Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements.
nmf is a technique to approximate a matrix like V = WH. Here dimension of V,W,H can be respectively m*n, m*p, p*n where p << n usually. Now W can be thought as a weight matrix for hidden variables. As p can be very small this can also be viewed as a dimensionality reduction technique like pca.
nmf is widely applicable in most real world cases where V can't have negative values like image-recognition, text-classification, recommender system etc. General applications of nmf include:
- Feature learning like Principal Component Analysis
- Topic recovery like Probabilistic Latent Semantic Analysis
- Clustering like K-means
- Temporal Segmentation like Hidden Markov Model
- Filtering and source separation like Independent Component Analysis
For this tag users should provide mathematical clarity as it is an advanced topic along with information about application to specific case.
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