PCA (Principal Component Analysis) Implementation
📝 Overview: This README file provides comprehensive insights into the Principal Component Analysis (PCA) method, elucidating its fundamental concepts and practical application steps. It is noteworthy that the implementation presented here utilizes custom functions rather than relying solely on the PCA library.
What is PCA? PCA stands for Principal Component Analysis, a statistical method employed to reduce the dimensionality of high-dimensional datasets. It achieves this by identifying the principal components in the data, effectively preserving essential features while reducing dimensionality.
Advantages of PCA 🚀: Dimensionality Reduction: Mitigates complexity in high-dimensional datasets. Understanding Variability: Facilitates a better understanding of variability within the dataset. Optimal Representation: Identifies the principal components that best represent the dataset.
Implementation Steps 🛠️: 1-Data Preparation: Clean the dataset and handle missing values. Standardize the dataset.
2-Computation of Covariance Matrix: Calculate the covariance matrix to comprehend relationships between variables.
3-Eigenvalue and Eigenvector Computation: Compute the eigenvalues and eigenvectors of the covariance matrix.
4-Sorting Eigenvalues: Sort eigenvalues in descending order to identify the most significant components.
5-Selection of Principal Components: Choose eigenvectors corresponding to the most important eigenvalues.
6-Creation of New Dataset: Form a new, reduced-dimensional dataset using the selected principal components.