Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering
This work addresses clustering of 2D data for applications where spatial information is crucial, representing an incremental improvement over existing methods.
The paper tackles the problem of clustering 2D data by proposing TS-NMF, a semi-nonnegative matrix factorization method that retains spatial information and integrates manifold learning, achieving effectiveness verified through comprehensive experiments against state-of-the-art algorithms.
In this paper, we propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step. In particular, projection matrices are sought under the guidance of building new data representations, such that the spatial information is retained and projections are enhanced by the goal of clustering, which helps construct optimal projection directions. Moreover, to exploit nonlinear structures of the data, manifold is constructed in the projected subspace, which is adaptively updated according to the projections and less afflicted with noise and outliers of the data and thus more representative in the projected space. Hence, seeking projections, building new data representations, and learning manifold are seamlessly integrated in a single model, which mutually enhance other and lead to a powerful data representation. Comprehensive experimental results verify the effectiveness of TS-NMF in comparison with several state-of-the-art algorithms, which suggests high potential of the proposed method for real world applications.