikovaAlexandra Vodjanikova 0001.jpg lfwAlexandra VodjanikovaAlexandra Vodjanikova 0002.jpg lfwAlexandre Daigle
lfwAlexandre DaigleAlexandre Daigle 0001.jpg lfwAlexandre Despatie
lfwAlexandre DespatieAlexandre Despatie 0001.jpg lfwAlexandre Herchcovitch
lfwAlexandre HerchcovitchAlexandre Herchcovitch 0001.jpg lfwAlexandre Vinokourov
lfwAlexandre VinokourovAlexandre Vinokourov 0001.jpg lfwAlexa Vega
lfwAlexa VegaAlexa Vega 0001.jpg
lfwAlex Barros
lfwAlex BarrosAlex Barros 0001.jpg
lfwAlex BarrosAlex Barros 0002.jpg
lfwAlex Cabrera
lfwAlex CabreraAlex Cabrera 0001.jpg
lfwAlex Cejka
lfwAlex CejkaAlex Cejka 0001.jpg
lfwAlex Corretja
lfwAlex CorretjaAlex Corretja 0001.jpg
lfwAlex Ferguson
lfwAlex FergusonAlex Ferguson 0001.jpg
lfwAlex Gonzalez
lfwAlex GonzalezAlex Gonzalez 0001.jpg
lfwAlex Holmes
lfwAlex HolmesAlex Holmes 0001.jpg
lfwAlexis Bledel
lfwAlexis BledelAlexis Bledel 0001.jpg
lfwAlexis Dennisoff
lfwAlexis DennisoffAlexis Dennisoff 0001.jpg
lfwAlex King
lfwAlex KingAlex King 0001.jpg
lfwAlex Penelas
15
lfwAlex PenelasAlex Penelas 0001.jpg lfwAlex PenelasAlex Penelas 0002.jpg lfwAlex Popov
lfwAlex PopovAlex Popov 0001.jpg lfwAlex Sink
lfwAlex SinkAlex Sink 0001.jpg lfwAlex SinkAlex Sink 0002.jpg lfwAlex SinkAlex Sink 0003.jpg lfwAlex Wallau
lfwAlex WallauAlex Wallau 0001.jpg lfwAlex Zanardi
lfwAlex ZanardiAlex Zanardi 0001.jpg lfwAlfonso Cuaron
lfwAlfonso CuaronAlfonso Cuaron 0001.jpg lfwAlfonso Portillo
lfwAlfonso PortilloAlfonso Portillo 0001.jpg lfwAlfonso Soriano
lfwAlfonso SorianoAlfonso Soriano 0001.jpg lfwAlfred Ford
lfwAlfred FordAlfred Ford 0001.jpg lfwAlfredo di Stefano
lfwAlfredo di StefanoAlfredo di Stefano 0001.jpg lfwAlfredo Moreno
lfwAlfredo MorenoAlfredo Moreno 0001.jpg lfwAlfredo Pena
lfwAlfredo PenaAlfredo Pena 0001.jpg lfwAlfred Sant
lfwAlfred SantAlfred Sant 0001.jpg lfwAl Gore
lfwAl GoreAl Gore 0001.jpg lfwAl GoreAl Gore 0002.jpg lfwAl GoreAl Gore 0003.jpg lfwAl GoreAl Gore 0004.jpg lfwAl GoreAl Gore 0005.jpg lfwAl GoreAl Gore 0006.jpg lfwAl GoreAl Gore 0007.jpg lfwAl GoreAl Gore 0008.jpg lfwAli Abbas
lfwAli AbbasAli Abbas 0001.jpg
lfwAli AbbasAli Abbas 0002.jpg
lfwAli Abdullah Saleh
lfwAli Abdullah SalehAli Abdullah Saleh 0001.jpg lfwAli Adbul Karim Madani
lfwAli Adbul Karim MadaniAli Adbul Karim Madani 0001.jpg lfwAli Ahmeti
lfwAli AhmetiAli Ahmeti 0001.jpg
lfwAli Bin Hussein
lfwAli Bin HusseinAli Bin Hussein 0001.jpg lfwAlice Fisher
lfwAlice FisherAlice Fisher 0001.jpg lfwAlice FisherAlice Fisher 0002.jpg lfwAlicia Hollowell
lfwAlicia HollowellAlicia Hollowell 0001.jpg lfwAlicia Keys
16
lfwAlicia KeysAlicia Keys 0001.jpg lfwAlicia Molik
lfwAlicia MolikAlicia Molik 0001.jpg lfwAlicia Silverstone
lfwAlicia SilverstoneAlicia Silverstone 0001.jpg lfwAlicia SilverstoneAlicia Silverstone 0002.jpg lfwAlicia Witt
lfwAlicia WittAlicia Witt 0001.jpg
lfwAli Fallahian
lfwAli FallahianAli Fallahian 0001.jpg
lfwAli Hammoud
lfwAli HammoudAli Hammoud 0001.jpg
lfwAli Khamenei
lfwAli KhameneiAli Khamenei 0001.jpg
lfwAli KhameneiAli Khamenei 0002.jpg
lfwAli KhameneiAli Khamenei 0003.jpg
lfwAli Mohammed Maher
lfwAli Mohammed MaherAli Mohammed Maher 0001.jpg lfwAlimzhan Tokhtakhounov
lfwAlimzhan TokhtakhounovAlimzhan Tokhtakhounov 0001.jpg lfwAlimzhan TokhtakhounovAlimzhan Tokhtakhounov 0002.jpg lfwAli Naimi
lfwAli NaimiAli Naimi 0001.jpg
lfwAli NaimiAli Naimi 0002.jpg
lfwAli NaimiAli Naimi 0003.jpg
lfwAli NaimiAli Naimi 0004.jpg
lfwAli NaimiAli Naimi 0005.jpg
lfwAli NaimiAli Naimi 0006.jpg
lfwAli NaimiAli Naimi 0007.jpg
lfwAli NaimiAli Naimi 0008.jpg
lfwAlina Kabaeva
lfwAlina KabaevaAlina Kabaeva 0001.jpg
lfwAline Chretien
lfwAline ChretienAline Chretien 0001.jpg
lfwAlisha Richman
lfwAlisha RichmanAlisha Richman 0001.jpg
lfwAlison Krauss
lfwAlison KraussAlison Krauss 0001.jpg
lfwAlison Lohman
lfwAlison LohmanAlison Lohman 0001.jpg
lfwAlison LohmanAlison Lohman 0002.jpg
lfwAlistair MacDonald
lfwAlistair MacDonaldAlistair MacDonald 0001.jpg lfwAllan Houston
lfwAllan HoustonAllan Houston 0001.jpg
lfwAllan Kemakeza
lfwAllan KemakezaAllan Kemakeza 0001.jpg
lfwAllan Wagner
lfwAllan WagnerAllan Wagner 0001.jpg
lfwAl Leiter
lfwAl LeiterAl Leiter 0001.jpg
lfwAllen Iverson
lfwAllen IversonAllen Iverson 0001.jpg
lfwAllen IversonAllen Iverson 0002.jpg
17
lfwAllen Rock
lfwAllen RockAllen Rock 0001.jpg
lfwAllison Janney
lfwAllison JanneyAllison Janney 0001.jpg
lfwAllison JanneyAllison Janney 0002.jpg
lfwAllison Searing
lfwAllison SearingAllison Searing 0001.jpg
lfwAlly Sheedy
lfwAlly SheedyAlly Sheedy 0001.jpg
lfwAllyson Felix
lfwAllyson FelixAllyson Felix 0001.jpg
lfwAllyson FelixAllyson Felix 0002.jpg
lfwAllyson FelixAllyson Felix 0003.jpg
lfwAllyson FelixAllyson Felix 0004.jpg
lfwAllyson FelixAllyson Felix 0005.jpg
lfwAlma Powell
lfwAlma PowellAlma Powell 0001.jpg
lfwAlmeida Baptista
lfwAlmeida BaptistaAlmeida Baptista 0001.jpg lfwAlonzo Mourning
lfwAlonzo MourningAlonzo Mourning 0001.jpg
lfwAl Pacino
lfwAl PacinoAl Pacino 0001.jpg
lfwAl PacinoAl Pacino 0002.jpg
lfwAl PacinoAl Pacino 0003.jpg
lfwAl Sharpton
lfwAl SharptonAl Sharpton 0001.jpg
lfwAl SharptonAl Sharpton 0002.jpg
lfwAl SharptonAl Sharpton 0003.jpg
lfwAl SharptonAl Sharpton 0004.jpg
lfwAl SharptonAl Sharpton 0005.jpg
lfwAl SharptonAl Sharpton 0006.jpg
lfwAl SharptonAl Sharpton 0007.jpg
lfwAlvaro Noboa
lfwAlvaro NoboaAlvaro Noboa 0001.jpg
lfwAlvaro NoboaAlvaro Noboa 0002.jpg
