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How is this significantly different than Principal Component Analysis (PCA)? The image processing examples essentially do what a Karhunen-Loeve Transform (KLT)
by waynecochran 8y ago
How is this significantly different than Principal Component Analysis (PCA)? The image processing examples essentially do what a Karhunen-Loeve Transform (KLT) does or a set of Eignenfaces.
- stabbles 8y agoWell... the nonnegative matrix factorization builds a basis for the column space where all entries of the basis vectors are positive. This might be meaningful if the entries are thought of as some positive quantity like weight or energy. In the SVD the basis vectors for the column space consist of entries that are not necessarily positive.
- currymj 8y agoYou can think of it as “PCA where all the principal component entries and loadings must be positive”. Harder optimization problem to solve though due to that constraint. The connection is especially clear when looking at the projected least squares algorithms for NMF — plain PCA minimizes the Euclidean reconstruction loss, while NMF algorithms alternates gradient descent steps to do that with projection steps to force everything positive.