| Summary: | In this paper, we model the unsupervised learning of a sequence of observed data vector as a problem of extracting joint patterns among random variables. In particular, we formulate an information-theoretic problem to extract common features of random variables by measuring the loss of total correlation given the feature. This problem can be solved by a local geometric approach, where the solutions can be represented as singular vectors of some matrices related to the pairwise distributions of the data. In addition, we illustrate how these solutions can be transferred to feature functions in machine learning, which can be computed by efficient algorithms from data vectors. Moreover, we present a generalization of the HGR maximal correlation based on these feature functions, which can be viewed as a nonlinear generalization to linear PCA. Finally, the simulation result shows that our extracted feature functions have great performance in real-world problems.
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