Principal component analysis and its application

This thesis examines the Principal Component Analysis (PCA) method and investigates dimensionality reduction and data analysis processes in high-dimensional datasets. PCA constructs linear components that explain the maximum variance in the data, reducing the dataset's dimensionality while preserving essential information. This method is widely used when working with datasets containing numerous variables, making the data more comprehensible and visually interpretable. In this study, the mathematical foundations of PCA (covariance matrix, eigenvalues, and eigenvectors) are explained in detail, and the implementation steps of this method are thoroughly addressed. During the application phase, the PCA method is applied to television rating data to analyze different audience groups' channel preferences and viewing habits. Rating data from the AB and 20+ABC1 groups, provided by TİAK, are compared to assess behavioral differences and similarities between these groups.