Stochastic Higher-Order Independent Component Analysis for Hyperspectral Dimensionality Reduction

Abstract

Hyperspectral imaging is a remote sensing technique that measures the spectrum of each pixel in the image of a scene. It can be used to detect objects or classify materials based on their optical reflectance spectra. Various methods have been developed to reduce the spectral dimension of hyperspectral images in order to facilitate their analysis. Independent Component Analysis (ICA) is a class of algorithms which extract statistically independent features. FastICA, is one of the most used ICA algorithms because it is simple and fast. However, FastICA often finds irrelevant stationary points (e.g., minima instead of maxima) and is not scalable as it uses at each iteration the whole set of pixels. In this paper, we present a new stochastic algorithm, called SHOICA, which smoothly approximates the non-convex loss functions of ICA using higher-order Taylor minorizers. Because SHOICA guarantees ascent of its objective function, it identifies (local) maxima. Moreover, because SHOICA is stochastic, it facilitates minibatching and thus is scalable and appropriate for large datasets. The quality of features extracted, as well as the time and epochs required by both FastICA and SHOICA are compared on dimensionality reduction and classification tasks of real hyperspectral images.

Gaussian-kernel weighted neighborhood preserving embedding algorithm and its application in fault detection

“…. ., α k ), associated with the matrix K, can be determined using equation (9). Subsequently, these eigenvalues λK ( λ1 , λ2 , λ3 , .…”

“…This heightened interest can be attributed to its lucid statistical interpretation, straightforward model training, and superior efficacy in addressing issues associated with small sample sizes. Established MSPM fault detection methods, including partial least squares (PLS), principal component analysis (PCA), and independent component analysis (ICA), have achieved widespread adoption [6][7][8][9]. However, with the proliferation of variables in industrial monitoring, data is progressively transitioning into high dimensions.…”

Hyperspectral image classification based on spectral feature extraction

“…Unsupervised feature extraction method is to realize the representation of original data without any prior knowledge. Typical unsupervised feature extraction methods include principal component analysis (PCA) [9], independent component analysis (ICA) [10] and discrete wavelet transform (DWT) [11]. The supervised feature extraction method uses marked samples to infer the separability of categories, and the most representative method is linear discriminant analysis (LDA) [12].…”

Hyperspectral Image Classification Based on 3D-2D Hybrid Convolution and Graph Attention Mechanism

“…However, the problems of low spatial resolution, high spectral dimensionality and lack of labelled samples in HSI pose great challenges to the classification task [10][11][12]. In the early days, researchers proposed a series of feature extraction methods such as principal component analysis [13,14], independent component analysis [15][16][17], and linear discriminant analysis [17,18], and combined them with machine learning classifiers such as support vector machines [19,20], random forests [21,22], and Gaussian mixture model [23,24] to classify the HSI. These methods can effectively alleviate the Hughes phenomenon [25] that classification accuracy decreases with increasing spectral dimension, but because only spectral features are considered and based on manual design, the classification accuracy and applicability are not ideal.…”