Incremental kernel non-negative matrix factorization for hyperspectral unmixing

Hyperspectral unmixing is one of the most important procedures for remote sensing image processing. The non-negative matrix factorization (NMF)-based method has been widely used for hyperspectral unmixing since it can get endmember and abundance matrices simultaneously. However, the inherent single-decomposition structure of NMF may not achieve good performance for highly mixed data. To solve this issue, we propose a spectral and spatial total-variation-regularized multilayer non-negative matrix factorization (SSTV-MLNMF) for hyperspectral unmixing. In SSTV-MLNMF, we designed an effective multilayer factorization process and combined spectral and spatial total variation as extra regularization. These could enhance the smoothness for spectral signatures and spatial fields, which could achieve better performance. Experiments on both synthetic and real datasets have validated the effectiveness of our method and have shown that it has outperformed several state-of-the-art approaches of hyperspectral unmixing.

Non-negative matrix factorization (NNMF) technique has been widely applicable for dimension reduction. NNMF has shown its usability to solve numerous challenges in areas such as signal processing, image classification, and text mining. Existing matrix factorization methods need a predefined value of rank of a base matrix. Our primary intention in this article is to automatically identify the optimum value of the rank to factorize the matrix. Here we propose an Incremental Cauchy NonNegative Matrix factorization (ICNNMF) which automatically finds the optimum rank and separates the overlapping sounds received from a single channel of a source. Classification is performed using an ensemble of one class fuzzy rule-based (FRB) classifiers. We evaluated the proposed method over the real data set, and the proposed model has shown better accuracy as compared to the traditional classifier. Moreover, the proposed matrix factorization method automatically determines the optimal value of the rank and adapt to new data.

In this paper, we extend the original non-negative matrix factorization (NMF) to kernel NMF (KNMF). The advantages of KNMF over NMF are: 1) it could extract more useful features hidden in the original data through some kernel-induced nonlinear mappings; 2) it can deal with data where only relationships (similarities or dissimilarities) between objects are known; 3) it can process data with negative values by using some specific kernel functions (e.g. Gaussian). Thus, KNMF is more general than NMF. To further improve the performance of KNMF, we also propose the SpKNMF, which performs KNMF on sub-patterns of the original data. The effectiveness of the proposed algorithms is validated by extensive experiments on UCI datasets and the FERET face database.

Incremental semi-supervised graph learning NMF with block-diagonal

Nonnegative matrix factorization with combined kernels for small data representation

In this paper, a novel multiple kernel learning (MKL) algorithm is proposed for the classification of hyperspectral images. The proposed MKL algorithm adopts a two-step strategy to learn a multiple kernel machine. In the first step, unsupervised learning is carried out to learn a combined kernel from the predefined base kernels. In our algorithms, low-rank nonnegative matrix factorization (NMF) is used to carry out the unsupervised learning and learn an optimal combined kernel. Furthermore, the kernel NMF (KNMF) is introduced to substitute NMF for enhancing the ability of the unsupervised learning with the predefined base kernels. In the second step, the optimal kernel is embedded into the standard optimization routine of support vector machine (SVM). In addition, we address a major challenge in hyperspectral data classification, i.e., using very few labeled samples in a high-dimensional space. Experiments are conducted on three real hyperspectral datasets, and the experimental results show that the proposed algorithms, especially for KNMF-based MKL, achieve the outstanding performance for hyperspectral image classification with few labeled samples when compared with several state-of-the-art algorithms.

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims to estimate a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. Nonnegative matrix factorization (NMF) and its various robust extensions have been widely applied to HU. Most existing robust NMF methods consider that noises only exist in one kind of formulation. However, the hyperspectral images (HSIs) are unavoidably corrupted by noisy bands and noisy pixels simultaneously in the real applications. This paper proposes a novel spectral-spatial robust NMF model by incorporating 12,1 norm and 11,2 norm, which achieves robustness to band noise and pixel noise simultaneously. The Huber's M-estimator is integrated into the proposed model to achieve better assignations of weights for each pixel and band with various noise intensities, which avoids the singularity problem and effectively improves the unmixing performance. The elegant updating rules of the proposed spectral-spatial robust model are also efficiently learned and provided. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate the effectiveness of the proposed methods in unmixing performance.

Hyperspectral unmixing is an important image interpre-tation technique that aims to estimate the pure constituent materials (endmembers) and their corresponding fractional abundances in each mixed pixel. Nonnegative matrix factorization (NMF) has attracted a lot of attention because of its ability to solve mixed pixel scenarios. The sparse NMF method achieves better unmixing results thanks to its full use of the sparse characteristics of the data. However, most existing sparse NMF unmixing techniques lack the consid-eration of spatial information. In fact, hyperspectral images contain intrinsic geometric information as well as rich spatial information. In this paper, a spatial graph regularized nonneg-ative matrix factorization unmixing framework (SGNMF) is established. For the proposed SGNMF, on the one hand, the graph regularization is introduced to characterize the latent manifold structure of the data, and on the other hand, the spatial weighting factor is used to mine the spatial correlation between pixels. The optimization problem of the SGNMF model can be solved by a multiplicative iterative rule. Exper-imental results on synthetic data sets indicate that the newly proposed SGNMF method is able to produce better results than other advanced spectral unmixing algorithms.

This paper attempts to represent the mapped data in the radial basis function (RBF) feature space under non-negativity constraints and develops a RBF kernel based non-negative matrix factorization (KNMF-RBF) algorithm. Based on an objective function with Frobenius norm, we obtain the multiplicative update rules of our KNMF-RBF approach using kernel theory and gradient descent method. The proposed KNMF-RBF method is theoretically shown to be convergence by means of the constructed auxiliary function. Our approach is successfully applied to face recognition in the FERET face database. Experimental results demonstrate that the proposed KNMF-RBF method surpasses some kernel based methods. The results are encouraging.