lfwAlvaro NoboaAlvaro Noboa 0003.jpg
lfwAlvaro Silva Calderon
lfwAlvaro Silva CalderonAlvaro Silva Calderon 0001.jpg lfwAlvaro Silva CalderonAlvaro Silva Calderon 0002.jpg lfwAlvaro Silva CalderonAlvaro Silva Calderon 0003.jpg lfwAlvaro Silva CalderonAlvaro Silva Calderon 0004.jpg lfwAlvaro Uribe
lfwAlvaro UribeAlvaro Uribe 0001.jpg
lfwAlvaro UribeAlvaro Uribe 0002.jpg
lfwAlvaro UribeAlvaro Uribe 0003.jpg
lfwAlvaro UribeAlvaro Uribe 0004.jpg
lfwAlvaro UribeAlvaro Uribe 0005.jpg
lfwAlvaro UribeAlvaro Uribe 0006.jpg
lfwAlvaro UribeAlvaro Uribe 0007.jpg
lfwAlvaro UribeAlvaro Uribe 0008.jpg
lfwAlvaro UribeAlvaro Uribe 0009.jpg
lfwAlvaro UribeAlvaro Uribe 0010.jpg
lfwAlvaro UribeAlvaro Uribe 0011.jpg
18
lfwAlvaro UribeAlvaro Uribe 0012.jpg lfwAlvaro UribeAlvaro Uribe 0013.jpg lfwAlvaro UribeAlvaro Uribe 0014.jpg lfwAlvaro UribeAlvaro Uribe 0015.jpg lfwAlvaro UribeAlvaro Uribe 0016.jpg lfwAlvaro UribeAlvaro Uribe 0017.jpg lfwAlvaro UribeAlvaro Uribe 0018.jpg lfwAlvaro UribeAlvaro Uribe 0019.jpg lfwAlvaro UribeAlvaro Uribe 0020.jpg lfwAlvaro UribeAlvaro Uribe 0021.jpg lfwAlvaro UribeAlvaro Uribe 0022.jpg lfwAlvaro UribeAlvaro Uribe 0023.jpg lfwAlvaro UribeAlvaro Uribe 0024.jpg lfwAlvaro UribeAlvaro Uribe 0025.jpg lfwAlvaro UribeAlvaro Uribe 0026.jpg lfwAlvaro UribeAlvaro Uribe 0027.jpg lfwAlvaro UribeAlvaro Uribe 0028.jpg lfwAlvaro UribeAlvaro Uribe 0029.jpg lfwAlvaro UribeAlvaro Uribe 0030.jpg lfwAlvaro UribeAlvaro Uribe 0031.jpg lfwAlvaro UribeAlvaro Uribe 0032.jpg lfwAlvaro UribeAlvaro Uribe 0033.jpg lfwAlvaro UribeAlvaro Uribe 0034.jpg lfwAlvaro UribeAlvaro Uribe 0035.jpg lfwAlyse Beaupre
lfwAlyse BeaupreAlyse Beaupre 0001.jpg lfwAlyson Hannigan
lfwAlyson HanniganAlyson Hannigan 0001.jpg lfwAly Wagner
lfwAly WagnerAly Wagner 0001.jpg lfwAmanda Beard
lfwAmanda BeardAmanda Beard 0001.jpg lfwAmanda BeardAmanda Beard 0002.jpg lfwAmanda Bynes
lfwAmanda BynesAmanda Bynes 0001.jpg lfwAmanda BynesAmanda Bynes 0002.jpg lfwAmanda BynesAmanda Bynes 0003.jpg lfwAmanda BynesAmanda Bynes 0004.jpg lfwAmanda Coetzer
lfwAmanda CoetzerAmanda Coetzer 0001.jpg lfwAmanda CoetzerAmanda Coetzer 0002.jpg lfwAmanda Marsh
lfwAmanda MarshAmanda Marsh 0001.jpg lfwAmanda Plumer
lfwAmanda PlumerAmanda Plumer 0001.jpg lfwAmber Frey
lfwAmber FreyAmber Frey 0001.jpg lfwAmber Tamblyn
lfwAmber TamblynAmber Tamblyn 0001.jpg lfwAmber TamblynAmber Tamblyn 0002.jpg lfwAmbrose Lee
lfwAmbrose LeeAmbrose Lee 0001.jpg lfwAmelia Vega
lfwAmelia VegaAmelia Vega 0001.jpg
19
lfwAmelia VegaAmelia Vega 0002.jpg lfwAmelia VegaAmelia Vega 0003.jpg lfwAmelia VegaAmelia Vega 0004.jpg lfwAmelia VegaAmelia Vega 0005.jpg lfwAmelia VegaAmelia Vega 0006.jpg lfwAmelia VegaAmelia Vega 0007.jpg lfwAmelie Mauresmo
lfwAmelie MauresmoAmelie Mauresmo 0001.jpg lfwAmelie MauresmoAmelie Mauresmo 0002.jpg lfwAmelie MauresmoAmelie Mauresmo 0003.jpg lfwAmelie MauresmoAmelie Mauresmo 0004.jpg lfwAmelie MauresmoAmelie Mauresmo 0005.jpg lfwAmelie MauresmoAmelie Mauresmo 0006.jpg lfwAmelie MauresmoAmelie Mauresmo 0007.jpg lfwAmelie MauresmoAmelie Mauresmo 0008.jpg lfwAmelie MauresmoAmelie Mauresmo 0009.jpg lfwAmelie MauresmoAmelie Mauresmo 0010.jpg lfwAmelie MauresmoAmelie Mauresmo 0011.jpg lfwAmelie MauresmoAmelie Mauresmo 0012.jpg lfwAmelie MauresmoAmelie Mauresmo 0013.jpg lfwAmelie MauresmoAmelie Mauresmo 0014.jpg lfwAmelie MauresmoAmelie Mauresmo 0015.jpg lfwAmelie MauresmoAmelie Mauresmo 0016.jpg lfwAmelie MauresmoAmelie Mauresmo 0017.jpg lfwAmelie MauresmoAmelie Mauresmo 0018.jpg lfwAmelie MauresmoAmelie Mauresmo 0019.jpg lfwAmelie MauresmoAmelie Mauresmo 0020.jpg lfwAmelie MauresmoAmelie Mauresmo 0021.jpg lfwAmer alSaadi
lfwAmer alSaadiAmer alSaadi 0001.jpg lfwAmer alSaadiAmer alSaadi 0002.jpg lfwAmer alSaadiAmer alSaadi 0003.jpg lfwAmer alSaadiAmer alSaadi 0004.jpg lfwAmporn Falise
lfwAmporn FaliseAmporn Falise 0001.jpg lfwAmram Mitzna
lfwAmram MitznaAmram Mitzna 0001.jpg lfwAmram MitznaAmram Mitzna 0002.jpg lfwAmr Moussa
lfwAmr MoussaAmr Moussa 0001.jpg lfwAmy Brenneman
lfwAmy BrennemanAmy Brenneman 0001.jpg lfwAmy Cotton
lfwAmy CottonAmy Cotton 0001.jpg lfwAmy Gale
lfwAmy GaleAmy Gale 0001.jpg lfwAmy Pascal
lfwAmy PascalAmy Pascal 0001.jpg lfwAmy Redford
lfwAmy RedfordAmy Redford 0001.jpg lfwAmy Smart
lfwAmy SmartAmy Smart 0001.jpg lfwAmy Yasbeck
lfwAmy YasbeckAmy Yasbeck 0001.jpg
20
lfwAna Claudia Talancon
lfwAna Claudia TalanconAna Claudia Talancon 0001.jpg lfwAna Guevara
lfwAna GuevaraAna Guevara 0001.jpg
lfwAna GuevaraAna Guevara 0002.jpg
lfwAna GuevaraAna Guevara 0003.jpg
lfwAna GuevaraAna Guevara 0004.jpg
lfwAna GuevaraAna Guevara 0005.jpg
lfwAna GuevaraAna Guevara 0006.jpg
lfwAna GuevaraAna Guevara 0007.jpg
lfwAna Isabel Sanchez
lfwAna Isabel SanchezAna Isabel Sanchez 0001.jpg lfwAna Palacio
lfwAna PalacioAna Palacio 0001.jpg
lfwAna PalacioAna Palacio 0002.jpg
lfwAna PalacioAna Palacio 0003.jpg
lfwAna PalacioAna Palacio 0004.jpg
lfwAna PalacioAna Palacio 0005.jpg
lfwAna PalacioAna Palacio 0006.jpg
lfwAna PalacioAna Palacio 0007.jpg
lfwAna PalacioAna Palacio 0008.jpg
lfwAna Paula Gerard
lfwAna Paula GerardAna Paula Gerard 0001.jpg
lfwAna Sebastiao
lfwAna SebastiaoAna Sebastiao 0001.jpg
lfwAnastasia Kelesidou
lfwAnastasia KelesidouAnastasia Kelesidou 0001.jpg lfwAnastasia Myskina
lfwAnastasia MyskinaAnastasia Myskina 0001.jpg lfwAnastasia MyskinaAnastasia Myskina 0002.jpg lfwAnastasia MyskinaAnastasia Myskina 0003.jpg lfwAnatoliy Kinakh
