# Superpixel-Based Singular Spectrum Analysis for Effective Spatial-Spectral Feature Extraction
## 1 Introduction  
Recent advancements in hyperspectral sensors resulted in the increased availability of Hyperspectral Images (HSI) and a boost in their circulation among the remote sensing community. HSI data enables the discrimination of objects even with minor differences as it contains several contiguous spectral bands acquired from the visible to the infrared region [1] so that every small spectral difference can, in principle, be captured. The information is available in the form of a 3-D structure that contains a 2-D spatial scene along with a 1-D spectral signature. These unique characteristics of HSI have made them popular in several application areas, such as agriculture [2], mineralogy [3], land cover classification [4], target detection [5], and others. However, effective classification of HSI is still an open challenge. Several classification techniques, such as K-nearest neighbor (KNN) [6], support vector machine (SVM) [7], multinomial logistic regression (MLR) [8], Extreme Learning Machine (ELM) [9], and Sparse Representation Classifier (SRC) [10] have been proposed in the past decades. The richness in spectral information attracted research efforts on pixel-based processing and classification. SVM is the most popular and widespread classifier due to its lower generalization error rate that makes it capable of identifying even minor changes in spectral signatures. Due to the high spectral dimensionality compared to a generally limited number of class-specific training samples, it is quite difficult to properly estimate the model parameters. Hence, there is a need to adopt effective spatial-spectral feature extraction approaches to overcome the aforementioned challenges. To deal with the issue of higher spectral dimensionality, several linear (e.g., Principal Component Analysis (PCA) [11], Independent Component Analysis (ICA) [12], and Linear Discriminant Analysis (LDA) [13]) and non-linear (manifold learning [14]) dimensionality reduction (DR) methods have been introduced. Band selection approaches may also be utilized to select the most informative bands out of several available bands [15; 16]. Spectral features alone, however, may not be sufficient to score very high accuracy values. To improve performance, it is necessary to incorporate spatio-spectral features that help increasing the separability of classes. Recently, various spatial feature extraction techniques have been proposed. Mathematical Morphology is one of the most popular approaches that is extensively utilized by researchers. The concept of Extended Morphological Profiles (EMP) for FE in HSI was first proposed by [PERSON] et al. [17]. This technique utilizes morphological opening and closing transformations to extract spatial geometrical information. Later, [PERSON] et al. [18] proposed Morphological Attribute Filters (MAP) for the spatial FE. From that point onwards, several variations of Attribute Profiles (AP) were created. [PERSON] et al. [19] conducted a comprehensive survey on the evolution in Attribute Profiles. Texture Descriptors, including Wavelet transform [20], Gray-Level Co-occurrence Matrix (GLCM) [21], Local Binary Patterns (LBP) [22], and Gabor filters [23], have also been used in the literature for spatial FE. Filtering, i.e., moving-window-based processing, is another approach to extract spatial-spectral features. Various edge-preserving filters, such as Bilateral Filters [24], Trilateral Filters [25], Guidance filters [26], and Domain Transform Recursive Filters [27] have been introduced for spatial FE in the literature. The texture and noise variations are minimized by performing smoothing operations; however, important details, such as edges and lines, are well preserved by these filters [28]. In addition to these techniques, 2D-SSA is another interesting approach for spatial feature extraction. Using this approach, each band image of HSI is initially decomposed into varying trends, oscillations, and noise. Later, HSI is reconstructed using the selected oscillations and trends [29; 30].