Sofya Chepushtanova

Band selection in hyperspectral imagery using sparse support vector machines

In this paper we propose an ι1-norm penalized sparse support vector machine (SSVM) as an embedded approach to the hyperspectral imagery band selection problem. SSVMs exhibit a model structure that includes a clearly identifiable gap between zero and non-zero weights that permits important bands to be definitively selected in conjunction with the classification problem. The SSVM Algorithm is trained using bootstrap aggregating to obtain a sample of SSVM models to reduce variability in the band selection process. This preliminary sample approach for band selection is followed by a secondary band selection which involves retraining the SSVM to further reduce the set of bands retained. We propose and compare three adaptations of the SSVM band selection algorithm for the multiclass problem. Two extensions of the SSVM Algorithm are based on pairwise band selection between classes. Their performance is validated by using one-against-one (OAO) SSVMs. The third proposed method is a combination of the filter band selection method WaLuMI in sequence with the (OAO) SSVM embedded band selection algorithm. We illustrate the perfomance of these methods on the AVIRIS Indian Pines data set and compare the results to other techniques in the literature. Additionally we illustrate the SSVM Algorithm on the Long-Wavelength Infrared (LWIR) data set consisting of hyperspectral videos of chemical plumes.

An application of persistent homology on Grassmann manifolds for the detection of signals in hyperspectral imagery

We present an application of persistent homology to the detection of chemical plumes in hyperspectral movies. The pixels of the raw hyperspectral data cubes are mapped to the geometric framework of the real Grassmann manifold G(k, n) (whose points parameterize the k-dimensional subspaces of ℝn) where they are analyzed, contrasting our approach with the more standard framework in Euclidean space. An advantage of this approach is that it allows the time slices in a hyperspectral movie to be collapsed to a sequence of points in such a way that some of the key structure within and between the slices is encoded by the points on the Grassmann manifold. This motivates the search for topological structure, associated with the evolution of the frames of a hyperspectral movie, within the corresponding points on the Grassmann manifold. The proposed framework affords the processing of large data sets, such as the hyperspectral movies explored in this investigation, while retaining valuable discriminative information.

Sparse Grassmannian Embeddings for Hyperspectral Data Representation and Classification

We propose an approach for the representation and classification of hyperspectral data that exploits the geometric framework, the Grassmann manifold, i.e., a parameterization of

Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies

k

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-dimensional subspaces of

Persistence images: a stable vector representation of persistent homology

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Persistence Images: An Alternative Persistent Homology Representation.

. Multiple pixels from a data class are used to capture the variability of the class information using a subspace representation. We use two metrics defined on the Grassmannian, chordal and geodesic, and several pseudometrics to measure the pairwise distances between the points, i.e., subspaces. Once a distance matrix is generated, classical multidimensional scaling is applied to find a configuration of points with preserved or approximated original distances, thus realizing an embedding of the Grassmannian in Euclidean space. A sparse support vector machine trained in the embedding space simultaneously classifies embedded subspaces and selects a subset of optimal dimensions (features) using a weight ratio criterion. The resulting embedding affords substantial model order reduction for classification and data visualization. In many cases, this framework provides linearly separable representations even when raw data are not linearly separable. We analyze frameworks and compare binary classification results for several distances. Finally, we illustrate the embedding of multiple data classes.

Classification of hyperspectral imagery on embedded Grassmannians

The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivated the development of new tools such as persistent homology for exploring topological invariants, or features, in large data sets. In this paper, we apply persistent homology to the characterization of gas plumes in time dependent sequences of hyperspectral cubes, i.e. the analysis of 4-way arrays. We investigate hyperspectral movies of Long-Wavelength Infrared data monitoring an experimental release of chemical simulant into the air. Our approach models regions of interest within the hyperspectral data cubes as points on the real Grassmann manifold Gk,i¾?n whose points parameterize the k-dimensional subspaces of

Dynamical Modeling of Viral Spread

\mathbb {R}^n