lfwAnatoliy KinakhAnatoliy Kinakh 0001.jpg
lfwAnders Ebbeson
lfwAnders EbbesonAnders Ebbeson 0001.jpg
lfwAnders EbbesonAnders Ebbeson 0002.jpg
lfwAnders EbbesonAnders Ebbeson 0003.jpg
lfwAnders Fogh Rasmussen
lfwAnders Fogh RasmussenAnders Fogh Rasmussen 0001.jpg lfwAnders Fogh RasmussenAnders Fogh Rasmussen 0002.jpg lfwAnders Fogh RasmussenAnders Fogh Rasmussen 0003.jpg lfwAnders Fogh RasmussenAnders Fogh Rasmussen 0004.jpg lfwAnderson Varejao
lfwAnderson VarejaoAnderson Varejao 0001.jpg lfwAndrea Bocelli
lfwAndrea BocelliAndrea Bocelli 0001.jpg
lfwAndrea De Cruz
lfwAndrea De CruzAndrea De Cruz 0001.jpg
lfwAndre Agassi
lfwAndre AgassiAndre Agassi 0001.jpg
lfwAndre AgassiAndre Agassi 0002.jpg
lfwAndre AgassiAndre Agassi 0003.jpg
lfwAndre AgassiAndre Agassi 0004.jpg
lfwAndre AgassiAndre Agassi 0005.jpg
21
lfwAndre AgassiAndre Agassi 0006.jpg lfwAndre AgassiAndre Agassi 0007.jpg lfwAndre AgassiAndre Agassi 0008.jpg lfwAndre AgassiAndre Agassi 0009.jpg lfwAndre AgassiAndre Agassi 0010.jpg lfwAndre AgassiAndre Agassi 0011.jpg lfwAndre AgassiAndre Agassi 0012.jpg lfwAndre AgassiAndre Agassi 0013.jpg lfwAndre AgassiAndre Agassi 0014.jpg lfwAndre AgassiAndre Agassi 0015.jpg lfwAndre AgassiAndre Agassi 0016.jpg lfwAndre AgassiAndre Agassi 0017.jpg lfwAndre AgassiAndre Agassi 0018.jpg lfwAndre AgassiAndre Agassi 0019.jpg lfwAndre AgassiAndre Agassi 0020.jpg lfwAndre AgassiAndre Agassi 0021.jpg lfwAndre AgassiAndre Agassi 0022.jpg lfwAndre AgassiAndre Agassi 0023.jpg lfwAndre AgassiAndre Agassi 0024.jpg lfwAndre AgassiAndre Agassi 0025.jpg lfwAndre AgassiAndre Agassi 0026.jpg lfwAndre AgassiAndre Agassi 0027.jpg lfwAndre AgassiAndre Agassi 0028.jpg lfwAndre AgassiAndre Agassi 0029.jpg lfwAndre AgassiAndre Agassi 0030.jpg lfwAndre AgassiAndre Agassi 0031.jpg lfwAndre AgassiAndre Agassi 0032.jpg lfwAndre AgassiAndre Agassi 0033.jpg lfwAndre AgassiAndre Agassi 0034.jpg lfwAndre AgassiAndre Agassi 0035.jpg lfwAndre AgassiAndre Agassi 0036.jpg lfwAndrea Kiser
lfwAndrea KiserAndrea Kiser 0001.jpg
lfwAndreas Vinciguerra
lfwAndreas VinciguerraAndreas Vinciguerra 0001.jpg
lfwAndrea Yates
lfwAndrea YatesAndrea Yates 0001.jpg
lfwAndre Bucher
lfwAndre BucherAndre Bucher 0001.jpg
lfwAndrei Konchalovsky
lfwAndrei KonchalovskyAndrei Konchalovsky 0001.jpg
lfwAndrei Mikhnevich
lfwAndrei MikhnevichAndrei Mikhnevich 0001.jpg
lfwAndrei MikhnevichAndrei Mikhnevich 0002.jpg
lfwAndrei Nikolishin
lfwAndrei NikolishinAndrei Nikolishin 0001.jpg
lfwAndre Lange
lfwAndre LangeAndre Lange 0001.jpg
lfwAndres DAlessandro
lfwAndres DAlessandroAndres DAlessandro 0001.jpg
lfwAndres Manuel Lopez Obrador
lfwAndres Manuel Lopez ObradorAndres Manuel Lopez Obrador 0001.jpg lfwAndre Smith
lfwAndre SmithAndre Smith 0001.jpg
22
lfwAndres Pastrana
lfwAndres PastranaAndres Pastrana 0001.jpg lfwAndre Techine
lfwAndre TechineAndre Techine 0001.jpg
lfwAndrew Bernard
lfwAndrew BernardAndrew Bernard 0001.jpg lfwAndrew Bunner
lfwAndrew BunnerAndrew Bunner 0001.jpg
lfwAndrew BunnerAndrew Bunner 0002.jpg
lfwAndrew Caldecott
lfwAndrew CaldecottAndrew Caldecott 0001.jpg lfwAndrew Cuomo
lfwAndrew CuomoAndrew Cuomo 0001.jpg
lfwAndrew CuomoAndrew Cuomo 0002.jpg
lfwAndrew Fastow
lfwAndrew FastowAndrew Fastow 0001.jpg
lfwAndrew Firestone
lfwAndrew FirestoneAndrew Firestone 0001.jpg lfwAndrew Gilligan
lfwAndrew GilliganAndrew Gilligan 0001.jpg lfwAndrew Jarecki
lfwAndrew JareckiAndrew Jarecki 0001.jpg lfwAndrew Luster
lfwAndrew LusterAndrew Luster 0001.jpg
lfwAndrew Niccol
lfwAndrew NiccolAndrew Niccol 0001.jpg
lfwAndrew NiccolAndrew Niccol 0002.jpg
lfwAndrew Sabey
lfwAndrew SabeyAndrew Sabey 0001.jpg
lfwAndrew Shutley
lfwAndrew ShutleyAndrew Shutley 0001.jpg lfwAndrew Weissmann
lfwAndrew WeissmannAndrew Weissmann 0001.jpg lfwAndrew WeissmannAndrew Weissmann 0002.jpg lfwAndrew WeissmannAndrew Weissmann 0003.jpg lfwAndrew Wetzler
lfwAndrew WetzlerAndrew Wetzler 0001.jpg lfwAndrzej Tyszkiewicz
lfwAndrzej TyszkiewiczAndrzej Tyszkiewicz 0001.jpg lfwAndy Benes
lfwAndy BenesAndy Benes 0001.jpg
lfwAndy Bryant
lfwAndy BryantAndy Bryant 0001.jpg
lfwAndy Dick
lfwAndy DickAndy Dick 0001.jpg
lfwAndy Garcia
lfwAndy GarciaAndy Garcia 0001.jpg
lfwAndy Graves
lfwAndy GravesAndy Graves 0001.jpg
lfwAndy Griffith
lfwAndy GriffithAndy Griffith 0001.jpg
lfwAndy Griggs
lfwAndy GriggsAndy Griggs 0001.jpg
lfwAndy Hebb
23
lfwAndy HebbAndy Hebb 0001.jpg lfwAndy HebbAndy Hebb 0002.jpg lfwAndy Lau
lfwAndy LauAndy Lau 0001.jpg lfwAndy Madikians
lfwAndy MadikiansAndy Madikians 0001.jpg lfwAndy North
lfwAndy NorthAndy North 0001.jpg lfwAndy Perez
lfwAndy PerezAndy Perez 0001.jpg lfwAndy Roddick
lfwAndy RoddickAndy Roddick 0001.jpg lfwAndy RoddickAndy Roddick 0002.jpg lfwAndy RoddickAndy Roddick 0003.jpg lfwAndy RoddickAndy Roddick 0004.jpg lfwAndy RoddickAndy Roddick 0005.jpg lfwAndy RoddickAndy Roddick 0006.jpg lfwAndy RoddickAndy Roddick 0007.jpg lfwAndy RoddickAndy Roddick 0008.jpg lfwAndy RoddickAndy Roddick 0009.jpg lfwAndy RoddickAndy Roddick 0010.jpg lfwAndy RoddickAndy Roddick 0011.jpg lfwAndy RoddickAndy Roddick 0012.jpg lfwAndy RoddickAndy Roddick 0013.jpg lfwAndy RoddickAndy Roddick 0014.jpg lfwAndy RoddickAndy Roddick 0015.jpg lfwAndy Rooney
lfwAndy RooneyAndy Rooney 0001.jpg lfwAndy Warhol
lfwAndy WarholAndy Warhol 0001.jpg lfwAndy Wisecarver
lfwAndy WisecarverAndy Wisecarver 0001.jpg lfwAnette Hosoi
