Singular value
A singular value is a nonnegative scalar in a matrix’s singular value decomposition that measures stretching along a corresponding singular direction.
Data Without Labels
A singular value is a nonnegative diagonal value in a singular value decomposition that quantifies the magnitude of a corresponding matrix direction.
- How it is used
- Supports SVD-based dimensionality reduction and variance-based component selection.
- How deep it goes
- Defines singular values mathematically and demonstrates their NumPy computation, but defers mathematical proofs.
- Examples
- Demonstrates encoded and standardized mushroom data, a variance-explained bar plot, and an edible-versus-poisonous component scatter plot.
- What you can do after
- Apply it via NumPy to compute variance explained and visualize selected components after preparing tabular data.
Math and Architectures of Deep Learning
A nonnegative quantity from singular value decomposition that measures how much a matrix stretches along an orthogonal direction.
- How it is used
- Connects matrix decomposition to PCA, latent semantic analysis, and identifying meaningful versus weak data directions.
- How deep it goes
- Defines singular values through SVD and AᵀA, proves nonnegativity, and applies them computationally without developing a full geometric proof.
- Examples
- Uses a correlated three-term document dataset, computed singular values, and a small-value dimension removed from the LSA representation.
- What you can do after
- Apply singular values with PyTorch SVD to identify dominant directions and discard weak variation in a dataset.
Read how Math and Architectures of Deep Learning explains singular value →
Related concepts
- singular value decompositionproduced by · Singular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal or unitary matrices and a diagonal matrix of nonnegative singular values.
- S / ATA / A^T A / A A^Tequivalent to · Matrices used in diagonalization and singular-value computations, including the matrix of eigenvectors S and the Gram matrices A^T A and A A^T.
- matrix-matrix multiplicationequivalent to · Matrix multiplication combines compatible matrices to form a result whose entries are sums of products between rows of the first matrix and columns of the second.
- eigenvalueequivalent to · An eigenvalue is a scalar by which a linear transformation scales a corresponding nonzero eigenvector without changing its direction.
- standard deviationproduced by · Standard deviation is the nonnegative square root of variance and measures the typical dispersion of values around their mean in the original units.
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