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Vectorial Dimension Reduction for Tensors Based on Bayesian Inference
Jul 03, 2017
Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order structures or resulting in undesired tensors, respectively. This paper introduces a probabilistic vectorial dimensionality reduction model for tensorial data. The model represents a tensor by employing a linear combination of same order basis tensors, thus it offers a mechanism to directly reduce a tensor to a vector. Under this expression, the projection base of the model is based on the tensor CandeComp/PARAFAC (CP) decomposition and the number of free parameters in the model only grows linearly with the number of modes rather than exponentially. A Bayesian inference has been established via the variational EM approach. A criterion to set the parameters (factor number of CP decomposition and the number of extracted features) is empirically given. The model outperforms several existing PCA-based methods and CP decomposition on several publicly available databases in terms of classification and clustering accuracy.
Mixture of Bilateral-Projection Two-dimensional Probabilistic Principal Component Analysis
Jan 07, 2016
The probabilistic principal component analysis (PPCA) is built upon a global linear mapping, with which it is insufficient to model complex data variation. This paper proposes a mixture of bilateral-projection probabilistic principal component analysis model (mixB2DPPCA) on 2D data. With multi-components in the mixture, this model can be seen as a soft cluster algorithm and has capability of modeling data with complex structures. A Bayesian inference scheme has been proposed based on the variational EM (Expectation-Maximization) approach for learning model parameters. Experiments on some publicly available databases show that the performance of mixB2DPPCA has been largely improved, resulting in more accurate reconstruction errors and recognition rates than the existing PCA-based algorithms.