Sequential Dimensionality Reduction for Extracting Localized Features

Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative matrix factorization (NMF) has become very popular as it is able to extract sparse, localized and easily interpretable features by imposing an additive combination of nonnegative basis elements. Nonnegative matrix underapproximation (NMU) is a closely related technique that has the advantage to identify features sequentially. In this paper, we propose a variant of NMU that is particularly well suited for image analysis as it incorporates the spatial information, that is, it takes into account the fact that neighboring pixels are more likely to be contained in the same features, and favors the extraction of localized features by looking for sparse basis elements. We show that our new approach competes favorably with comparable state-of-the-art techniques on synthetic, facial and hyperspectral image data sets.Comment: 24 pages, 12 figures. New numerical experiments on synthetic data sets, discussion about the convergenc

A comparison of non-negative matrix underapproximation methods for the decomposition of magnetic resonance spectroscopy data from human brain tumors

Altres ajuts: acords transformatius de la UABMagnetic resonance spectroscopy (MRS) is an MR technique that provides information about the biochemistry of tissues in a noninvasive way. MRS has been widely used for the study of brain tumors, both preoperatively and during follow-up. In this study, we investigated the performance of a range of variants of unsupervised matrix factorization methods of the non-negative matrix underapproximation (NMU) family, namely, sparse NMU, global NMU, and recursive NMU, and compared them with convex non-negative matrix factorization (C-NMF), which has previously shown a good performance on brain tumor diagnostic support problems using MRS data. The purpose of the investigation was 2-fold: first, to ascertain the differences among the sources extracted by these methods; and second, to compare the influence of each method in the diagnostic accuracy of the classification of brain tumors, using them as feature extractors. We discovered that, first, NMU variants found meaningful sources in terms of biological interpretability, but representing parts of the spectrum, in contrast to C-NMF; and second, that NMU methods achieved better classification accuracy than C-NMF for the classification tasks when one class was not meningioma

Hyperspectral Data Acquisition and Its Application for Face Recognition

Current face recognition systems are rife with serious challenges in uncontrolled conditions: e.g., unrestrained lighting, pose variations, accessories, etc. Hyperspectral imaging (HI) is typically employed to counter many of those challenges, by incorporating the spectral information within different bands. Although numerous methods based on hyperspectral imaging have been developed for face recognition with promising results, three fundamental challenges remain: 1) low signal to noise ratios and low intensity values in the bands of the hyperspectral image specifically near blue bands; 2) high dimensionality of hyperspectral data; and 3) inter-band misalignment (IBM) correlated with subject motion during data acquisition. This dissertation concentrates mainly on addressing the aforementioned challenges in HI. First, to address low quality of the bands of the hyperspectral image, we utilize a custom light source that has more radiant power at shorter wavelengths and properly adjust camera exposure times corresponding to lower transmittance of the filter and lower radiant power of our light source. Second, the high dimensionality of spectral data imposes limitations on numerical analysis. As such, there is an emerging demand for robust data compression techniques with lows of less relevant information to manage real spectral data. To cope with these challenging problems, we describe a reduced-order data modeling technique based on local proper orthogonal decomposition in order to compute low-dimensional models by projecting high-dimensional clusters onto subspaces spanned by local reduced-order bases. Third, we investigate 11 leading alignment approaches to address IBM correlated with subject motion during data acquisition. To overcome the limitations of the considered alignment approaches, we propose an accurate alignment approach ( A3) by incorporating the strengths of point correspondence and a low-rank model. In addition, we develop two qualitative prediction models to assess the alignment quality of hyperspectral images in determining improved alignment among the conducted alignment approaches. Finally, we show that the proposed alignment approach leads to promising improvement on face recognition performance of a probabilistic linear discriminant analysis approach