lfwAnette HosoiAnette Hosoi 0001.jpg lfwAnFernce Negron
lfwAnFernce NegronAnFernce Negron 0001.jpg lfwAngela Alvarado Rosa
lfwAngela Alvarado RosaAngela Alvarado Rosa 0001.jpg lfwAngela Bassett
lfwAngela BassettAngela Bassett 0001.jpg lfwAngela BassettAngela Bassett 0002.jpg lfwAngela BassettAngela Bassett 0003.jpg lfwAngela BassettAngela Bassett 0004.jpg lfwAngela BassettAngela Bassett 0005.jpg lfwAngela BassettAngela Bassett 0006.jpg lfwAngela Lansbury
lfwAngela LansburyAngela Lansbury 0001.jpg lfwAngela LansburyAngela Lansbury 0002.jpg lfwAngela MasciaFrye
lfwAngela MasciaFryeAngela MasciaFrye 0001.jpg lfwAngela Merkel
lfwAngela MerkelAngela Merkel 0001.jpg lfwAngela MerkelAngela Merkel 0002.jpg lfwAngela MerkelAngela Merkel 0003.jpg
24
lfwAngela MerkelAngela Merkel 0004.jpg lfwAngela MerkelAngela Merkel 0005.jpg lfwAngelica Romero
lfwAngelica RomeroAngelica Romero 0001.jpg lfwAngelina Jolie
lfwAngelina JolieAngelina Jolie 0001.jpg lfwAngelina JolieAngelina Jolie 0002.jpg lfwAngelina JolieAngelina Jolie 0003.jpg lfwAngelina JolieAngelina Jolie 0004.jpg lfwAngelina JolieAngelina Jolie 0005.jpg lfwAngelina JolieAngelina Jolie 0006.jpg lfwAngelina JolieAngelina Jolie 0007.jpg lfwAngelina JolieAngelina Jolie 0008.jpg lfwAngelina JolieAngelina Jolie 0009.jpg lfwAngelina JolieAngelina Jolie 0010.jpg lfwAngelina JolieAngelina Jolie 0011.jpg lfwAngelina JolieAngelina Jolie 0012.jpg lfwAngelina JolieAngelina Jolie 0013.jpg lfwAngelina JolieAngelina Jolie 0014.jpg lfwAngelina JolieAngelina Jolie 0015.jpg lfwAngelina JolieAngelina Jolie 0016.jpg lfwAngelina JolieAngelina Jolie 0017.jpg lfwAngelina JolieAngelina Jolie 0018.jpg lfwAngelina JolieAngelina Jolie 0019.jpg lfwAngelina JolieAngelina Jolie 0020.jpg lfwAngel Lockward
lfwAngel LockwardAngel Lockward 0001.jpg lfwAngel Maza
lfwAngel MazaAngel Maza 0001.jpg lfwAngelo Genova
lfwAngelo GenovaAngelo Genova 0001.jpg lfwAngelo Reyes
lfwAngelo ReyesAngelo Reyes 0001.jpg lfwAngelo ReyesAngelo Reyes 0002.jpg lfwAngelo ReyesAngelo Reyes 0003.jpg lfwAngelo ReyesAngelo Reyes 0004.jpg lfwAngie Arzola
lfwAngie ArzolaAngie Arzola 0001.jpg lfwAngie Martinez
lfwAngie MartinezAngie Martinez 0001.jpg lfwAnibal Ibarra
lfwAnibal IbarraAnibal Ibarra 0001.jpg lfwAnibal IbarraAnibal Ibarra 0002.jpg lfwAnibal IbarraAnibal Ibarra 0003.jpg lfwAnil Ramsook
lfwAnil RamsookAnil Ramsook 0001.jpg lfwAnita DeFrantz
lfwAnita DeFrantzAnita DeFrantz 0001.jpg lfwAnja Paerson
lfwAnja PaersonAnja Paerson 0001.jpg lfwAnjum Hussain
lfwAnjum HussainAnjum Hussain 0001.jpg lfwAnna Chicherova
lfwAnna ChicherovaAnna Chicherova 0001.jpg
25
lfwAnna Faris
lfwAnna FarisAnna Faris 0001.jpg
lfwAnna Jones
lfwAnna JonesAnna Jones 0001.jpg
lfwAnna Kournikova
lfwAnna KournikovaAnna Kournikova 0001.jpg
lfwAnna KournikovaAnna Kournikova 0002.jpg
lfwAnna KournikovaAnna Kournikova 0003.jpg
lfwAnna KournikovaAnna Kournikova 0004.jpg
lfwAnna KournikovaAnna Kournikova 0005.jpg
lfwAnna KournikovaAnna Kournikova 0006.jpg
lfwAnna KournikovaAnna Kournikova 0007.jpg
lfwAnna KournikovaAnna Kournikova 0008.jpg
lfwAnna KournikovaAnna Kournikova 0009.jpg
lfwAnna KournikovaAnna Kournikova 0010.jpg
lfwAnna KournikovaAnna Kournikova 0011.jpg
lfwAnna KournikovaAnna Kournikova 0012.jpg
lfwAnna Nicole Smith
lfwAnna Nicole SmithAnna Nicole Smith 0001.jpg lfwAnna Nicole SmithAnna Nicole Smith 0002.jpg lfwAnne Cavers
lfwAnne CaversAnne Cavers 0001.jpg
lfwAnne Donovan
lfwAnne DonovanAnne Donovan 0001.jpg
lfwAnne Heche
lfwAnne HecheAnne Heche 0001.jpg
lfwAnne Krueger
lfwAnne KruegerAnne Krueger 0001.jpg
lfwAnne KruegerAnne Krueger 0002.jpg
lfwAnne KruegerAnne Krueger 0003.jpg
lfwAnneli Jaatteenmaki
lfwAnneli JaatteenmakiAnneli Jaatteenmaki 0001.jpg lfwAnneli JaatteenmakiAnneli Jaatteenmaki 0002.jpg lfwAnne McLellan
lfwAnne McLellanAnne McLellan 0001.jpg
lfwAnne McLellanAnne McLellan 0002.jpg
lfwAnne McLellanAnne McLellan 0003.jpg
lfwAnne ONeil
lfwAnne ONeilAnne ONeil 0001.jpg
lfwAnnette Bening
lfwAnnette BeningAnnette Bening 0001.jpg
lfwAnnette BeningAnnette Bening 0002.jpg
lfwAnnette Lu
lfwAnnette LuAnnette Lu 0001.jpg
lfwAnnette LuAnnette Lu 0002.jpg
lfwAnnette LuAnnette Lu 0003.jpg
lfwAnn Godbehere
lfwAnn GodbehereAnn Godbehere 0001.jpg
lfwAnnie Chaplin
lfwAnnie ChaplinAnnie Chaplin 0001.jpg lfwAnnieJeanne Reynaud
lfwAnnieJeanne ReynaudAnnieJeanne Reynaud 0001.jpg lfwAnnie Machon
lfwAnnie MachonAnnie Machon 0001.jpg
26
lfwAnnika Sorenstam
lfwAnnika SorenstamAnnika Sorenstam 0001.jpg lfwAnn Landers
lfwAnn LandersAnn Landers 0001.jpg
lfwAnn Morgan
lfwAnn MorganAnn Morgan 0001.jpg
lfwAnn Veneman
lfwAnn VenemanAnn Veneman 0001.jpg
lfwAnn VenemanAnn Veneman 0002.jpg
lfwAnn VenemanAnn Veneman 0003.jpg
lfwAnn VenemanAnn Veneman 0004.jpg
lfwAnn VenemanAnn Veneman 0005.jpg
lfwAnn VenemanAnn Veneman 0006.jpg
lfwAnn VenemanAnn Veneman 0007.jpg
lfwAnn VenemanAnn Veneman 0008.jpg
lfwAnn VenemanAnn Veneman 0009.jpg
lfwAnn VenemanAnn Veneman 0010.jpg
lfwAnn VenemanAnn Veneman 0011.jpg
lfwAntanas Valionis
lfwAntanas ValionisAntanas Valionis 0001.jpg lfwAnthony Carter
lfwAnthony CarterAnthony Carter 0001.jpg lfwAnthony Corso
lfwAnthony CorsoAnthony Corso 0001.jpg
lfwAnthony Ervin
lfwAnthony ErvinAnthony Ervin 0001.jpg
lfwAnthony Fauci
lfwAnthony FauciAnthony Fauci 0001.jpg
lfwAnthony FauciAnthony Fauci 0002.jpg
lfwAnthony Garotinho
lfwAnthony GarotinhoAnthony Garotinho 0001.jpg lfwAnthony Hazen
