Sparse Poisson coding for high dimensional document clustering

Chenxia Wu, Haiqin Yang, Jianke Zhu, Jiemi Zhang, Irwin King, Michael R. Lyu

Abstract: Document clustering plays an important role in large scale textual data analysis, which generally faces with great challenge of the high dimensional textual data. One remedy is to learn the high-level sparse representation by the sparse coding techniques. In contrast to traditional Gaussian noise-based sparse coding methods, in this paper, we employ a Poisson distribution model to represent the word-count frequency feature of a text for sparse coding. Moreover, a novel sparse-constrained Poisson regression algorithm is proposed to solve the induced optimization problem. Different from previous Poisson regression with the family of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularization to enhance the sparse solution, we introduce a sparsity ratio measure which make use of both ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm on the learned weight. An important advantage of the sparsity ratio is that it bounded in the range of 0 and 1. This makes it easy to set for practical applications. To further make the algorithm trackable for the high dimensional textual data, a projected gradient descent algorithm is proposed to solve the regression problem. Extensive experiments have been conducted to show that our proposed approach can achieve effective representation for document clustering compared with state-of-the-art regression methods.