Unsupervised Feature Learning via Sparse Hierarchical Representations [ 1 ]

Matrix factorization methods can be viewed as decomposing each input example as a linear combination of basis vectors. X = BS, where X 2 Rd⇥m, B 2 Rd⇥n, S 2 Rn⇥m, where d is the dimension of the data, m is the number of examples, and each column of X corresponds to an individual input example, n is the number of basis vectors, and each column of B corresponds to an individual basis vector. Therefore, each column of S represents “coe cients” of the basis vectors for each input example. Algorithms such as PCA can be viewed as matrix factorization methods. There are several variants of matrix factorization, such as sparse matrix factorization(e.g. assuming the entries of B and S are sparse), factor analysis, and probabilistic matrix factorization. Other notable matrix factorization methods include independent component analysis(ICA) and non-negative matrix factorization(NMF).