Fast Implementation of Singular Spectrum Analysis for Effective Feature Extraction in Hyperspectral Imaging

Abstract

This version is available at https://strathprints.strath.ac.uk/53416/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract-As a recent approach for time series analysis, singular spectrum analysis (SSA) has been successfully applied for feature extraction in hyperspectral imaging (HSI), leading to increased accuracy in pixel-based classification tasks. However, one of the main drawbacks of conventional SSA in HSI is the extremely high computational complexity, where each pixel requires individual and complete singular value decomposition (SVD) analysis. To address this issue, a fast implementation of SSA (F-SSA) is proposed for efficient feature extraction in HSI. Rather than applying pixel-based SVD as conventional SSA does, the fast implementation only needs one SVD applied to a representative pixel, i.e. either the median or the mean spectral vector of the HSI hypercube. The result of SVD is employed as a unique transform matrix for all the pixels within the hypercube. As demonstrated in experiments using two well-known publicly available data sets, almost identical results are produced by the fast implementation in terms of accuracy of data classification, using the support vector machine (SVM) classifier. However, the overall computational complexity has been significantly reduced.

Fast implementation of two-dimensional singular spectrum analysis for effective data classification in hyperspectral imaging

“…This SVD can actually be computed by several algorithms described in the literature, where equivalent implementations based on EVD are also possible. As stated in [14], an equivalent EVD applied to…”

“…The grouping stage is represented by the equation in (2), and even though in [14] we computed the multiplication T t t U U , actually computing the two multiplications from ) ( 2D T X U U t t keeping the order from brackets is less complex, so the complexity is stated as (…”

“…This pixel-or band-based implementation translates into reiteration of some complex steps, such as the SVD, which has inevitably resulted in substantially increased overall computational complexity. To address this issue, a fast implementation F-1D-SSA was proposed in [14], following a mathematical trick that is possible thanks to the use of the same configuration for every item (pixel). Now, it is essential to adapt and create a fast implementation for the 2-D case (F-2D-SSA) to finally complete our SSA exploration (Fig.…”

“…As all the scenes are indeed acquired by the same sensor, at the same time and in the same conditions, it is assumed that a scene resulting from the mean, or alternatively the median value from the scenes in the cube will contain adequately the properties of the whole data set, analogously to the 1-D case [14]. Therefore, suggesting the use of the mean (or median) image as SVD input, the implementation steps of F-2D-SSA in HSI are now listed in Algorithm 1, where experimental results are presented in Section IV to fully validate the effectiveness of the proposed F-2D-SSA algorithm.…”

Optimized Kernel Minimum Noise Fraction Transformation for Hyperspectral Image Classification

“…Dimensionality reduction is a very effective technique to solve this problem [5,6]. Dimensionality reduced data should well represent the original data, and can be considered as the extracted features for classification [7][8][9]. When the data dimensionality is…”