Foreground detection is widely used in many applications of computer vision and artificial intelligence. In this paper, a novel online algorithm of detecting moving objects in complex scenes is proposed based on incremental nonnegative matrix factorization (INMF). In this algorithm, a new video frame is modeled as a linear combination of basis vectors of background subspace, plus a sparse term which denotes the foreground. In order to take advantage of nonnegative matrix factorization methods, the nonnegative constraints are applied on the update for the coefficient vector and background subspace. Traditionally in many algorithms, the foreground is considered as a pixel-wise sparse term although actually it is structured sparse. So in this paper structured sparsity-inducing norm is introduced to regularize foreground. Besides, in order to efficiently adapt to the dynamically changing background, the contribution of old and new frames can be balanced when updating the background subspace. Experiments on widely used dataset CDnet show that our algorithm has strong adaptability to complex scenes and can detect foreground accurately.

Nonnegative matrix factorization(NMF) has been applied to hyperspectral unmixing in recent years. Different constraints based on geometrical or statistical properties of endmember and abundance are incorporated into NMF model to improve unmixing result. In this paper, a new regularizer based on spectral cluster information is proposed to strengthen the constrained relationship between original image and abundance maps. The new algorithm makes abundances of similar pixels close and abundances of dissimilar pixels be separated completely. Additionally, L 1/2 sparsity constraint is adopted to make the solutions sparse. Comparative results on real and synthetic hyperspectral datasets prove our proposed method could improve the hyperspectral unmixing accuracy.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2013Application of kernel NMF in quadratic-trace TFPF for seismic record denoisingAuthors: Yanan TianYue LiYanan TianSchool of Information and Engineering, Jilin USearch for more papers by this author and Yue LiSchool of Information and Engineering, Jilin USearch for more papers by this authorhttps://doi.org/10.1190/segam2013-0194.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Time-frequency peak filtering (TFPF) has been applied to seismic record denoising in recent years. However, it processes all frequencies signals with the same window length, which results in a large estimation bias. Thus, some improved methods are proposed one after another. However, in these methods, the filtering trace selection is still a problem, which deserves discussion further. In this paper, we present a novel filtering trace selection method based upon kernel nonnegative matrix factorization (KNMF) algorithm and apply it in quadratic-trace TFPF. The experimental results demonstrate that it can estimate the contour of the reflection events accurately, which provides a good premise for the filtering trace selection in quadratic-trace TFPF. The denoising results by the selected traces further verify its effectiveness and feasibility. Permalink: https://doi.org/10.1190/segam2013-0194.1FiguresReferencesRelatedDetails SEG Technical Program Expanded Abstracts 2013ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2013 Pages: 5258 Publisher:Society of Exploration Geophysicists HistoryPublished: 19 Aug 2013 CITATION INFORMATION Yanan Tian and Yue Li, (2013), "Application of kernel NMF in quadratic-trace TFPF for seismic record denoising," SEG Technical Program Expanded Abstracts : 4362-4366. https://doi.org/10.1190/segam2013-0194.1 Plain-Language Summary PDF DownloadLoading ...

Accurate segmentation of pathological lungs from large-size chest computed tomographic images is crucial for computer-assisted lung cancer diagnostics. In this paper, a new framework for automatic pathological lung segmentation is proposed. The proposed INMF-based segmentation approach has the ability to handle the in-homogeneities caused by the arteries, veins, bronchi, and possible pathologies that may exist in the lung tissues, and to detect the number of clusters in the image in an automated manner. The proposed INMF-based segmentation framework is quantitatively validated on simulated realistic lung phantoms that mimic different lung pathologies (7 datasets), in vivo data sets for 17 subjects, and for lung disease with severe pathologies. Three metrics are used: the Dice coefficient, modified Hausdorff distance, and absolute lung volume difference. Results show that the proposed approach outperforms existing lung segmentation techniques and can handle in-homogenities caused by different pathologies.

Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.

Hyperspectral unmixing (HU) has become an important technique in exploiting hyperspectral data since it decomposes a mixed pixel into a collection of endmembers weighted by fractional abundances. The endmembers of a hyperspectral image (HSI) are more likely to be generated by independent sources and be mixed in a macroscopic degree before arriving at the sensor element of the imaging spectrometer as mixed spectra. Over the past few decades, many attempts have focused on imposing auxiliary regularizes on the conventional nonnegative matrix factorization (NMF) framework in order to effectively unmix these mixed spectra. As a promising step toward finding an optimum regularizer to extract endmembers, this paper presents a novel blind HU algorithm, referred to as Kurtosis-based Smooth Nonnegative Matrix Factorization (KbSNMF) which incorporates a novel regularizer based on the statistical independence of the probability density functions of endmember spectra. Imposing this regularizer on the conventional NMF framework promotes the extraction of independent endmembers while further enhancing the parts-based representation of data. Experiments conducted on diverse synthetic HSI datasets (with numerous numbers of endmembers, spectral bands, pixels, and noise levels) and three standard real HSI datasets demonstrate the validity of the proposed KbSNMF algorithm compared to several stateof- the-art NMF-based HU baselines. The proposed algorithm exhibits superior performance especially in terms of extracting endmember spectra from hyperspectral data; therefore, it could uplift the performance of recent deep learning HU methods which utilize the endmember spectra as supervisory input data for abundance extraction.