Linzhang Lu

Non-negative Tucker decomposition (NTD) is one of the general and prominent decomposition tools designed for high-order tensor data, with its advantages reflected in feature extraction and low-dimensional representation of data. Most NTD-based methods only apply intrinsic and different constraints to the last factor matrix that is a low-dimensional representation of the original tensor information. This processing procedure may result in the loss of the relationship between the factor matrices in all dimensions. To enhance the representation ability of NTD, we propose a consistent regularized non-negative Tucker decomposition for three-dimensional tensor data representation. Consistent regularization is symmetrically presented and mathematically expressed by intrinsic cues in multiple dimensions, that is, manifold structure and orthogonality information. The paired constraint constructed by the double parameter operator is utilized to unlock hidden semantics and maintain the consistent geometric structure of the three-dimensional tensor. Moreover, we develop the iterative updating method based on the multiplicative update rule to solve the proposed model and provide its convergence and computational complexity. The extensive numerical results of unsupervised image clustering experiments on eight real-world datasets demonstrated the feasibility and efficiency of the new method.

The Nonnegative Matrix Factorization (NMF) algorithm and its variants have gained widespread popularity across various domains, including neural networks, text clustering, image processing, and signal analysis. In the context of hyperspectral unmixing (HU), an important task involving the accurate extraction of endmembers from mixed spectra, researchers have been actively exploring different regularization techniques within the traditional NMF framework. These techniques aim to improve the precision and reliability of the endmember extraction process in HU. In this study, we propose a novel HU algorithm called KMBNMF, which introduces an average kurtosis regularization term based on endmember spectra to enhance endmember extraction, additionally, it integrates a manifold regularization term into the average kurtosis-constrained NMF by constructing a symmetric weight matrix. This combination of these two regularization techniques not only optimizes the extraction process of independent endmembers but also improves the part-based representation capability of hyperspectral data. Experimental results obtained from simulated and real-world hyperspectral datasets demonstrate the competitive performance of the proposed KMBNMF algorithm when compared to state-of-the-art algorithms.