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convex non-negative matrix factorization

Convex non-negative matrix factorization is a matrix decomposition technique in which a dataset is approximated as the product of lower-rank factor matrices, with the specific constraint that the learned basis vectors are represented as convex combinations of the original data points. Unlike standard non-negative matrix factorization, which requires non-negative input data and discovers unconstrained abstract components, convex non-negative matrix factorization restricts each basis vector to lie within the convex hull of the observations while keeping the encoding coefficients non-negative. This formulation ensures that the derived components can be interpreted directly as weighted averages of real sample points, allows the method to process data containing both positive and negative values, and facilitates nonlinear kernel extensions for clustering and dimensionality reduction.

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