Canonical Correlation Analysis: Linear and Kernel CCA

This lecture covers Canonical Correlation Analysis (CCA), a method to determine features in separate datasets that jointly represent the data well. It extends to multimodal datasets like audio & images, biometric data, and text. The derivation of CCA involves finding projections that maximize correlation, leading to a generalized eigenvalue problem. Kernel CCA is introduced to handle non-linear features by using kernel functions. The solution involves expressing projection vectors as a linear combination of datapoints in feature space. The lecture also discusses the interpretation of CCA solutions, the visualization of projection vectors, and the application of CCA to multiple modalities. CCA is compared to Principal Component Analysis (PCA), highlighting its ability to discover appropriate projections for multi-modal data.