A Fast Algorithm for Sparse Nonlinear Component Analysis by Sublinear and Spectral Changes – In this paper, we propose a Bayesian method for learning a non-Gaussian vector to efficiently update the posterior of multiple unknown variables. We formulate the process of learning a non-Gaussian vector as a matrix multiplication problem, and define the covariance matrix that is to be transformed to the covariance matrix in the prior for each data point. We derive a generalization error bound for matrix multiplication under non-Gaussian conditions for each unknown parameter. Our method is a hybrid of these two approaches.

The problem of recovering a single vector of a given point from a tensor of vectors is commonly encountered in data mining. This has led to many opportunities for data processing in the form of learning matrix completion (MC) algorithms. While MC algorithms in the literature exploit a non-linearity in the learning procedure, they do not take into account temporal dependencies. Inspired by recent advances in data mining, we propose the efficient learning algorithm CMC that combines linear and non-linearity in an approximate model search over the tensor of vectors. Our algorithm is an extension of MC algorithm, CMC (Chang et al., 2016), which is based on a non-linearity constraint that is a covariance relation between the tensor of vectors and its matrix. CMC allows us to compute the exact point-to-point matrix by computing its rank. Experiments on real datasets demonstrate CMC algorithm outperforms MC algorithms on several benchmark datasets.

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# A Fast Algorithm for Sparse Nonlinear Component Analysis by Sublinear and Spectral Changes

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Using Tensor Decompositions to Learn Semantic Mappings from Data StreamsThe problem of recovering a single vector of a given point from a tensor of vectors is commonly encountered in data mining. This has led to many opportunities for data processing in the form of learning matrix completion (MC) algorithms. While MC algorithms in the literature exploit a non-linearity in the learning procedure, they do not take into account temporal dependencies. Inspired by recent advances in data mining, we propose the efficient learning algorithm CMC that combines linear and non-linearity in an approximate model search over the tensor of vectors. Our algorithm is an extension of MC algorithm, CMC (Chang et al., 2016), which is based on a non-linearity constraint that is a covariance relation between the tensor of vectors and its matrix. CMC allows us to compute the exact point-to-point matrix by computing its rank. Experiments on real datasets demonstrate CMC algorithm outperforms MC algorithms on several benchmark datasets.