A matrix factorization that expresses a matrix as the product of orthogonal matrices and a diagonal matrix of singular values.
Singular value decomposition (SVD) reduces a complex numeric dataset to a few summary dimensions, making patterns, clusters, and isolated anomalies easier to inspect visually. section 2.4.3
Use SVD as a practical exploratory projection when:
Your multivariate data is numeric, or categorical values have been discretized. section 2.4.3
You want to compress many features into a few weighted summary dimensions and plot them. section 2.4.3
You need an initial visual check for patterns, clusters, or potentially anomalous observations. section 2.4.3
You can accept that linear combinations may miss nonlinear structure and that reduced plots lose information. section 2.4.3
How Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI covers it
How deep it goes
Explains projection purpose and linear limitations but stops short of factorization mathematics or implementation.
Examples
Projects tabular observations into a few summary dimensions and plots them to inspect clusters and isolated points.
What it assumes
Requires numeric multivariate features, while permitting discretization of numeric values for multivariate analysis.
What you can do after
Evaluate numeric tabular data through lower-dimensional plots that support pattern, cluster, and anomaly inspection.
How it connects
Connects SVD with PCA, t-SNE, UMAP, dimensionality reduction, exploratory data analysis, and anomaly detection.
Data Without LabelsSingular value decomposition is a matrix factorization that expresses a matrix as the product of two orthogonal matrices and a diagonal matrix of singular values.
Math and Architectures of Deep LearningThe statement that any matrix can be decomposed as a product of orthogonal matrices and a diagonal matrix in singular value decomposition form.
Natural Language Processing in Action, Second EditionSingular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal singular-vector matrices and a diagonal singular-value matrix.
Grokking Machine LearningA matrix decomposition that expresses a matrix as the product of orthogonal matrices and a diagonal matrix of singular values.
principal component analysisused by · Principal component analysis is a linear dimensionality-reduction technique that transforms data into orthogonal components ordered by the variance they capture.
singular valueproduces · A singular value is a nonnegative scalar in a matrix’s singular value decomposition that measures stretching along a corresponding singular direction.
co-occurrence matrixuses · A co-occurrence matrix is a table whose entries record the frequency or weight with which pairs of items occur together within specified contexts.
dimensionality reductionuses · Dimensionality reduction is the transformation of data into a representation with fewer dimensions while retaining selected information, structure, or relationships.
truncated singular value decompositionincludes · Truncated singular value decomposition is a matrix factorization technique that approximates a matrix using a selected number of singular components.
compressionuses · Compression is the transformation of information into a more compact representation to reduce storage or transmission requirements while retaining information needed for recovery or use.
This explainer was generated by Manning's knowledge graph from the text of Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI. The section links point to the parts of the book it draws on.
