Weighted Sparse Partial Least Squares for Joint Sample and Feature
  Selection
Wenwen Min Taosheng Xu Chris Ding
Sparse Partial Least Squares (sPLS) is a common dimensionality reduction
technique for data fusion, which projects data samples from two views by
seeking linear combinations with a small number of variables with the maximum
variance. However, sPLS extracts the combinations between two data sets with
all data samples so that it cannot detect latent subsets of samples. To extend
the application of sPLS by identifying a specific subset of samples and remove
outliers, we propose an $\ell_\infty/\ell_0$-norm constrained weighted sparse
PLS ($\ell_\infty/\ell_0$-wsPLS) method for joint sample and feature selection,
where the $\ell_\infty/\ell_0$-norm constrains are used to select a subset of
samples. We prove that the $\ell_\infty/\ell_0$-norm constrains have the
Kurdyka-\L{ojasiewicz}~property so that a globally convergent algorithm is
developed to solve it. Moreover, multi-view data with a same set of samples can
be available in various real problems. To this end, we extend the
$\ell_\infty/\ell_0$-wsPLS model and propose two multi-view wsPLS models for
multi-view data fusion. We develop an efficient iterative algorithm for each
multi-view wsPLS model and show its convergence property. As well as numerical
and biomedical data experiments demonstrate the efficiency of the proposed
methods.