[SOLVED] Aiml 231 assignment 3: regression, clustering and nns

This question involves using linear regression techniques to predict the fuel efficiency, measured by miles per gallon (MPG) of vehicles based on various attributes in the Auto MPG
dataset. This analysis will help understand the influence of different vehicle characteristics
such as engine size, weight, and horsepower on fuel economy. The Auto MPG dataset describes city-cycle fuel consumption in MPG with several car attributes such as car weight, displacement, horsepower, etc. You will use the Auto MPG dataset provided by seaborn.load dataset.Data Loading and Preprocessing
• Load the Auto MPG dataset using seaborn.load dataset(’mpg’).
• Use the function train test split from sklearn.model selection to perform a 80/20 split to
form the training and test sets. Set the random seed to 231 for reproducibility.(a) Conduct exploratory data analysis (EDA) to visualize and summarize the training set.
You should include histograms to show distributions of variables and scatter plots to understand relationships between each pair of variables. Highlight important patterns in the
report.(b) Data Preprocessing before linear regression:
• Examine the dataset to find any missing values. Implement an appropriate imputation technique to manage missing data. Clearly document the method you choose
for imputation.• Examine the dataset to find any categorical variables. Review the encoding techniques discussed in our lectures and select the most appropriate method for each
categorical variable in the dataset considering factors such as the number of categories and the ordinal nature of the data. Document the chosen encoding methods.Provide a brief justification for your choice.
(c) Construct a linear regression model to predict MPG of a vehicle using the dataset’s features. Report the coefficients, the training and test performance of your model using
R-squared and mean squared error (MSE).Explore and compare the performance of K-means clustering and hierarchical clustering on a
synthetic dataset to identify natural groups within the data.Data Preparation
• use make blobs from sklearn.datasets to generate a dataset with four features, three clusters, and 300 samples. Leave other parameters to be default values and set the random
seed to 231 for reproducibility.(a) Implement K-means clustering using sklearn.cluster.KMeans on the dataset. Determine
the best K by evaluating the silhouette scores for various K values ranging from 2 to 5.
(b) Visualisation of your clusters with Principal Component Analysis (PCA): utilize PCA to
reduce the dimensionality of your dataset. Specifically, project the data onto the first two
principal components, which will serve as the new axes for visualisation. Construct and
present a scatter plot using these two principal components. Each cluster should have a
different color.(c) Apply hierarchical clustering to the same dataset using sklearn.cluster.Agglomerative
Clustering with the following linkage methods: single, complete, and average. Create
dendrograms using scipy.cluster.hierarchy.dendrogram to visually represent the clusters. Ensure that each dendrogram is clearly labeled. Compare the effect of these linkage
methods on creating clusters in this scenario.(d) Discuss the advantages and disadvantages of hierarchical clustering compared with Kmeans clustering in this scenario.This question is to show a basic understanding of neural networks by implementing a multilayer perceptron (MLP) model in PyTorch to classify handwritten digits from the Digits dataset.
The dataset contains 1,797 images of handwritten digits, each image being an 8×8 pixel grayscale
image of a digit (0-9). Each image is represented as a 64-feature input vector, corresponding to
the grayscale values of the pixels. As part of this question, there will be a compulsory in-person
marking for your code part which will contribute 10 out of the total 60 marks. You will be required to demonstrate the neural network model you have developed. During the in-person
marking session, you will present your code and explain your decision-making process regarding the building, and training of your neural network model.Data Loading and Preprocessing
• Load the Digits dataset using sklearn.datasets.load digits().
• Split the data into a training set (80%) and a testing set (20%). Set the random seed to
231 for reproducibility.• Normalize the images by scaling the pixel values to a range of 0 to 1.
• Convert the datasets into PyTorch tensors and create DataLoader objects for both training
and testing sets.(a) Define a neural network class by extending torch.nn.Module. The network should have
one input layer, one hidden layer with 128 neurons, and one output layer. Use the ReLU
activation function for the hidden layer, and the softmax activation function for the output layer. Determine the number of neurons in the input and output layers and justify
your answer. Implement your neural network class accordingly.(b) Use the torch.nn.CrossEntropyLoss for your loss function, choose an optimizer from
torch.optim.SGD and torch.optim.Adam and set an appropriate learning rate, provide
justifications for your choices. Train the model for 15 epochs. After each epoch, print the
training loss and accuracy.(c) After training, evaluate the model on the test set to measure its accuracy. Print the test
accuracy and show five example predictions along with their actual labels.
(d) Evaluate and compare the effectiveness of different activation functions including Sigmoid and Tanh in place of ReLU.(e) Consider the network architecture, how would adding more hidden layers or changing
the number of neurons in a layer affect the model’s performance?
Expected Outputs (Remember to put the outputs in your report)• Training Output: At the end of each training epoch, your program should display:
– Average loss for the epoch.
– Training accuracy for the epoch.
Example output after each epoch:
Epoch 1: Loss = 2.302, Accuracy = 11%
Epoch 2: Loss = 1.904, Accuracy = 32%
…
Epoch 15: Loss = 0.312, Accuracy = 90%• Testing Output: After the model has been trained, report the overall accuracy on the test
dataset. Also, include a few example images from the test set alongside their predicted
and actual labels to visually demonstrate the model’s performance.Example output:
Test Accuracy: 88%
Additionally, display several test images along with their predicted and actual labels to
visually assess the model’s performance. This can be presented in a table or as image
plots with captions. For example:
Test Image 1: Predicted Label = 3, Actual Label = 3
Test Image 2: Predicted Label = 7, Actual Label = 7
…
Test Image 5: Predicted Label = 4, Actual Label = 9Assessment
Format: You can use any font to write the report, with a minimum of single spacing and 11
point size (hand writing is not permitted unless with approval from the lecturers). Reports are
expected to be at most 8 pages that cover all the questions described above.
Late Penalty: Late submissions for assignments will be managed under the ”Three Late Day
Policy”. You will have three automatic extension days, which can be applied to any assignments throughout the course. No formal application is required; instead, any remaining late
hours will be automatically deducted when submitting assignments after the due date. You
have the flexibility to use only a portion of your late day and retain the remainder for future
use.Please note that these three days are for the whole course, not for each assignment. The
penalty for assignments that are handed in late without prior arrangement (or use of ”late
days”) is one grade reduction per day. Assignments that are more than one week late will not
be marked. If you require any extension due to exceptional circumstances (like medical), you
need to email the course coordinator.Submission: You are required to submit a .pdf report and your source code files as a Jupyter
notebook(.ipynb file) and/or a python code (.py) file through the web submission system from
the AIML231 course website by the due time.