Dimensionality Reduction and Decomposition Techniques

Explore advanced dimensionality reduction and decomposition methods that enhance clustering performance. Topics covered include Principal Component Analysis (PCA), Singular Value Decomposition (SVD), Canonical Correlation Analysis (CCA), Non-Negative Matrix Factorization (NMF), Multidimensional Scaling (MDS), and Tensor Decompositions.

PCA for Clustering

In-depth exploration of Principal Component Analysis (PCA) for clustering, including its mathematical foundations, use in dimensionality reduction, and its role in enhancing clustering algorithms.

Singular Value Decomposition (SVD) for Clustering

An in-depth exploration of Singular Value Decomposition (SVD) applied to clustering, including a comparison with PCA and practical examples.

Canonical Correlation Analysis (CCA)

An in-depth exploration of Canonical Correlation Analysis (CCA), its mathematical foundation, and its applications in data science, particularly in understanding the relationships between two sets of variables.

Non-Negative Matrix Factorization (NMF)

An in-depth exploration of Non-Negative Matrix Factorization (NMF), including its mathematical foundation, applications in clustering, and comparison with other matrix factorization techniques.

Multidimensional Scaling (MDS)

An in-depth exploration of Multidimensional Scaling (MDS), its mathematical foundation, and its applications in visualizing high-dimensional data by reducing dimensionality.

Tensor Decompositions

An in-depth exploration of tensor decompositions, including their mathematical foundations, types, and applications in machine learning and data science.