Our two papers will be presented in The 18th IEEE International Conference on Data Mining (ICDM 2016), Barcelona, Spain, Dec 12-15 2016.
Title: Heterogeneous Representation Learning with Structured Sparsity Regularization
Authors: Pei Yang, Jingrui He
Abstract: Motivated by real applications, heterogeneous learning has emerged as an important research area, which aims to model the co-existence of multiple types of heterogeneity. In this paper, we propose a HEterogeneous REpresentation learning model with structured Sparsity regularization (HERES) to learn from multiple types of heterogeneity. HERES aims to leverage two kinds of information to build a robust learning system. One is the rich correlations among heterogeneous data such as task relatedness, view consistency, and label correlation. The other is the prior knowledge of the data in the form of, e.g., the soft-clustering of the tasks. HERES is a generic framework for heterogeneous learning, which integrates multi-task, multi-view, and multi-label learning into a principled framework based on representation learning. The objective of HERES is to minimize the reconstruction loss of using the factor matrices to recover the input matrix for heterogeneous data, regularized by the structured sparsity constraint. The resulting optimization problem is challenging due to the non-smoothness and non-separability of structured sparsity. We develop an iterative updating method to solve the problem. Furthermore, we prove that the reformulation of structured sparsity is separable, which leads to a family of efficient and scalable algorithms for solving structured sparsity penalized problems. The experimental results in comparison with state-of-the-art methods demonstrate the effectiveness of the proposed approach.
Title: Functional Regression with Mode-Sparsity Constraint
Authors: Pei Yang, Jingrui He
Abstract: Functional data is ubiquitous in many domains such as healthcare, social media, manufacturing process, sensor networks, etc. Functional data analysis involves the analysis of data which is treated as infinite-dimensional continuous functions rather than discrete, finite-dimensional vectors. In this paper, we propose a novel function-on-function regression model based on mode-sparsity regularization. The main idea is to represent the regression coefficient function between predictor and response as the double expansion of basis functions, and then use mode-sparsity constraint to automatically filter out the irrelevant basis functions for both predictors and responses. The mode-sparsity regularization covers a wide spectrum of sparse models for function-on-function regression. The resulting optimization problem is challenging due to the non-smooth property of the mode-sparsity. We develop an efficient and convergence-guaranteed algorithm to solve the problem. The effectiveness of the proposed approach is verified on benchmark functional data sets in various domains.
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