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Dataset You will work with the colon.csv file, which contains gene data from each patient. The dataset includes various gene expression measurements ( features )
Dataset You will work with the colon.csv file, which contains gene data from each patient. The dataset includes various gene expression measurements features and a label indicating the stage information. Part : Principal Component Analysis PCA Implement PCA from Scratch: a Write Python code to implement PCA from scratch. Include functions to compute the covariance matrix, eigenvalues, and eigenvectors. b Apply your PCA implementation to reduce the dimensionality of the features in colon.csv c Choose an appropriate number of principal components to retain a significant amount of variance eg PCA using scikitlearn: a Use the PCA module from sklearn to perform dimensionality reduction on the dataset. b Compare the results with your fromscratch implementation in terms of explained variance and the reduced feature set. Part : Kernel PCA KPCA KPCA with RBF Kernel: a Implement Kernel PCA with the Radial Basis Function RBF kernel from scratch. b Apply your KPCA implementation to the dataset. KPCA with Polynomial Kernel: a Implement Kernel PCA with a Polynomial kernel from scratch. b Apply your KPCA implementation to the dataset. KPCA with Linear Kernel: a Implement Kernel PCA with a Linear kernel from scratch. b Apply your KPCA implementation to the dataset. Combining Kernels: a Combine two different kernels eg RBF and Polynomial and apply the combined KPCA to the dataset. b Evaluate the classification performance using accuracy metrics for the combined kernels. Part : Testing and Evaluation Split your colon.csv into Train and Test datasets. Applying PCA and KPCA to the Test Dataset: a Use the PCA and KPCA models RBF Polynomial, Linear, and combined kernels trained on the Train dataset to transform the Test dataset. b Ensure the dimensionality reduction is consistent with what was performed on the training data. Covariance Matrix Analysis: a Calculate the covariance matrix of the dataset. b Identify the top features with the highest covariance values. c Extract these top features and evaluate the classification performance using accuracy metrics. Classification Experiment: a Choose a classifier minimum distance classifier: provided at the end of this assignment to classify the observations in the Test dataset. b Evaluate the classification performance using accuracy metrics and compare the effectiveness of PCA and KPCA features.
Dataset
You will work with the colon.csv file, which contains gene data from each patient. The dataset includes various gene expression measurements features and a label indicating the stage information.
Part : Principal Component Analysis PCA
Implement PCA from Scratch:
a Write Python code to implement PCA from scratch. Include functions to compute the covariance matrix, eigenvalues, and eigenvectors.
b Apply your PCA implementation to reduce the dimensionality of the features in colon.csv
c Choose an appropriate number of principal components to retain a significant amount of variance eg
PCA using scikitlearn:
a Use the PCA module from sklearn to perform dimensionality reduction on the dataset.
b Compare the results with your fromscratch implementation in terms of explained variance and the reduced feature set.
Part : Kernel PCA KPCA
KPCA with RBF Kernel:
a Implement Kernel PCA with the Radial Basis Function RBF kernel from scratch.
b Apply your KPCA implementation to the dataset.
KPCA with Polynomial Kernel:
a Implement Kernel PCA with a Polynomial kernel from scratch.
b Apply your KPCA implementation to the dataset.
KPCA with Linear Kernel:
a Implement Kernel PCA with a Linear kernel from scratch.
b Apply your KPCA implementation to the dataset.
Combining Kernels:
a Combine two different kernels eg RBF and Polynomial and apply the combined KPCA to the dataset.
b Evaluate the classification performance using accuracy metrics for the combined kernels.
Part : Testing and Evaluation
Split your colon.csv into Train and Test datasets.
Applying PCA and KPCA to the Test Dataset:
a Use the PCA and KPCA models RBF Polynomial, Linear, and combined kernels trained on the Train dataset to transform the Test dataset.
b Ensure the dimensionality reduction is consistent with what was performed on the training data.
Covariance Matrix Analysis:
a Calculate the covariance matrix of the dataset.
b Identify the top features with the highest covariance values.
c Extract these top features and evaluate the classification performance using accuracy metrics.
Classification Experiment:
a Choose a classifier minimum distance classifier: provided at the end of this assignment to classify the observations in the Test dataset.
b Evaluate the classification performance using accuracy metrics and compare the effectiveness of PCA and KPCA features.
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