关键词: 多线性回归, 正则化, 张量, 特征选择, LASSO

Abstract:

As one of the conventional regression algorithms, LASSO (least absolute shrinkage and selection operator) algorithm is mostly employed to analyze the vectorized dataset. However, the vectorization of a dataset may undermine the original structure and inner relations of the dataset and hide the high-order dependencies. Further, it also increases the data dimensionality as well as time and space complexity. This paper proposes a tensor-based regularized multilinear regression algorithm, named multilinear LASSO (mLASSO), by reformulating the LASSO algorithm for tensor space. The proposed algorithm firstly decomposes tensor space to vector space by applying mode production and employing weighted vectors. Then, the algorithm iteratively uses LASSO to update the weighted vectors for converging the proposed model. Finally, the optimum weighted vectors are applied to all direction in the tensor space in order to generate the regression model. The contribution of this paper is twofold: (1) The algorithm employs the whole structural information of the dataset for generating a regression model. (2) Since the proposed algorithm employs LASSO, it can significantly improve the performance of the generated model by using embedded feature selection. Experimental studies confirm that the proposed algorithm achieves satisfactory performance on the multilinear data.

Key words: multilinear regression, regularized, tensor, feature selection, LASSO