Stochastic Higher-Order Independent Component Analysis for Hyperspectral Dimensionality Reduction
Daniela Lupu, Ion Necoara, Joseph L. Garrett, Tor Arne Johansen
Abstract
Hyperspectral imaging is a remote sensing technique that measures the spectrum of each pixel in the image of a scene. 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. Hence, we show that our method is faster and the extracted features are better than those of FastICA. The quality of features extracted, as well as time and epochs required by FastICA and SHOICA are compared practically, on dimensionality reduction and classification tasks of real hyperspectral images.