Abstract
Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.
Highlights
Cluster analysis has been studied over the past fifty years in the machine learning community and is one of the central topics in unsupervised learning with a wide range of possible research directions and application fields, including image segmentation, document clustering, and bioinformatics [1]
We have considered various orthogonal nonnegative matrix factorization (ONMF) models, together with different optimization approaches for clustering hyperspectral data, as the main application field
We have introduced total variation regularization in the proposed Orthogonal Nonnegative Matrix Factorization (ONMF) models to ensure spatial coherence in the obtained clusterings constituting the main innovation in this paper motivated by numerous spectral imaging applications, which naturally satisfy the spatial coherence in the data
Summary
Cluster analysis has been studied over the past fifty years in the machine learning community and is one of the central topics in unsupervised learning with a wide range of possible research directions and application fields, including image segmentation, document clustering, and bioinformatics [1]. Different from the widely used Principal Component Analysis (PCA), which is based on the singular value decomposition and allows for computation of a best rank K approximation of a given arbitrary matrix, the NMF constrains the matrix factors to be nonnegative. This property makes the NMF the method of choice where the considered data naturally fulfills a nonnegativity constraint so that the interpretability of the factor matrices is ensured. Possible application fields are hyperspectral unmixing [30,31,32], document clustering [8,39], and music analysis [40] and medical imaging problems, such as dynamic computed tomography, to perform a joint reconstruction and low-rank decomposition of the corresponding dynamic inverse problem [41], or Matrix-Assisted Laser Desorption/Ionization (MALDI) imaging, where it can be used for tumor typing in the field of bioinformatics as a supervised classification method [42]
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