A) Understand and explore a data set
Three data sets (set A, B, and C) have been created following normally distributed classes. These data sets provide examples of male and female population where:
- The first column represents the height in feet.
- The second column represents the weight in pounds.
- The third (last) column corresponds to the gender (0 for male, and 1 for female).
Each data set contains 2,000 samples for each gender.
For each data set, do the following:
- Plot the data for male and female students.
- Manually draw (by hand) a separation line. This will be a linear separator (or decision function) which separates female and male students.
- Determine the equation of this linear separator
- Write the definition of a neuron. Note: Think of the inequality we covered in class.
- Determine the weights and threshold. Comment.
- Calculate false positives and false negatives (refer to confusion matrix).
- Calculate accuracy, error, true positive rate and true negative rate, false positive rate and false negative rate.
- Compare results for each data set and explain the differences. How are these datasets different?
Important: Assume the example of true positive: the class is “it is a female” and prediction is “female”
B)McCulloch-Pitts neurons
- Create a truth table for the artificial neuron below. What is the functionality of this neuron?
- Given the same set of weights and the determined functionality of a neuron, what would be the range of possible values for threshold?
Note: Consider unipolar hard threshold activation function (possible inputs/outputs are obviously 0 & 1). | |
Always start with the unit definition (net, output). |
Hint: The truth table (similar to the one in class) should present inequalities that will evidence the | |
functionality of a neuron (prove that it works as promised). |
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