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An Improved Self-Representation Approach for Missing Value Imputation

Recovering missing values (MVs) from incomplete data is an important problem for many real-world applications. In this work, we propose a novel MVs imputation method by combing sample self-representation strategy and underlying local structure of data in a uniformed framework. Specifically, the proposed method firstly obtain the first-round estimation of MVs using an existing method. Then, a graph, characterizing local proximity structure of data, is constructed. Next, a novel model coined as graph regularized local self-representation (GRLSR) is proposed by integrating two crucial elements: local self-representation and graph regularization. The former assumes each sample can be well represented (reconstructed) by linearly combining the neighboring samples while the latter further requires the neighboring samples should not deviate too much from each other after reconstruction. By doing so, MVs can be more accurately restored due to the joint imputation as well as local linear reconstruction. We also develop an effective alternating optimization algorithm in order to solve GRLSR model, thereby achieving final imputation. Experimental results on a real-world road network traffic flow data and several UCI benchmark datasets demonstrate the effectiveness of our proposed method.