Dataset

You will work with the Thyloid.csv file, which contains gene data from each patient. The dataset includes various gene expression measurements $($features$)$ and a label indicating the stage information.

$1.$ Preparing the Data:

a$.$ Split your Thyloid.csv into Train and Test datasets.

b$.$ Apply the PCA and KPCA models $($RBF$,$ Polynomial, Linear, and combined kernels$)$ trained on the Train dataset to transform the Test dataset.

c$.$ Ensure the dimensionality reduction is consistent with what was performed on the training data.

$2.$ Covariance Matrix Analysis:

a$.$ Calculate the covariance matrix of the dataset.

b$.$ Identify the top $10$ features with the highest covariance values.

$3.$ Classification Experiment:

For this part, you will implement the following classifiers using sklearn and compare their performance:

KNN

Bayes

Naive Bayes

LDA

SVM

You will implement the Bayes classifier from scratch.

a$.$ Implement a Bayes classifier from scratch.

b$.$ For each classifier $($KNN$,$ Bayes, Naive Bayes, LDA, and SVM$),$ test the classifiers on:

Whole data

Data reduced by PCA

Data reduced by KPCA with RBF$,$ Polynomial, and Linear kernels

Data reduced by top $10$ features

c$.$ For each classifier and each dimensionality reduction technique, find the best number of dimensions that yields the highest classification accuracy.

d$.$ Evaluate the classification performance using accuracy metrics $($e$.$g$.,$ accuracy, precision, recall$)$ and compare the effectiveness of PCA features $,$ KPCA features $,$ and Data reduced by top $10$ features.