The paper by Michael E. Tipping and Christopher M. Bishop introduces a probabilistic approach to Principal Component Analysis (PCA), a widely used technique for dimensionality reduction. The authors demonstrate that PCA can be derived within a density estimation framework by formulating it as a maximum likelihood estimation problem in a latent variable model related to factor analysis. They show that the principal axes of the data can be determined through iterative estimation of parameters using an Expectation-Maximization (EM) algorithm. This probabilistic formulation offers several advantages, including the ability to handle missing data, extend PCA to mixture models, and control the complexity of the model through the choice of the number of latent variables. The paper also provides practical examples to illustrate the effectiveness of the probabilistic PCA approach in various applications, such as data visualization and image compression.The paper by Michael E. Tipping and Christopher M. Bishop introduces a probabilistic approach to Principal Component Analysis (PCA), a widely used technique for dimensionality reduction. The authors demonstrate that PCA can be derived within a density estimation framework by formulating it as a maximum likelihood estimation problem in a latent variable model related to factor analysis. They show that the principal axes of the data can be determined through iterative estimation of parameters using an Expectation-Maximization (EM) algorithm. This probabilistic formulation offers several advantages, including the ability to handle missing data, extend PCA to mixture models, and control the complexity of the model through the choice of the number of latent variables. The paper also provides practical examples to illustrate the effectiveness of the probabilistic PCA approach in various applications, such as data visualization and image compression.