Title: Mutual Kernel Matrix Completion,
Abstract: With the huge influx of various data nowadays, extracting knowledge from them
has become an interesting but tedious task among data scientists, particularly
when the data come in heterogeneous form and have missing information. Many
data completion techniques had been introduced, especially in the advent of
kernel methods. However, among the many data completion techniques available in
the literature, studies about mutually completing several incomplete kernel
matrices have not been given much attention yet. In this paper, we present a
new method, called Mutual Kernel Matrix Completion (MKMC) algorithm, that
tackles this problem of mutually inferring the missing entries of multiple
kernel matrices by combining the notions of data fusion and kernel matrix
completion, applied on biological data sets to be used for classification task.
We first introduced an objective function that will be minimized by exploiting
the EM algorithm, which in turn results to an estimate of the missing entries
of the kernel matrices involved. The completed kernel matrices are then
combined to produce a model matrix that can be used to further improve the
obtained estimates. An interesting result of our study is that the E-step and
the M-step are given in closed form, which makes our algorithm efficient in
terms of time and memory. After completion, the (completed) kernel matrices are
then used to train an SVM classifier to test how well the relationships among
the entries are preserved. Our empirical results show that the proposed
algorithm bested the traditional completion techniques in preserving the
relationships among the data points, and in accurately recovering the missing
kernel matrix entries. By far, MKMC offers a promising solution to the problem
of mutual estimation of a number of relevant incomplete kernel matrices.