Unified View Imputation and Feature Selection Learning for Incomplete Multi-view Data

Although multi-view unsupervised feature selection (MUFS) is an effective technology for reducing dimensionality in machine learning, existing methods cannot directly deal with incomplete multi-view data where some samples are missing in certain views. These methods should first apply predetermined values to impute missing data, then perform feature selection on the complete dataset. Separating imputation and feature selection processes fails to capitalize on the potential synergy where local structural information gleaned from feature selection could guide the imputation, thereby improving the feature selection performance in turn. Additionally, previous methods only focus on leveraging samples' local structure information, while ignoring the intrinsic locality of the feature space. To tackle these problems, a novel MUFS method, called UNified view Imputation and Feature selectIon lEaRning (UNIFIER), is proposed. UNIFIER explores the local structure of multi-view data by adaptively learning similarity-induced graphs from both the sample and feature spaces. Then, UNIFIER dynamically recovers the missing views, guided by the sample and feature similarity graphs during the feature selection procedure. Furthermore, the half-quadratic minimization technique is used to automatically weight different instances, alleviating the impact of outliers and unreliable restored data. Comprehensive experimental results demonstrate that UNIFIER outperforms other state-of-the-art methods.