Hyperspectral unmixing (HU) is a crucial method for interpreting remotely sensed hyperspectral images (HSIs), with the aim of splitting the image into pure spectral components (endmembers) and their abundance fractions in every pixel of the scene. However, the effectiveness of this procedure is hindered by the presence of noise and anomalies. These kind of disruptions mainly arise from real-world factors such as atmospheric effects and endmember variability. To address this challenge, a novel approach called Graph-Regularized Oblique Projection Weighted NMF (GOP-WNMF) is introduced, which is grounded in a more precise separation of signal and noise subspaces, aiming to enhance the accuracy and robustness of the analysis. GOP-WNMF achieves this by constructing an oblique projector that projects each pixel onto the signal subspace, i.e., the space formed by signatures of endmembers, and parallel to the noise subspace. This approach effectively suppresses noise while preserving crucial spectral information. Furthermore, our new oblique NMF framework includes a unique residual-based weighting approach to detect and remove anomalies in pixels and spectral bands simultaneously. In addition to this, another weighting matrix is proposed by establishing a bipartite graph connecting endmembers and pixels to promote smoothness and sparsity in the resulting abundance maps. GOP-WNMF also enhances abundance map estimation accuracy by mitigating the negative effects of pixel outliers through the utilization of Laplacian eigenmaps technique to maintain the manifold structure of data. The effectiveness of GOP-WNMF is evaluated through comprehensive testing on synthetic and real HSIs, and its superiority is demonstrated over multiple state-of-the-art approaches. The source code is also available at https://github.com/yasinhashemi/GOP-WNMF .

Despite its effectiveness, spectral clustering is often impractical for large-scale data due to its high computational complexity$(O(n^{2}))$and limited clustering quality arising from three fundamental limitations: (1) reliance on a fixed similarity graph that cannot adapt to complex local structures, (2) inability to capture higher-order relationships, and (3) a decoupled two-step pipeline that separates embedding and clustering. To address these issues, we propose OA2H-SP, a novel framework that achieves linear-time spectral clustering$(O(nm)$with$m\ll n)$while enhancing clustering accuracy and scalability. Our method constructs an anchor-adaptive hypergraph to model both adaptive and higher-order affinities efficiently. It further unifies representation learning and discrete clustering in a one-step optimization scheme, avoiding the need for k-means post-processing. Extensive experiments on benchmark datasets demonstrate that$\text{OA}^{2}\mathrm{H}$. SP delivers superior performance in terms of accuracy, robustness, and runtime compared to existing hypergraph-based and anchor-driven spectral clustering methods.

Abstract Hyperspectral unmixing (HU) involves separating mixed pixel spectra into pure endmember spectra and their corresponding abundance fractions. However, it faces significant challenges due to outliers in the hyperspectral data, which often appear as pixel and band anomalies. Outliers in pixels could result in incorrect classification and inaccurate quantification of materials, while outliers in bands could alter spectral characteristics, leading to misidentifying endmembers and incorrect estimates of abundance. To tackle these issues, this paper introduces a new approach, named simultaneous outlier detection and elimination via weighted non-negative matrix tri-factorization (SODE-WNMTF), which offers an efficient means of addressing the impact of outliers in the unmixing process. Leveraging the co-clustering property of NMTF, SODE-WNMTF introduces a novel weighting matrix, which involves simultaneous clustering of both pixels and spectral bands to effectively detect and mitigate the negative impact of both pixel and band outliers during the unmixing process. At the same time, the inherent structure of the hyperspectral image (HSI) is utilized through the examination of local and global connections among pixels and spectral bands, consequently improving the co-clustering procedure. In addition, SODE-WNMTF proposes a spatial weighting factor, which utilizes the similarity of adjacent pixels, to promote piecewise smoothness in abundance maps while mitigating the impact of outliers. Moreover, since pixels in regions dominated by a single endmember exhibit spectra closely resembling that endmember, SODE-WNMTF incorporates a sparse estimation technique for endmember signatures. Finally, to verify the performance of SODE-WNMTF, a series of experiments is conducted on both synthetic and real HSIs, with outcomes proving its superiority against other cutting-edge approaches. The source code is also available at https://github.com/yasinhashemi/SODE-WNMTF .

Subspace distance is an invaluable tool exploited in a wide range of feature selection methods. The power of subspace distance is that it can identify a representative subspace, including a group of features that can efficiently approximate the space of original features. On the other hand, employing intrinsic statistical information of data can play a significant role in a feature selection process. Nevertheless, most of the existing feature selection methods founded on the subspace distance are limited in properly fulfilling this objective. To pursue this void, we propose a framework that takes a subspace distance into account which is called "Variance-Covariance subspace distance". The approach gains advantages from the correlation of information included in the features of data, thus determines all the feature subsets whose corresponding Variance-Covariance matrix has the minimum norm property. Consequently, a novel, yet efficient unsupervised feature selection framework is introduced based on the Variance-Covariance distance to handle both the dimensionality reduction and subspace learning tasks. The proposed framework has the ability to exclude those features that have the least variance from the original feature set. Moreover, an efficient update algorithm is provided along with its associated convergence analysis to solve the optimization side of the proposed approach. An extensive number of experiments on nine benchmark datasets are also conducted to assess the performance of our method from which the results demonstrate its superiority over a variety of state-of-the-art unsupervised feature selection methods. The source code is available at https://github.com/SaeedKarami/VCSDFS.

The extraction of predictive features from the complex high-dimensional multi-omic data is necessary for decoding and overcoming the therapeutic responses in systems pharmacology. Developing computational methods to reduce high-dimensional space of features in in vitro, in vivo and clinical data is essential to discover the evolution and mechanisms of the drug responses and drug resistance. In this paper, we have utilized the matrix factorization (MF) as a modality for high dimensionality reduction in systems pharmacology. In this respect, we have proposed three novel feature selection methods using the mathematical conception of a basis for features. We have applied these techniques as well as three other MF methods to analyze eight different gene expression datasets to investigate and compare their performance for feature selection. Our results show that these methods are capable of reducing the feature spaces and find predictive features in terms of phenotype determination. The three proposed techniques outperform the other methods used and can extract a 2-gene signature predictive of a tyrosine kinase inhibitor treatment response in the Cancer Cell Line Encyclopedia.

Gene expression data have become increasingly important in machine learning and computational biology over the past few years. In the field of gene expression analysis, several matrix factorization-based dimensionality reduction methods have been developed. However, such methods can still be improved in terms of efficiency and reliability. In this paper, an innovative approach to feature selection, called Dual Regularized Unsupervised Feature Selection Based on Matrix Factorization and Minimum Redundancy (DR-FS-MFMR), is introduced. The major focus of DR-FS-MFMR is to discard redundant features from the set of original features. In order to reach this target, the primary feature selection problem is defined in terms of two aspects: (1) the matrix factorization of data matrix in terms of the feature weight matrix and the representation matrix, and (2) the correlation information related to the selected features set. Then, the objective function is enriched by employing two data representation characteristics along with an inner product regularization criterion to perform both the redundancy minimization process and the sparsity task more precisely. To demonstrate the proficiency of the DR-FS-MFMR method, a large number of experimental studies are conducted on nine gene expression datasets. The obtained computational results indicate the efficiency and productivity of DR-FS-MFMR for the gene selection task.