Unsupervised Feature Selection Based on Ultrametricity and Sparse Training Data: A Case Study for the Classification of High-Dimensional Hyperspectral Data

Abstract

In this paper, we investigate the potential of unsupervised feature selection techniques for classification tasks, where only sparse training data are available. This is motivated by the fact that unsupervised feature selection techniques combine the advantages of standard dimensionality reduction techniques (which only rely on the given feature vectors and not on the corresponding labels) and supervised feature selection techniques (which retain a subset of the original set of features). Thus, feature selection becomes independent of the given classification task and, consequently, a subset of generally versatile features is retained. We present different techniques relying on the topology of the given sparse training data. Thereby, the topology is described with an ultrametricity index. For the latter, we take into account the Murtagh Ultrametricity Index (MUI) which is defined on the basis of triangles within the given data and the Topological Ultrametricity Index (TUI) which is defined on the basis of a specific graph structure. In a case study addressing the classification of high-dimensional hyperspectral data based on sparse training data, we demonstrate the performance of the proposed unsupervised feature selection techniques in comparison to standard dimensionality reduction and supervised feature selection techniques on four commonly used benchmark datasets. The achieved classification results reveal that involving supervised feature selection techniques leads to similar classification results as involving unsupervised feature selection techniques, while the latter perform feature selection independently from the given classification task and thus deliver generally versatile features.

Biomass retrieval based on genetic algorithm feature selection and support vector regression in Alpine grassland using ground-based hyperspectral and Sentinel-1 SAR data

“…Wang et al, 2017). This allows gaining predictive ability and retaining meaningful features with respect to a given task (Bradley et al, 2018;Xue & Su, 2017). Moreover, some studies showed that SVM approaches are sensitive to data set dimensionality reduction (Gidudu & Heinz, 2007;Jain, 1997;Pal & Foody, 2010).…”

Fusion of Hyperspectral, Multispectral, Color and 3d Point Cloud Information for the Semantic Interpretation of Urban Environments

“…In addition to the aforementioned progress, the use of hyperspectral data has also come into the focus of research on environmental mapping over years (Plaza et al, 2009;Camps-Valls et al, 2014), as such information e.g. allows distinguishing different types of vegetation (Bradley et al, 2018; and different materials (Ilehag et al, 2017). This, in turn, can be helpful if the corresponding geometric structure of the observed scene is similar.…”

“…When using high-dimensional hyperspectral data, however, the high degree of redundancy contained in these data typically decreases the predictive accuracy of a classifier (Melgani and Bruzzone, 2004;Bradley et al, 2018), so that approaches for dimensionality reduction or band selection are commonly involved. In this context, dimensionality reduction techniques focus on deriving a new data representation based on fewer, but potentially better features extracted from the given data representation.…”

“…In addition, we take into account that the spectral bands of hyperspectral data are directly next to each other so that the acquired reflectance values of neighboring spectral bands tend to be strongly correlated and thus contain a high degree of redundancy which, in turn, typically has a detrimental effect on the classification results (Melgani and Bruzzone, 2004;Keller et al, 2016;Bradley et al, 2018). Consequently, we also involve several encodings/transformations of the given hyperspectral data.…”

Optimization Performance Comparison of Three Different Group Intelligence Algorithms on a SVM for Hyperspectral Imagery Classification

“…However, the Hughes phenomenon [35], where a large number of bands with narrow intervals lead to high correlation between adjacent bands and redundant information, which interferes with classification is a major issue that affects high spectral dimensions. Therefore, many studies tried to reduce the number bands of hyperspectral remote sensing imagery, but with little loss of information to address this "dimensionality disaster" [17,36,37]. Using GI algorithms to search for the optimal combination of bands is one state-of-the art approach towards dimension reduction [38].…”