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Sparse Grassmannian Embeddings for Hyperspectral Data Representation and Classification
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DOI：10.1109/LGRS.2017.2648514.png)
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摘要
En 中文
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 k-dimensional subspaces of Rn. 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.
Keyword:
Dimension selection
Grassmann manifold
Grassmannian embedding
hyperspectral image classification
multidimensional scaling (MDS)
sparse support vector machines (SSVMs)
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