Recently non-negative matrix factorization (NMF) has received a lot of attentions in information retrieval, computer vision and pattern recognition. NMF aims to find two non-negative matrices whose product can well ap...
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ISBN:
(纸本)9780769535029
Recently non-negative matrix factorization (NMF) has received a lot of attentions in information retrieval, computer vision and pattern recognition. NMF aims to find two non-negative matrices whose product can well approximate the original matrix. The sizes of these two matrices are usually smaller than the original matrix. This results in a compressed version of the original data matrix. The solution of NMF yields a natural parts-based representation for the data, When NMF is applied for data representation, a major disadvantage is that it fails to consider the geometric structure in the data. In this paper, we develop a graph based approach for parts-based data representation in order to overcome this limitation. We construct an affinity graph to encode the geometrical information and seek a matrixfactorization which respects the graph structure. We demonstrate the success of this novel algorithm by applying it on real world problems.
A common anomaly detection algorithm for hyperspectral imagery is the RX algorithm based on the Mahalanobis distance of each pixel from the image mean. This is a benchmark algorithm which can be applied either directl...
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ISBN:
(数字)9781510635623
ISBN:
(纸本)9781510635623
A common anomaly detection algorithm for hyperspectral imagery is the RX algorithm based on the Mahalanobis distance of each pixel from the image mean. This is a benchmark algorithm which can be applied either directly on a hyperspectral image or on a dimensionality-reduced hyperspectral image. Recent work on non-negative matrix factorization (NNMF) provides a fast-iterative algorithm for decomposing a hyperspectral cube and achieving dimensionality reduction. In this paper, we study the implementation of the NNMF algorithm on a hyperspectral data cube and propose two new anomaly detection algorithms, based on combining the NNMF and the RX algorithms. In the first version, we apply the NNMF algorithm on a hyperspectral image reducing the dimensionality;we then apply the RX algorithm. In the second version, we segment and cluster the dataset after applying the NNMF algorithm. Anomaly detection is then performed on this dataset. Using either of these algorithms overcomes a weakness of the RX algorithm in handling background clusters which are close to each other. The algorithm was tested on the RIT blind test dataset. From our results, we conclude that the two versions of the algorithm are sensitive to different types of anomalies;a two-dimensional scatterplot of the data comparing the RX values to either of the NNMF algorithms enables us to distinguish between the anomaly types. The ground truth shows that we have achieved high accuracy and less false alarms.
In this presentation two event-related potentials, mismatch negativity (MMN) and P3a, are extracted from EEG by non-negative matrix factorization (NMF) simultaneously. Typically MMN recordings show a mixture of MMN, P...
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ISBN:
(纸本)9781424435494
In this presentation two event-related potentials, mismatch negativity (MMN) and P3a, are extracted from EEG by non-negative matrix factorization (NMF) simultaneously. Typically MMN recordings show a mixture of MMN, P3a, and responses to repeated standard stimuli. NMF may release the source independence assumption and data length limitations required by Fast independent component analysis (FastICA). Thus, in theory NMF could reach better separation of the responses. In the current experiment MMN was elicited by auditory duration deviations in 102 children. NMF was performed on the time-frequency representation of the raw data to estimate sources. Support to Absence Ratio (SAR) of the MMN component was utilized to evaluate the performance of NMF and FastICA. To the raw data, FastICA-MMN component, and NMF-MMN component, SARs were 31, 34 and 49dB respectively. NMF outperformed FastICA by 15dB. This study also demonstrates that children with reading disability have larger P3a than control children under NMF.
We introduce non-negative matrix factorization with orthogonality constraints (NMFOC) for detection of a target spectrum in a given set of Raman spectra data. An orthogonality measure is defined and two different orth...
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We introduce non-negative matrix factorization with orthogonality constraints (NMFOC) for detection of a target spectrum in a given set of Raman spectra data. An orthogonality measure is defined and two different orthogonality constraints are imposed on the standard NMF to incorporate prior information into the estimation and hence to facilitate the subsequent detection procedure. Both multiplicative and gradient type update rules have been developed. Experimental results are presented to compare NMFOC with the basic NMF in detection, and to demonstrate its effectiveness in the chemical agent detection problem.
