Assignment_1_write up_Alvin_Joseph

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EECE -5644 Machine Learning Assignment 1 Alvin Joseph NU ID: 002197786 1. Part A 1. 2. Given below are the samples generated using the mean, covariance, and class values.
Given below are the mapped decisions of the classifier: The figure below shows thee ROC curve implemented on the ERM classifier by varying the risk classifier on the 10000 samples and varying the threshold from zero to infinity.
3. The red cross marked on the ROC curve indicates the experimental minimum error which was found to be 0.0575 from the generated data. The experimental gamma value generated from the samples is 1.857142. This experimental gamma value is closely aligned with the theoretical gamma value calculated in (1) which is 1.857 The following table summarizes the experimental and theoretical results. γ Minimum probability of error Theoretical 1.857 0.208 Calculated from Data 1.823 0.160 In my results, there is a difference of 0.048 between the theoretical probability of error an γ Minimum Error Probability Theoretical 1.857 0.0208 Obtained Value 1.857142 0.0575 Part B: ERM classification attempt using incorrect knowledge of data distribution Given below are the samples generated using the mean, covariance, and class values.
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Given below are the mapped decisions of the classifier:
The red cross marked on the ROC curve indicates the experimental minimum error which was found to be 0.0574 from the generated data. The experimental gamma value generated from the samples is 1.857142. There isn ’ t much difference is the theoretical values and ERM classifier values obtained and hence ERM performs well in this dataset. Part C: Fisher Linear Discriminant Analysis based Classifier Given below are the ROC curves and decision labels for Fisher ’s LDA based classifier
Fisher LDA analysis: Based on the values obtained for for tau and minimum probability of error generated, we can infer that Fisher Linear Discriminant Analysis performed worse than the ERM classifier
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2. Part A - MAP Classifier:- 1. 2.
3. The confusion matrix for the classifier is displayed below and the minimum probability of error obtained is 0.2767
Part B - ERM Classifier:- The confusion matrix of the ERM classifier is displayed below. The minimum probability of error obtained is 0.2767
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From the plots based on the MAP classifier approach and ERM classification approach, there isn ’ t much of a significant difference between the confusion matrix values and minimum probability errors. The loss matrix could have played a part in the resulting observation.
3. Distribution of features: White-wine data set Regularizing lambda observed is 366.593249
Distribution of features: HAR dataset
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Regularizing lambda observed is 366.593249 – for HAR Dataset PCA Projections: PCA plot for trained dataset (white wine dataset) PCA plot for test dataset (white wine dataset)
PCA plot of Test data for HAR Dataset: PCA plot of trained data for HAR Dataset:
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Appendix : Reference:- Majority of the code snippets referred from Professor Mark ’ s uploaded files and other open source platforms 1.
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2.
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3.
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