Unified View Imputation and Feature Selection Learning for Incomplete
  Multi-view Data
Yanyong Huang Zongxin Shen Tianrui Li Fengmao Lv
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.