Hyperspectral Image Classification Using Graph Clustering Methods

Abstract

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classification of large datasets in high dimensions. This paper presents two classes of graph-based classification methods for hyperspectral imagery. Using the full dimensionality of the data, we consider a similarity graph based on pairwise comparisons of pixels. The graph is segmented using a pseudospectral algorithm for graph clustering that requires information about the eigenfunctions of the graph Laplacian but does not require computation of the full graph. We develop a parallel version of the Nyström extension method to randomly sample the graph to construct a low rank approximation of the graph Laplacian. With at most a few hundred eigenfunctions, we can implement the clustering method designed to solve a variational problem for a graph-cut-based semi-supervised or unsupervised classification problem. We implement OpenMP directive-based parallelism in our algorithms and show performance improvement and strong, almost ideal, scaling behavior. The method can handle very large datasets including a video sequence with over a million pixels, and the problem of segmenting a data set into a pre-determined number of classes. Source CodeThe reviewed source code and documentation for this algorithm are available from the web page of this article 1 . Compilation and usage instructions are included in the README.txt file of the archive.

OpenMP Parallelization and Optimization of Graph-Based Machine Learning Algorithms

“…This is a standard problem in machine learning. Recently, novel algorithms have been proposed [1] that are motivated by PDE-based image segmentation methods and are modified to apply to discrete data sets [4]. Serial results show that these algorithms improve both accuracy of solution and efficiency of the computation and can be potentially faster in parallel than various classification algorithms such as spectral clustering with k-means [6].…”

Computing Nonlinear Eigenfunctions via Gradient Flow Extinction

“…In this model each data point is represented by a vertex of the graph while the similarity between two data points is represented by a weighted edge connecting the respective vertices. For details on data analysis using finite weighted graphs we Figure 3 for the individual eigenfunctions refer to [9,12]. In the literature it is well-known that there exists a strong mathematical relationship between spectral clustering and various minimum graph cut problems.…”

“…After determining the eigenvectors of L one performs the actual clustering, e.g., via a standard k-means algorithm or simple thresholding. Note that in various applications a spectral clustering based on solely one eigenvector, i.e., the corresponding eigenvector of the second-smallest eigenvalue, already yields interesting results, e.g., for image segmentation [12]. On the other hand, due to the linear nature of the graph Laplacian this approach is rather restricted in many real world applications.…”

Spectral–Spatial Diffusion Geometry for Hyperspectral Image Clustering

“…However, the different clusters in the datacorresponding to regions with distinct material propertiesoften exhibit low-dimensional, though nonlinear, structure. In order to efficiently exploit this structure, methods for clustering HSI that learn the underlying nonlinear geometry have been developed, including methods based on non-negative matrix factorization [5], regularized graph Laplacians [6], angle distances [7], and deep neural networks [8].…”