lfwAnthony HazenAnthony Hazen 0001.jpg
lfwAnthony Hopkins
lfwAnthony HopkinsAnthony Hopkins 0001.jpg lfwAnthony HopkinsAnthony Hopkins 0002.jpg lfwAnthony LaPaglia
lfwAnthony LaPagliaAnthony LaPaglia 0001.jpg lfwAnthony LaPagliaAnthony LaPaglia 0002.jpg lfwAnthony Lee Johnson
lfwAnthony Lee JohnsonAnthony Lee Johnson 0001.jpg lfwAnthony Mazur
lfwAnthony MazurAnthony Mazur 0001.jpg
lfwAnthony Pico
lfwAnthony PicoAnthony Pico 0001.jpg
lfwAnthony Pisciotti
lfwAnthony PisciottiAnthony Pisciotti 0001.jpg lfwAnthony Principi
lfwAnthony PrincipiAnthony Principi 0001.jpg lfwAnthony Rackauckas
lfwAnthony RackauckasAnthony Rackauckas 0001.jpg lfwAnthony Scott Miller
lfwAnthony Scott MillerAnthony Scott Miller 0001.jpg lfwAntje Buschschulte
27
lfwAntje BuschschulteAntje Buschschulte 0001.jpg lfwAnton Balasingham
lfwAnton BalasinghamAnton Balasingham 0001.jpg lfwAntonio Banderas
lfwAntonio BanderasAntonio Banderas 0001.jpg lfwAntonio BanderasAntonio Banderas 0002.jpg lfwAntonio BanderasAntonio Banderas 0003.jpg lfwAntonio BanderasAntonio Banderas 0004.jpg lfwAntonio BanderasAntonio Banderas 0005.jpg lfwAntonio Bernardo
lfwAntonio BernardoAntonio Bernardo 0001.jpg lfwAntonio Cassano
lfwAntonio CassanoAntonio Cassano 0001.jpg lfwAntonio Catania
lfwAntonio CataniaAntonio Catania 0001.jpg lfwAntonio Elias Saca
lfwAntonio Elias SacaAntonio Elias Saca 0001.jpg lfwAntonio Palocci
lfwAntonio PalocciAntonio Palocci 0001.jpg lfwAntonio PalocciAntonio Palocci 0002.jpg lfwAntonio PalocciAntonio Palocci 0003.jpg lfwAntonio PalocciAntonio Palocci 0004.jpg lfwAntonio PalocciAntonio Palocci 0005.jpg lfwAntonio PalocciAntonio Palocci 0006.jpg lfwAntonio PalocciAntonio Palocci 0007.jpg lfwAntonio PalocciAntonio Palocci 0008.jpg lfwAntonio Trillanes
lfwAntonio TrillanesAntonio Trillanes 0001.jpg lfwAntonio TrillanesAntonio Trillanes 0002.jpg lfwAntonio TrillanesAntonio Trillanes 0003.jpg lfwAntony Leung
lfwAntony LeungAntony Leung 0001.jpg lfwAntony LeungAntony Leung 0002.jpg lfwAntony LeungAntony Leung 0003.jpg lfwAntony LeungAntony Leung 0004.jpg lfwAntwun Echols
lfwAntwun EcholsAntwun Echols 0001.jpg lfwAnwar Ibrahim
lfwAnwar IbrahimAnwar Ibrahim 0001.jpg lfwAnwar IbrahimAnwar Ibrahim 0002.jpg lfwAnzori Kikalishvili
lfwAnzori KikalishviliAnzori Kikalishvili 0001.jpg lfwAparna Pillai
lfwAparna PillaiAparna Pillai 0001.jpg
lfwAram Adler
lfwAram AdlerAram Adler 0001.jpg
lfwArantxa SanchezVicario
lfwArantxa SanchezVicarioArantxa SanchezVicario 0001.jpg lfwArantxa SanchezVicarioArantxa SanchezVicario 0002.jpg lfwAretha Franklin
lfwAretha FranklinAretha Franklin 0001.jpg
lfwArianna Huffington
lfwArianna HuffingtonArianna Huffington 0001.jpg lfwArianna HuffingtonArianna Huffington 0002.jpg
28
lfwArianna HuffingtonArianna Huffington 0003.jpg lfwArianna HuffingtonArianna Huffington 0004.jpg lfwAri Bousbib
lfwAri BousbibAri Bousbib 0001.jpg
lfwArie Haan
lfwArie HaanArie Haan 0001.jpg lfwAriel Sharon
lfwAriel SharonAriel Sharon 0001.jpg lfwAriel SharonAriel Sharon 0002.jpg lfwAriel SharonAriel Sharon 0003.jpg lfwAriel SharonAriel Sharon 0004.jpg lfwAriel SharonAriel Sharon 0005.jpg lfwAriel SharonAriel Sharon 0006.jpg lfwAriel SharonAriel Sharon 0007.jpg lfwAriel SharonAriel Sharon 0008.jpg lfwAriel SharonAriel Sharon 0009.jpg lfwAriel SharonAriel Sharon 0010.jpg lfwAriel SharonAriel Sharon 0011.jpg lfwAriel SharonAriel Sharon 0012.jpg lfwAriel SharonAriel Sharon 0013.jpg lfwAriel SharonAriel Sharon 0014.jpg lfwAriel SharonAriel Sharon 0015.jpg lfwAriel SharonAriel Sharon 0016.jpg lfwAriel SharonAriel Sharon 0017.jpg lfwAriel SharonAriel Sharon 0018.jpg lfwAriel SharonAriel Sharon 0019.jpg lfwAriel SharonAriel Sharon 0020.jpg lfwAriel SharonAriel Sharon 0021.jpg lfwAriel SharonAriel Sharon 0022.jpg lfwAriel SharonAriel Sharon 0023.jpg lfwAriel SharonAriel Sharon 0024.jpg lfwAriel SharonAriel Sharon 0025.jpg lfwAriel SharonAriel Sharon 0026.jpg lfwAriel SharonAriel Sharon 0027.jpg lfwAriel SharonAriel Sharon 0028.jpg lfwAriel SharonAriel Sharon 0029.jpg lfwAriel SharonAriel Sharon 0030.jpg lfwAriel SharonAriel Sharon 0031.jpg lfwAriel SharonAriel Sharon 0032.jpg lfwAriel SharonAriel Sharon 0033.jpg lfwAriel SharonAriel Sharon 0034.jpg lfwAriel SharonAriel Sharon 0035.jpg lfwAriel SharonAriel Sharon 0036.jpg lfwAriel SharonAriel Sharon 0037.jpg lfwAriel SharonAriel Sharon 0038.jpg lfwAriel SharonAriel Sharon 0039.jpg lfwAriel SharonAriel Sharon 0040.jpg lfwAriel SharonAriel Sharon 0041.jpg lfwAriel SharonAriel Sharon 0042.jpg lfwAriel SharonAriel Sharon 0043.jpg lfwAriel SharonAriel Sharon 0044.jpg lfwAriel SharonAriel Sharon 0045.jpg lfwAriel SharonAriel Sharon 0046.jpg lfwAriel SharonAriel Sharon 0047.jpg
29
lfwAriel SharonAriel Sharon 0048.jpg lfwAriel SharonAriel Sharon 0049.jpg lfwAriel SharonAriel Sharon 0050.jpg lfwAriel SharonAriel Sharon 0051.jpg lfwAriel SharonAriel Sharon 0052.jpg lfwAriel SharonAriel Sharon 0053.jpg lfwAriel SharonAriel Sharon 0054.jpg lfwAriel SharonAriel Sharon 0055.jpg lfwAriel SharonAriel Sharon 0056.jpg lfwAriel SharonAriel Sharon 0057.jpg lfwAriel SharonAriel Sharon 0058.jpg lfwAriel SharonAriel Sharon 0059.jpg lfwAriel SharonAriel Sharon 0060.jpg lfwAriel SharonAriel Sharon 0061.jpg lfwAriel SharonAriel Sharon 0062.jpg lfwAriel SharonAriel Sharon 0063.jpg lfwAriel SharonAriel Sharon 0064.jpg lfwAriel SharonAriel Sharon 0065.jpg lfwAriel SharonAriel Sharon 0066.jpg lfwAriel SharonAriel Sharon 0067.jpg lfwAriel SharonAriel Sharon 0068.jpg lfwAriel SharonAriel Sharon 0069.jpg lfwAriel SharonAriel Sharon 0070.jpg lfwAriel SharonAriel Sharon 0071.jpg lfwAriel SharonAriel Sharon 0072.jpg lfwAriel SharonAriel Sharon 0073.jpg lfwAriel SharonAriel Sharon 0074.jpg lfwAriel SharonAriel Sharon 0075.jpg lfwAriel SharonAriel Sharon 0076.jpg lfwAriel SharonAriel Sharon 0077.jpg lfwAri Fleischer
