Sliced Inverse Regression With Adaptive Spectral Sparsity for Dimension Reduction
针对切片逆回归计算复杂度高和投影子空间稀疏性不足的问题，提出在谱空间计算投影向量并用自适应Lasso获得稀疏解，同时设计基于相关熵的类回归模型用于鲁棒分类，在真实高维数据上取得竞争结果。
Dimension reduction is an important topic in pattern analysis and machine learning, and it has wide applications in feature representation and pattern classification. In the past two decades, sliced inverse regression (SIR) has attracted much research efforts due to its effectiveness and efficacy in dimension reduction. However, two drawbacks limit further applications of SIR. First, the computation complexity of SIR is usually high in the situation of high-dimensional data. Second, sparsity of projection subspace is not well mined for improving the feature selection and model interpretation abilities. This paper proposes to compute the SIR projection vectors in the spectral space, then an approximated regression solution can be obtained with a faster speed. Moreover, the adaptive lasso is used to attain a sparse and globally optimal solution, which is important in variable selection. To complete the robust pattern classification task with corruptions, a correntropy-based and class-wise regression model is designed in this paper. It takes a smooth penalty instead of sparsity constraint in the regression coefficients, and it can be conducted in class-wise, thus it is more flexible in practice. Extensive experiments are conducted by using some real and benchmark data sets, e.g., high-dimensional facial images and gene microarray data, to evaluate the new algorithms. The new proposals attain competitive results and are compared with other state-of-the-art methods.