Shanshan Qin

Haiyan Jiang, Shanshan Qin, Oscar Hernan Madrid Padilla

In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated regularization with naturally adjustable sparsity and grouping effects, and propose the Feature Grouping and Sparse Principal Component Analysis (FGSPCA). The proposed FGSPCA method encourages the factor loadings with similar values to collapse into disjoint homogeneous groups for feature grouping or into a special zero-valued group for feature selection, which in turn helps reducing model complexity and increasing model interpretation. Usually, existing structured PCA methods require prior knowledge to construct the regularization term. However, the proposed FGSPCA can simultaneously capture the grouping and/or sparse structures of factor loadings without any prior information. To solve the resulting non-convex optimization problem, we propose an alternating algorithm that incorporates the difference-of-convex programming, augmented Lagrange method and coordinate descent method. Experimental results demonstrate the promising performance and efficiency of the new method on both synthetic and real-world datasets. An R implementation of FGSPCA can be found on github {https://github.com/higeeks/FGSPCA}.

Shanshan Qin, Nayantara Mudur, Cengiz Pehlevan

We propose a novel biologically-plausible solution to the credit assignment problem motivated by observations in the ventral visual pathway and trained deep neural networks. In both, representations of objects in the same category become progressively more similar, while objects belonging to different categories become less similar. We use this observation to motivate a layer-specific learning goal in a deep network: each layer aims to learn a representational similarity matrix that interpolates between previous and later layers. We formulate this idea using a contrastive similarity matching objective function and derive from it deep neural networks with feedforward, lateral, and feedback connections, and neurons that exhibit biologically-plausible Hebbian and anti-Hebbian plasticity. Contrastive similarity matching can be interpreted as an energy-based learning algorithm, but with significant differences from others in how a contrastive function is constructed.