lfwAri FleischerAri Fleischer 0001.jpg lfwAri FleischerAri Fleischer 0002.jpg lfwAri FleischerAri Fleischer 0003.jpg lfwAri FleischerAri Fleischer 0004.jpg lfwAri FleischerAri Fleischer 0005.jpg lfwAri FleischerAri Fleischer 0006.jpg lfwAri FleischerAri Fleischer 0007.jpg lfwAri FleischerAri Fleischer 0008.jpg lfwAri FleischerAri Fleischer 0009.jpg lfwAri FleischerAri Fleischer 0010.jpg lfwAri FleischerAri Fleischer 0011.jpg lfwAri FleischerAri Fleischer 0012.jpg lfwAri FleischerAri Fleischer 0013.jpg lfwArif Mardin
lfwArif MardinArif Mardin 0001.jpg lfwArlen Specter
lfwArlen SpecterArlen Specter 0001.jpg lfwArlen SpecterArlen Specter 0002.jpg lfwArlen SpecterArlen Specter 0003.jpg lfwArmando Avila Panchame
lfwArmando Avila PanchameArmando Avila Panchame 0001.jpg lfwArmando Calderon Sol
lfwArmando Calderon SolArmando Calderon Sol 0001.jpg
30
lfwArmando Carrillo
lfwArmando CarrilloArmando Carrillo 0001.jpg lfwArmand Sargen
lfwArmand SargenArmand Sargen 0001.jpg
lfwArminio Fraga
lfwArminio FragaArminio Fraga 0001.jpg
lfwArminio FragaArminio Fraga 0002.jpg
lfwArminio FragaArminio Fraga 0003.jpg
lfwArminio FragaArminio Fraga 0004.jpg
lfwArminio FragaArminio Fraga 0005.jpg
lfwArminio FragaArminio Fraga 0006.jpg
lfwArnaud Clement
lfwArnaud ClementArnaud Clement 0001.jpg
lfwArnaud ClementArnaud Clement 0002.jpg
lfwArnaud Lagardere
lfwArnaud LagardereArnaud Lagardere 0001.jpg
lfwArnie Boehm
lfwArnie BoehmArnie Boehm 0001.jpg
lfwArnoldo Aleman
lfwArnoldo AlemanArnoldo Aleman 0001.jpg
lfwArnoldo AlemanArnoldo Aleman 0002.jpg
lfwArnoldo AlemanArnoldo Aleman 0003.jpg
lfwArnoldo AlemanArnoldo Aleman 0004.jpg
lfwArnoldo AlemanArnoldo Aleman 0005.jpg
lfwArnold Palmer
lfwArnold PalmerArnold Palmer 0001.jpg
lfwArnold PalmerArnold Palmer 0002.jpg
lfwArnold PalmerArnold Palmer 0003.jpg
lfwArnold Schwarzenegger
lfwArnold SchwarzeneggerArnold Schwarzenegger 0001.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0002.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0003.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0004.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0005.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0006.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0007.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0008.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0009.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0010.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0011.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0012.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0013.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0014.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0015.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0016.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0017.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0018.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0019.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0020.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0021.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0022.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0023.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0024.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0025.jpg
31
lfwArnold SchwarzeneggerArnold Schwarzenegger 0026.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0027.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0028.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0029.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0030.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0031.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0032.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0033.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0034.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0035.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0036.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0037.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0038.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0039.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0040.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0041.jpg lfwArnold SchwarzeneggerArnold Schwarzenegger 0042.jpg lfwArnold Scott
lfwArnold ScottArnold Scott 0001.jpg lfwAron Ralston
lfwAron RalstonAron Ralston 0001.jpg lfwAron RalstonAron Ralston 0002.jpg lfwArsinee Khanjian
lfwArsinee KhanjianArsinee Khanjian 0001.jpg lfwArsinee KhanjianArsinee Khanjian 0002.jpg lfwArt Cooper
lfwArt CooperArt Cooper 0001.jpg
lfwArt Hoffmann
lfwArt HoffmannArt Hoffmann 0001.jpg lfwArt HoffmannArt Hoffmann 0002.jpg lfwArt Howe
lfwArt HoweArt Howe 0001.jpg
lfwArt HoweArt Howe 0002.jpg
lfwArt HoweArt Howe 0003.jpg
lfwArt HoweArt Howe 0004.jpg
lfwArthur Johnson
lfwArthur JohnsonArthur Johnson 0001.jpg lfwArthur Martinez
lfwArthur MartinezArthur Martinez 0001.jpg lfwArtieas Shanks
