# Superpixel-Based Singular Spectrum Analysis for Effective Spatial-Spectral Feature Extraction
## 1 Introduction
In 2D-SSA, the spatial structural information is extracted by utilizing the characteristics of the surrounding pixels in a specific embedding window. It can withstand high levels of noise and generally achieves good data classification results. 2D-SSA suffers, however, from several limitations, such as reduced utilization of the abundant spectral information available in data, and over-smoothing or under-smoothing of classification results because of the fixed embedding window size. To overcome the challenge of selecting the optimal embedding window size, recently, multi-scale 2D-SSA has been proposed for the effective extraction of discriminative spatial features under different noise conditions [31; 32]. Superpixel segmentation techniques have gained popularity in recent years due to their capability of exploiting spatial structural information adaptively in an image. In [33], a survey on superpixel segmentation as a preprocessing step in HSI analysis was presented. A superpixel-based classification via multiple kernels (SCMK) approach was proposed in [34]. In [35], a region-based relaxed multiple kernel (R2 MK) method was proposed that combines the multiscale spectral and spatial features using a kernel collaborative representation classification technique. To obtain superior classification performance and solve the problem of optimal superpixel number selection, an adjacent superpixel-based multiscale spatial-spectral kernel (ASMGSSK) was proposed in [36]. In [37], a multiscale segmentation-based SuperPCA model (MSuperPCA) was developed, which can effectively integrate multiscale spatial information to obtain the optimal classification result by decision fusion. Recently, deep learning techniques have become quite popular in the classification of HSI data due to their ability to extract discriminant and abstract features by using a series of hierarchical layers. The initial layers usually extract texture and edge information, whereas deeper layers highlight more complicated features. Some of the most popular deep learning frameworks include stacked autoencoders (SAE) [38], Deep Belief Networks (DBN) [39], Convolution Neural Networks (CNN) [40], Recurrent Neural Networks (RNN) [41], Generative Adversarial Networks (GAN) [42], etc. Although deep learning approaches have several advantages, they also pose significant challenges in HSI applications. First of all, to achieve better classification result, often deep learning techniques demand large volumes of training samples. Moreover, a large number of hyper-parameters (like the kernel sizes, learning rate, etc.) are involved in training complex deep learning networks mainly designed for feature extraction and classification. Hence, the process becomes computationally expensive. The disadvantages of combining SSA with structured approaches to incorporating spatial information may be overcome by using more flexible ways to spatially partition the dataset. In line with this consideration, in this work, a superpixel-based SSA (SP-SSA) algorithm was proposed as a means to increase the classifier performance. Instead of performing direct reconstruction, an object-specific reconstruction is performed to accurately preserve the local contextual information. Superpixel segmentation is first applied on the input HSI to generate a segmented HSI where each sub-region carries similar characteristic features, and its shape and size is adjusted according to the local image structure information. Next, 2D-SSA is individually applied on each segmented region to produce the reconstructed HSI. Lastly, the final classification map is generated by using the popular SVM classifier. The major novel contributions of this work are highlighted in the following list:  
1. Direct reconstruction is usually performed in standard 2D-SSA algorithms, where the full image is reconstructed. In HSIs, however, object-specific reconstruction is always better than direct reconstruction, as, in this way, local contextual information can be captured accurately.