We propose a new non-parametric level set model for automatic image clustering and segmentation based on non-negative matrix factorization (NMF). We show that NMF: (i) clusters the image into distinct homogeneous regi...
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ISBN:
(纸本)9781509006199
We propose a new non-parametric level set model for automatic image clustering and segmentation based on non-negative matrix factorization (NMF). We show that NMF: (i) clusters the image into distinct homogeneous regions and (ii) provides the local spatial distribution of each region within the image. Furthermore, NMF has a controllable resolution and can discover homogeneous regions as small as one pixel. Coupled with the level-set approach, NMF is an efficient method for image segmentation. The proposed model is unsupervised and relies on local histogram modeling to define an energy functional, whose optimization leads to the final segmentation. A unique and desirable feature of the proposed method is that it does not incorporate any spurious model parameters;hence, the optimization is performed only w.r.t level set functions. We apply the proposed non-parametric Unsupervised Segmentation approach (geNIUS) to synthetic and real images and compare it to three state-of-the-art parametric and non-parametric level set approaches: the localized Gaussian distribution fitting model (LGDF) [1], the local histogram fitting (LHF) model [2], and our recent work: NMF-LSM in [3]. The proposed geNIUS model results in a superior accuracy and more efficient implementation, which is a result of its free-model parameter feature.
We propose an approach for non-negative matrix factorization (NMF) with sparseness constraints on feature vectors. It has been believed that the non-negativity constraint in NMF contributes to making the learned featu...
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In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as non-negative matrix factorization (NMF) as interpretive exploratory data analysis tools. We first explore the ...
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ISBN:
(纸本)9781615671090
In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as non-negative matrix factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive factorization. We subsequently explore four novel approaches to finding globally-optimal NMF solutions using various ideas from convex optimization. We then develop a new method, isometric NMF (isoNMF), which preserves non-negativity while also providing an isometric embedding, simultaneously achieving two properties which are helpful for interpretation. Though it results in a more difficult optimization problem, we show experimentally that the resulting method is scalable and even achieves more compact spectra than standard NMF.
Identifying biologically-active protein structure(s) from an ensemble of computed three-dimensional structures is a major challenge. Clustering-based methods are time-consuming and often under perform on structure dat...
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ISBN:
(纸本)9781728118673
Identifying biologically-active protein structure(s) from an ensemble of computed three-dimensional structures is a major challenge. Clustering-based methods are time-consuming and often under perform on structure datasets that are highly imbalanced. Energy landscape-based methods improve performance over imbalanced datasets but incur significant time costs. In this paper we propose a novel method based on non-negative matrix factorization. The method outperforms energy landscape-based clustering methods, addressing both time costs and challenges with imbalanced structure datasets.
non-negativefactorizations of spectra have been a very popular tool for various audio tasks recently. A long-standing problem with these methods methods is that they cannot be easily applied on other kinds of spectra...
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ISBN:
(纸本)9781479909728
non-negativefactorizations of spectra have been a very popular tool for various audio tasks recently. A long-standing problem with these methods methods is that they cannot be easily applied on other kinds of spectral decompositions such as sinusoidal models, constant-Q transforms, wavelets and reassigned spectra. This is because with these transforms the frequency and/or time values are real-valued and not sampled on a regular grid. We therefore cannot represent them as a matrix that we can later factorize. In this paper we present a formulation of non-negative matrix factorization that can be applied on data with real-valued indices, thereby making the application of this family of methods feasible on a broader family of time/frequency transforms.
This paper is concerned with the design of a non-negative matrix factorization algorithm for image analysis. This can be used in the context of blind source separation, where each observed image is a linear combinatio...
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ISBN:
(纸本)9781424423415
This paper is concerned with the design of a non-negative matrix factorization algorithm for image analysis. This can be used in the context of blind source separation, where each observed image is a linear combination of a few basis functions, and that both the coefficients for the linear combination and the bases are unknown. In addition, the observed images are commonly corrupted by noise. While algorithms have been developed when the noise obeys Gaussian or Poisson statistics, here we take it to be Laplacian, which is more representative for other leptokurtic distributions. It is applicable for cases such as transform coefficient distributions and when there are insufficient noise sources for the Central Limit Theorem to apply. We formulate the problem as an L-1 minimization and solve it via linear programming.
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