Rethinking k-means from manifold learning perspective
Quanxue Gao Qianqian Wang Han Lu Wei Xia Xinbo Gao
Although numerous clustering algorithms have been developed, many existing
methods still leverage k-means technique to detect clusters of data points.
However, the performance of k-means heavily depends on the estimation of
centers of clusters, which is very difficult to achieve an optimal solution.
Another major drawback is that it is sensitive to noise and outlier data. In
this paper, from manifold learning perspective, we rethink k-means and present
a new clustering algorithm which directly detects clusters of data without mean
estimation. Specifically, we construct distance matrix between data points by
Butterworth filter such that distance between any two data points in the same
clusters equals to a small constant, while increasing the distance between
other data pairs from different clusters. To well exploit the complementary
information embedded in different views, we leverage the tensor Schatten p-norm
regularization on the 3rd-order tensor which consists of indicator matrices of
different views. Finally, an efficient alternating algorithm is derived to
optimize our model. The constructed sequence was proved to converge to the
stationary KKT point. Extensive experimental results indicate the superiority
of our proposed method.