Non-negative matrix factorization (NMF) has been one of the most popular methods for feature learning in the field of machine learning and computer vision. Most existing works directly apply NMF on high-dimensional image datasets for computing the effective representation of the raw images. However, in fact, the common essential information of a given class of images is hidden in their low rank parts. For obtaining an effective low-rank data representation, we in this paper propose a non-negative low-rank matrix factorization (NLMF) method for image clustering. For the purpose of improving its robustness for the data in a manifold structure, we further propose a graph regularized NLMF by incorporating the manifold structure information into our proposed objective function. Finally, we develop an efficient alternating iterative algorithm to learn the low-dimensional representation of low-rank parts of images for clustering. Alternatively, we also incorporate robust principal component analysis into our proposed scheme. Experimental results on four image datasets reveal that our proposed methods outperform four representative methods.
Nonnegative matrix factorization (NMF) is one widely used feature extraction technology in the tasks of image clustering and image classification. For the former task, various unsupervised NMF methods based on the data distribution structure information have been proposed. While for the latter task, the label information of the dataset is one very important guiding. However, most previous proposed supervised NMF methods emphasis on imposing the discriminant constraints on the coefficient matrix. When dealing with new coming samples, the transpose or the pseudoinverse of the basis matrix is used to project these samples to the low dimension space. In this way, the label influence to the basis matrix is indirect. Although, there are also some methods trying to constrain the basis matrix in NMF framework, either they only restrict within-class samples or impose improper constraint on the basis matrix. To address these problems, in this article a novel NMF framework named discriminative and orthogonal subspace constraints-based nonnegative matrix factorization (DOSNMF) is proposed. In DOSNMF, the discriminative constraints are imposed on the projected subspace instead of the directly learned representation. In this manner, the discriminative information is directly connected with the projected subspace. At the same time, an orthogonal term is incorporated in DOSNMF to adjust the orthogonality of the learned basis matrix, which can ensure the orthogonality of the learned subspace and improve the sparseness of the basis matrix at the same time. This framework can be implemented in two ways. The first way is based on the manifold learning theory. In this way, two graphs, i.e., the intrinsic graph and the penalty graph, are constructed to capture the intra-class structure and the inter-class distinctness. With this design, both the manifold structure information and the discriminative information of the dataset are utilized. For convenience, we name this method as the name of the framework, i.e., DOSNMF. The second way is based on the Fisher’s criterion, we name it Fisher’s criterion-based DOSNMF (FDOSNMF). The objective functions of DOSNMF and FDOSNMF can be easily optimized using multiplicative update (MU) rules. The new methods are tested on five datasets and compared with several supervised and unsupervised variants of NMF. The experimental results reveal the effectiveness of the proposed methods.
Post-transcriptional regulators, microRNAs (miRNAs), are involved in the occurrence and progression of various diseases. However, due to the complexity of disease-related miRNA regulatory networks, the typing and identification of miRNAs have remained challenging. Herein, a linear ladder-like DNA nanoarchitecture (LDN) was constructed to promote the movement efficiency of the tripedal DNA walker (T-walker), which was combined with the DNA-based logic gates and the PTCDA@PDA/CdS/WO3 photoelectrode to develop a novel biosensor for the detection of dual-miRNAs. Two miRNAs, miR-122 and miR-21, were used as targets to operate the logic module, while its output, trigger strands (TSs), initiated a catalytic hairpin assembly (CHA) reaction to form a T-walker. By using LDN as the track, the T-walker efficiently unfolded hairpin 4, which further hybridized with the alkaline phosphatase-modified hairpin 5 (AP-H5). The remaining AP can catalyze the ascorbic acid 2-phosphate (AAP) into ascorbic acid (AA), an ideal electron donor, thus resulting in a photocurrent change. The photocurrent signals of both AND and OR gates displayed a linear relationship with the logarithm of dual-miRNA concentrations with detection limits of 10.1 and 13.6 fM, respectively. Moreover, the intelligent and rational design of DNA tracks gives impetus to create a well-organized sensing interface with wide application in clinical diagnosis and cancer monitoring.
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