lfwArtieas ShanksArtieas Shanks 0001.jpg lfwArt Lopez
lfwArt LopezArt Lopez 0001.jpg
lfwArturo Gatti
lfwArturo GattiArturo Gatti 0001.jpg lfwArturo GattiArturo Gatti 0002.jpg lfwArturo GattiArturo Gatti 0003.jpg lfwArye Mekel
lfwArye MekelArye Mekel 0001.jpg
lfwArye MekelArye Mekel 0002.jpg
lfwAsa Hutchinson
lfwAsa HutchinsonAsa Hutchinson 0001.jpg lfwAsa HutchinsonAsa Hutchinson 0002.jpg lfwAscencion Barajas
32
lfwAscencion BarajasAscencion Barajas 0001.jpg lfwAshanti
lfwAshantiAshanti 0001.jpg lfwAshantiAshanti 0002.jpg lfwAshantiAshanti 0003.jpg lfwAshantiAshanti 0004.jpg lfwAshantiAshanti 0005.jpg
lfwAshlea Talbot
lfwAshlea TalbotAshlea Talbot 0001.jpg
lfwAshley Judd
lfwAshley JuddAshley Judd 0001.jpg
lfwAshley Olsen
lfwAshley OlsenAshley Olsen 0001.jpg
lfwAshley Postell
lfwAshley PostellAshley Postell 0001.jpg
lfwAshraf Alasmar
lfwAshraf AlasmarAshraf Alasmar 0001.jpg
lfwAshraf Ghani
lfwAshraf GhaniAshraf Ghani 0001.jpg
lfwAshton Kutcher
lfwAshton KutcherAshton Kutcher 0001.jpg
lfwAshton KutcherAshton Kutcher 0002.jpg
lfwAshton KutcherAshton Kutcher 0003.jpg
lfwAsif Ali Zardari
lfwAsif Ali ZardariAsif Ali Zardari 0001.jpg lfwAsif Hanif
lfwAsif HanifAsif Hanif 0001.jpg
lfwAskar Akayev
lfwAskar AkayevAskar Akayev 0001.jpg
lfwAsmaa Assad
lfwAsmaa AssadAsmaa Assad 0001.jpg
lfwAssad Ahmadi
lfwAssad AhmadiAssad Ahmadi 0001.jpg
lfwAstou NdiayeDiatta
lfwAstou NdiayeDiattaAstou NdiayeDiatta 0001.jpg lfwAstrid Betancourt
lfwAstrid BetancourtAstrid Betancourt 0001.jpg lfwAstrid Eyzaguirre
lfwAstrid EyzaguirreAstrid Eyzaguirre 0001.jpg lfwAtal Bihari Vajpayee
lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0001.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0002.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0003.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0004.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0005.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0006.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0007.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0008.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0009.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0010.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0011.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0012.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0013.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0014.jpg
33
lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0015.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0016.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0017.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0018.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0019.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0020.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0021.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0022.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0023.jpg lfwAtal Bihari VajpayeeAtal Bihari Vajpayee 0024.jpg lfwAtaollah Mohajerani
lfwAtaollah MohajeraniAtaollah Mohajerani 0001.jpg lfwAtiabet Ijan Amabel
lfwAtiabet Ijan AmabelAtiabet Ijan Amabel 0001.jpg lfwAtom Egoyan
lfwAtom EgoyanAtom Egoyan 0001.jpg lfwAtsushi Sato
lfwAtsushi SatoAtsushi Sato 0001.jpg lfwAudrey Lacroix
lfwAudrey LacroixAudrey Lacroix 0001.jpg lfwAudrey Sauret
lfwAudrey SauretAudrey Sauret 0001.jpg lfwAugustin Calleri
lfwAugustin CalleriAugustin Calleri 0001.jpg lfwAugustin CalleriAugustin Calleri 0002.jpg lfwAugustin CalleriAugustin Calleri 0003.jpg lfwAugustin CalleriAugustin Calleri 0004.jpg lfwAugusto Pinochet
lfwAugusto PinochetAugusto Pinochet 0001.jpg lfwAugusto PinochetAugusto Pinochet 0002.jpg lfwAugusto Roa Bastos
lfwAugusto Roa BastosAugusto Roa Bastos 0001.jpg lfwAugusto Roa BastosAugusto Roa Bastos 0002.jpg lfwAung San Suu Kyi
lfwAung San Suu KyiAung San Suu Kyi 0001.jpg lfwAung San Suu KyiAung San Suu Kyi 0002.jpg lfwAustin Kearns
lfwAustin KearnsAustin Kearns 0001.jpg lfwAvril Lavigne
lfwAvril LavigneAvril Lavigne 0001.jpg lfwAzmi Bishara
lfwAzmi BisharaAzmi Bishara 0001.jpg lfwAzra Akin
lfwAzra AkinAzra Akin 0001.jpg lfwAzra AkinAzra Akin 0002.jpg lfwAzra AkinAzra Akin 0003.jpg lfwAzra AkinAzra Akin 0004.jpg
In 0:constants IMAGEDIRlfw
DEFAULTSIZE250, 250
In 0:Reads images from filesystem and returns Array of images and imageNames. def readImagesimagePathIMAGEDIR, defaultSizeDEFAULTSIZE:
images
34
imageNames
imageDirsimage for image in os.listdirimagePath if not image.startswith.
for imageDir in imageDirs:
dirPathos.path.joinimagePath, imageDir
dirImageNamesimage for image in os.listdirdirPath if not image.startswith.
for imageName in dirImageNames:
imageImage.openos.path.joindirPath, imageName
imageimage.convert LL stands for Luminance: converts image to grayscale
if defaultSize is not None:
imageimage.resizedefaultSize, Image.ANTIALIASresize image
images.appendnp.asarrayimage, dtypenp.uint8
imageNames.appendimageDir
return images, imageNames
In 0: X, yreadImages
In 0: typeX, lenX
Out0: list, 1054
In 0: typeX0, X0.shape
Out0: numpy.ndarray, 250, 250
In 0: typey, leny
Out0: list, 1054
1.4.2 Exploratory Data Analysis
Check from dataset if this image has correct label.
In 0: printImage name is: , y2
plt.imshowX2, cmapplt.cm.gray
plt.show
Image name is: Aleksander Kwasniewski
35
Creating a mean face from all dataset faces.
