Lijun Zhang

The goal of feature selection is to identify the most informative features for compact representation, whereas the goal of active learning is to select the most informative instances for prediction. Previous studies separately address these two problems, despite of the fact that selecting features and instances are dual operations over a data matrix. In this paper, we consider the novel problem of simultaneously selecting the most informative features and instances and develop a solution from the perspective of optimum experimental design. That is, by using the selected features as the new representation and the selected instances as training data, the variance of the parameter estimate of a learning function can be minimized. Specifically, we propose a novel approach, which is called Unified criterion for Feature and Instance selection (UFI), to simultaneously identify the most informative features and instances that minimize the trace of the parameter covariance matrix. A greedy algorithm is introduced to efficiently solve the optimization problem. Experimental results on two benchmark data sets demonstrate the effectiveness of our proposed method.

Different from traditional one-sided clustering techniques, coclustering makes use of the duality between samples and features to partition them simultaneously. Most of the existing co-clustering algorithms focus on modeling the relationship between samples and features, whereas the intersample and interfeature relationships are ignored. In this paper, we propose a novel coclustering algorithm named Locally Discriminative Coclustering (LDCC) to explore the relationship between samples and features as well as the intersample and interfeature relationships. Specifically, the sample-feature relationship is modeled by a bipartite graph between samples and features. And we apply local linear regression to discovering the intrinsic discriminative structures of both sample space and feature space. For each local patch in the sample and feature spaces, a local linear function is estimated to predict the labels of the points in this patch. The intersample and interfeature relationships are thus captured by minimizing the fitting errors of all the local linear functions. In this way, LDCC groups strongly associated samples and features together, while respecting the local structures of both sample and feature spaces. Our experimental results on several benchmark data sets have demonstrated the effectiveness of the proposed method.