USC-EE559-HW01

Name: Tejas Acharya
Class: EE-559
Date: 14-06-2023
Assignment: Homework 1

OS: Linux Mint
Distribution: Anaconda

Synthetic-1

Model: Nearest Means Classifier
Training Error Rate: 21.00%
Test Error Rate: 24.00%

Training Data Decision Boundary:

Predicted Training Data Decision Boundary:

Synthetic-2

Model: Nearest Means Classifier
Training Error Rate: 3.00%
Test Error Rate: 4.00%

Training Data Decision Boundary:

Predicted Training Data Decision Boundary:

(b)

There is a significant difference in error rates between Synthetic-1 and Synthetic-2 dataset with Synthetic-2 showing a low error rate. This is either due to:

• Synthetic-2 data is more separable than Synthetic-1
• NearestMeansClassifier is a poor algorithm for Synthetic-1, because when we observe y_train.png for Synthetic-1, the natural labelling of the class is not due to the distance from the class means.

Wine

Model: Nearest Means Classifier

(c)

Training Error Rate: 20.22%
Test Error Rate: 22.47%

Training Data Decision Boundary:

Predicted Training Data Decision Boundary:

(d)

Best Feature: 0, 11
Train Error Rate(Best Feature): 7.87%
Test Error Rate(Best Feature): 12.36%

Training Data Decision Boundary(for best feature):

Predicted Training Data Decision Boundary(for best feature):

Description to find Best Feature:

• Build a list of pairwise set of features, feature set must be unique
• For each pairwise feature set:
  • Build a model
  • Obtain the Prediction(y_train_predict) on Training Set(X_train)
  • Get Train Error Rate(y_train_error_rate) for each model and Prediction
  • Append the Train Error Rate to Train Error Rate list
• Get the minimum element of Train Error Rate list and it's index.

(e)

Standard Deviation in Train Error Rate over different pairs of Features: 12.87
Coefficient of variation of Train Error Rate: 0.37
With a Train CV below 1, there is not a significant difference in Train Error Rates across all features.

Standard Deviation in Test Error Rate over different pairs of Features: 9.83
Coefficient of variation of Test Error Rate: 0.29
With a Test CV below 1, there is not a significant difference in Test Error Rates across all features.