In 0: def asRowMatrixX:
if lenX0: return np.array
rowMatrixnp.empty0, X0.size, dtypeX0.dtype
for img in X:
rowMatrixnp.vstackrowMatrix, np.asarrayimg.reshape1, 1
return rowMatrix
In 0: XMatasRowMatrixX;
meanImagenp.reshapeXMat.meanaxis0, X0.shape
plt.imshowmeanImage, cmapplt.cm.gray
plt.titleMean Face
plt.show
36
1.4.3 EigendecompositionComputing Eigenvectors and Eigenvalues
Using Covariance Matrix
In 0: def getBasisCountThatPreservesVarianceeigenValues, variance.95:
for idx, cumulativeSum in enumeratenp.cumsumeigenValuesnp.sumeigenValues:
if cumulativeSumvariance:
return idx
def pcaX, y:
n, dX.shape
muX.meanaxis0
XXmustandardising data
if nd:
Cnp.dotX.T, Xcovariance matrix eigenValues, eigenVectorsnp.linalg.eighC
else:
Cnp.dotX, X.Tcovariance matrix eigenValues, eigenVectorsnp.linalg.eighC eigenVectorsnp.dotX.T, eigenVectors
for i in rangen:
eigenVectors:,ieigenVectors:, inp.linalg.normeigenVectors:, i
sort eigenVectors in descending order by their eigenValue
idxnp.argsorteigenValues
eigenValueseigenValuesidx
eigenVectorseigenVectors:, idx
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select based on numOfBasis
numOfBasisgetBasisCountThatPreservesVarianceeigenValues
printNumber of useful eigenBasis are: , numOfBasis
eigenValueseigenValues0:numOfBasis.copy
eigenVectorseigenVectors:, 0:numOfBasis.copy
return eigenValues, eigenVectors, mu Below image explains the PCA code above:
In 0: eigenValues, eigenVectors, meanpcaXMat, y
Number of useful eigenBasis are:298
In 0:Above code in pca method is written because below code is computationally time taking.Cnp.dotXMat.T, XMatcovariance matrix
eigenValues, eigenVectorsnp.linalg.eighC
EigenFaces What were dimensions of eigenVector in the case of Iris example?
Array of sizenumber of features 4 in the case of Iris. Array of size 4.
What will be dimensions of eigenVector in this example?
Array of sizefeature size 62500.
In 0: eigenVectors:, 0.shape
Out0: 62500,
If the dimensions of eigenVector is same as the vectorised image. What if eigenVector is displayed in image format.
This is called eigenFace.
In 0:show the first eigenFace
plt.imshoweigenVectors:, 0.reshape1, 250, cmapplt.cm.gray
Out0: matplotlib.image.AxesImage at 0x7f9402eae710
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In 0:print first 6 eigen faces COUNT6
ROWSmath.ceilCOUNT3
figplt.figurefigsize12, ROWS4
for i in range0, COUNT:
plt.subplotROWS, 3, i1
plt.imshoweigenVectors:, i.reshape1, 250, cmapplt.cm.gray
plt.title.formati1
By only using first few eigenFaces: 1. How would you get a face with white hair. 2. Answer the same for black hair.
Have a good look at eigenFace number 5. Good luck sleeping tonight.
1. Plot the next 6 eigenFaces.
2. Do you observe any difference observed between the first 6 and second 6.
1.4.4 Pro jections
Now, we will reconstruct an image from the dataset using eigenFaces eigenVectors.
In 0: IMAGEIDX10image idx in dataset
In 0: def project W , X , mu:
return np.dot Xmu , W
def reconstruct W , Y , mu :
return np.dot Y , W.Tmu
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In 0:create reconstructed images
COUNT6count of first eigenVectors used to reconstruct the image reconImages
for numEvs in range 1, COUNT1:
PprojecteigenVectors:, 0:numEvs, XIMAGEIDX.reshape1, 1, mean
RreconstructeigenVectors:, 0:numEvs, P, mean
reconImages.appendR.reshapeX0.shape
In 0:plot reconstructed images ROWSmath.ceilCOUNT3
figplt.figurefigsize12, ROWS4
for i in range0, COUNT:
plt.subplotROWS, 3, i1
plt.imshowreconImagesi, cmapplt.cm.gray
plt.title.formati1
In 0:create reconstructed images
numEvsSet100, 200, 298these no. of eigenVectors will be used to reconstruct the image. COUNTlennumEvsSet
reconImages
for numEvs in numEvsSet:
PprojecteigenVectors:, 0:numEvs, XIMAGEIDX.reshape1, 1, mean
RreconstructeigenVectors:, 0:numEvs, P, mean
reconImages.appendR.reshapeX0.shape
In 0:plot reconstructed images ROWSmath.ceilCOUNT3
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figplt.figurefigsize12, ROWS4
for i in range0, COUNT:
plt.subplotROWS, 3, i1
plt.imshowreconImagesi, cmapplt.cm.gray
plt.title.formati1
In 0:actual image
plt.imshowXIMAGEIDX, cmapplt.cm.gray plt.show
Can you identify the person after 298 eigenVector reconstruction?
1.4.5 Facial Recognition Optional
How a new point would be classified on the IRIS dataset after PCA.
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1. Projecting all training samples into the PCA subspace.
2. Projecting the query image into the PCA subspace.
3. Finding the nearest neighbor one algorithm to accomplish this between the projected training images
and the projected query image.
How would a new face be classified facial recognition after PCA.
FunFact: EigenFaces is still often considered as a baseline comparison method to demon strate the minimum expected performance of a facial recognition system.
1.5 Time Series DataExercises
The clock is ticking.
The dataset is of Tuberculosis prevalence over various countries between the given time period.
Data url: https:raw.githubusercontent.comaps10702019datasetsmastertbdata.csv.
Answer the below questions.
You are free to do the below analysis over other timeseries datasets of your interest eg: financial stock
data, etc., provided the dataset has at least 15 columns time pointsfeatures and at least 100 rows data points.
1.5.1
1.
2.
1.5.2
1. 2.
1.5.3
1. 2.
3.
1.5.4
1.
2.
1.5.5
1.
Question 1
Display 30 random samples of the original time series data in a 10 x 3 3 plots each in 10 rows graph format.1
Do you see any recurring patterns ie oscillations, monotonic increase or decrease, other trends?0.5
Question 2
Show the first 6 principle components plotted as a time series in a 3 plotsrow format.1
Based on your knowledge of the dataset contents, can you explain what any of the principle components might represent?0.5
Question 3
Pick an interesting data sample ie, data from a single country and display it.1
Next, show its incremental reconstruction using the first 16 components again plotted as a time series in a 3 plotsrow format.1
In addition, show another plot with the residual error of each reconstruction compared to the original sample and a title that states the RMSE of the reconstruction for each of the 6 components.1
Question 4
Plot the eigenvalues of the first 15 or more principle components and choose a number k of principle components that you believe will allow you to reconstruct the data well.1
How many did you choose and why?1
Question 5
Compute the mean M and standard deviation StD of the interesting data sample selected in question 3.0.5
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Random walk refers to any process in which there is no observable pattern or trend; that is, where the movements of an object, or the values taken by a certain variable, are completely random. Each step taken in a random walk can be sampled from a distribution. You may find the methods numpy.random.normal, numpy.cumsum useful for creating random walks.
2. Make 6 time series of random walks of the same length as the time series in this dataset. Random walks created should have the same mean M and standard deviation StD as the data sample choosen. Each next step in the random walk is some Uniform or Gaussian perturbation from the previous sample.1
Show for a sample random walk its mean and standard deviation matches M and StD respectively.Visualize these 6 time series in a 2 x 3 plot.
3. Show the reconstruction of each time series using k principle components overlayed on the original random walk. Plot this in a 2 x 3 plot and report the RMSE of the reconstruction in the title of each plot.1
4. Compare these RMSE values with the ones you got for question 3.1
1.5.6 Question 6
Explain how could you use PCA to do anomaly detection.1
1.6 References
Understanding PCA and SVD: 1. https:towardsdatascience.compcaandsvdexplainedwithnumpy 5d13b0d2a4d8 2. https:stats.stackexchange.comquestions134282relationshipbetweensvdandpca howtousesvdtoperformpca 3. https:stats.stackexchange.comquestions2691makingsenseof principalcomponentanalysiseigenvectorseigenvalues 4. https:hadrienj.github.iopostsDeepLearning BookSeries2.8SingularValueDecomposition
PCA: 1. Snippets from: https:plot.lyipythonnotebooksprincipalcomponentanalysis 2. https:www.valueatrisk.netprincipalcomponentanalysis
Eigenfaces: 1. Snippets from: https:github.comsvetlanatopalovaeigenfacesblobmasterEigenfaces.ipynb 2. https:sandipanweb.wordpress.com20180106eigenfacesandasimplefacedetectorwithpcasvdin python
Author: Parth Jaggi
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