K-Means Matrix Factorization PDF
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This document discusses k-means as a matrix factorization technique, and its relation to non-negative matrix factorization. It includes mathematical formulas and concepts related to clustering and dimensionality reduction. The document focuses on the mathematical aspects of the algorithms, suitable for graduate studies.
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k-Means is a Matrix Factorization [Bauc16; DiHe05] -Means minimizes the squared errors of if point is assigned to center.➜ where where is an indicator matrix ( , exactly one 1 per column). A very strong constraint on the shape of ! In the image example: reduce the image to different rows/columns 21...
k-Means is a Matrix Factorization [Bauc16; DiHe05] -Means minimizes the squared errors of if point is assigned to center.➜ where where is an indicator matrix ( , exactly one 1 per column). A very strong constraint on the shape of ! In the image example: reduce the image to different rows/columns 21 From k-Means to Non-negative Matrix Factorization [Bauc16; DiHe05] Because the cluster centers of -means are the arithmetic mean of the assigned we have , use and we can rewrite , where If we now drop (most of) the constraints of -means, we obtain a variant of Non-negative Matrix Factorization (NMF): 22
