n this assignment, you will work with an Activity Recognition dataset to explore, preprocess, and apply various classification algorithms. You will build a Bayesian Classifier from scratch and implement Kernel Discriminant Analysis $($KDA$)$ using different kernels. Additionally, you will apply multiple classifiers using the scikit$-$learn library on both the entire dataset and the PCA$-$reduced dataset, comparing their performance.

Part $1$: Data Preprocessing

Loading the Dataset:

Load the Activity Recognition dataset into a pandas DataFrame.Display the first few rows and check for any missing values.Handle missing values if necessary.

Train$-$Test Split:

Split the dataset into training and testing sets.Use an $80/20$ split, where $80\%$ of the data is used for training and $20\%$ for testing.$$

Part $2$: Classification on the Entire Dataset

In this part, you will apply several classifiers to the entire dataset without any dimensionality reduction.

Bayesian Classifier $($from scratch$)$:

Implement a Bayesian classifier by calculating the prior probabilities and modeling the likelihood with a Gaussian distribution.Use Bayes' Theorem to compute the posterior probability for each class and classify the test data.

Other Classifiers $($using scikit$-$learn$)$: Apply the following classifiers from scikit$-$learn:

Support Vector Machine $($SVM$)$:

Use both Linear SVM and Kernel SVM $($RBF and Polynomial kernels$).$

k$-$Nearest Neighbors $($KNN$)$:

Experiment with different values for k$.$

Naive Bayes:

Implement Gaussian Naive Bayes using GaussianNB.

Linear Discriminant Analysis $($LDA$)$:

Use LinearDiscriminantAnalysis.

Kernel Discriminant Analysis $($KDA$)$:

Implement KDA using different kernels $($RBF$,$ Polynomial$).$

Evaluation:

Evaluate the performance of all classifiers on the test set using the following metrics:

AccuracyPrecisionRecallF$1-$Score

Generate a confusion matrix for each classifier.

Part $3$: Dimensionality Reduction Using PCA

Principal Component Analysis $($PCA$)$:

Apply PCA to the dataset to reduce its dimensionality.Choose the number of components based on the explained variance ratio $($e$.$g$.,$ retain $95\%$ of the variance$).$Visualize the first two principal components.

Kernel PCA $($Optional$)$:

Experiment with Kernel PCA using different kernels $($linear$,$ RBF$,$ polynomial$)$ and visualize the results.

$$

Part $4$: Classification on the PCA$-$Reduced Dataset

Now, apply the same classifiers used in Part $2$ to the PCA$-$reduced dataset:

Bayesian Classifier $($from scratch$)$:

Apply the Bayesian Classifier you built from scratch to the PCA$-$reduced data.

Other Classifiers $($using scikit$-$learn$)$:

Apply the following classifiers on the PCA$-$reduced dataset:

Linear SVM and Kernel SVM$.$k$-$Nearest Neighbors $($KNN$).$Naive Bayes.Linear Discriminant Analysis $($LDA$).$Kernel Discriminant Analysis $($KDA$).$

Evaluation:

Evaluate the classifiers again using the same metrics $($accuracy$,$ precision, recall, F$1-$score$).$Compare their performance with and without PCA.

Part $5$: Performance Comparison

Evaluation:

Create a summary table comparing the performance of all classifiers on the entire dataset and the PCA$-$reduced dataset.Discuss how the classifiers performed with and without PCA.

Comparison and Discussion:

Compare the Bayesian classifier built from scratch to its scikit$-$learn counterparts.Analyze the impact of PCA on the classifiers$$ performance.Discuss the effect of using different kernels in SVM and KDA.

Submission Instructions:

Submit your work in a Jupyter notebook named firstname$\_$lastname.ipynb.