Reducing Dimensionality of Hyperspectral Data with Diffusion Maps and Clustering with K-means and Fuzzy ART

It is very difficult to analyse large amounts of hyperspectral data. Here we present a method based on reducing the dimensionality of the data and clustering the result in moving toward classification of the data. Dimensionality reduction is done with diffusion maps, which interpret the eigenfunctions of Markov matrices as a system of coordinates on the original dataset in order to obtain an efficient representation of data geometric descriptions. Clustering is done using k-means and a neural network clustering theory, Fuzzy ART (FA). The process is done on a subset of core data from AngloGold Ashanti, and compared to results obtained by AngloGold Ashanti\u27s proprietary method. Experimental results show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals in core samples

SpectralDiff: A Generative Framework for Hyperspectral Image Classification with Diffusion Models

Hyperspectral Image (HSI) classification is an important issue in remote sensing field with extensive applications in earth science. In recent years, a large number of deep learning-based HSI classification methods have been proposed. However, existing methods have limited ability to handle high-dimensional, highly redundant, and complex data, making it challenging to capture the spectral-spatial distributions of data and relationships between samples. To address this issue, we propose a generative framework for HSI classification with diffusion models (SpectralDiff) that effectively mines the distribution information of high-dimensional and highly redundant data by iteratively denoising and explicitly constructing the data generation process, thus better reflecting the relationships between samples. The framework consists of a spectral-spatial diffusion module, and an attention-based classification module. The spectral-spatial diffusion module adopts forward and reverse spectral-spatial diffusion processes to achieve adaptive construction of sample relationships without requiring prior knowledge of graphical structure or neighborhood information. It captures spectral-spatial distribution and contextual information of objects in HSI and mines unsupervised spectral-spatial diffusion features within the reverse diffusion process. Finally, these features are fed into the attention-based classification module for per-pixel classification. The diffusion features can facilitate cross-sample perception via reconstruction distribution, leading to improved classification performance. Experiments on three public HSI datasets demonstrate that the proposed method can achieve better performance than state-of-the-art methods. For the sake of reproducibility, the source code of SpectralDiff will be publicly available at https://github.com/chenning0115/SpectralDiff

Extensions of Laplacian Eigenmaps for Manifold Learning

This thesis deals with the theory and practice of manifold learning, especially as they relate to the problem of classification. We begin with a well known algorithm, Laplacian Eigenmaps, and then proceed to extend it in two independent directions. First, we generalize this algorithm to allow for the use of partially labeled data, and establish the theoretical foundation of the resulting semi-supervised learning method. Second, we consider two ways of accelerating the most computationally intensive step of Laplacian Eigenmaps, the construction of an adjacency graph. Both of them produce high quality approximations, and we conclude by showing that they work well together to achieve a dramatic reduction in computational time

Histopathological image analysis : a review

Over the past decade, dramatic increases in computational power and improvement in image analysis algorithms have allowed the development of powerful computer-assisted analytical approaches to radiological data. With the recent advent of whole slide digital scanners, tissue histopathology slides can now be digitized and stored in digital image form. Consequently, digitized tissue histopathology has now become amenable to the application of computerized image analysis and machine learning techniques. Analogous to the role of computer-assisted diagnosis (CAD) algorithms in medical imaging to complement the opinion of a radiologist, CAD algorithms have begun to be developed for disease detection, diagnosis, and prognosis prediction to complement the opinion of the pathologist. In this paper, we review the recent state of the art CAD technology for digitized histopathology. This paper also briefly describes the development and application of novel image analysis technology for a few specific histopathology related problems being pursued in the United States and Europe

Adaptive Resonance Theory and Diffusion Maps for Clustering Applications in Pattern Analysis

Adaptive Resonance is primarily a theory that learning is regulated by resonance phenomena in neural circuits. Diffusion maps are a class of kernel methods on edge-weighted graphs. While either of these approaches have demonstrated success in image analysis, their combination is particularly effective. These techniques are reviewed and some example applications are given

Schroedinger Eigenmaps for Manifold Alignment of Multimodal Hyperspectral Images

Multimodal remote sensing is an upcoming field as it allows for many views of the same region of interest. Domain adaption attempts to fuse these multimodal remotely sensed images by utilizing the concept of transfer learning to understand data from different sources to learn a fused outcome. Semisupervised Manifold Alignment (SSMA) maps multiple Hyperspectral images (HSIs) from high dimensional source spaces to a low dimensional latent space where similar elements reside closely together. SSMA preserves the original geometric structure of respective HSIs whilst pulling similar data points together and pushing dissimilar data points apart. The SSMA algorithm is comprised of a geometric component, a similarity component and dissimilarity component. The geometric component of the SSMA method has roots in the original Laplacian Eigenmaps (LE) dimension reduction algorithm and the projection functions have roots in the original Locality Preserving Projections (LPP) dimensionality reduction framework. The similarity and dissimilarity component is a semisupervised component that allows expert labeled information to improve the image fusion process. Spatial-Spectral Schroedinger Eigenmaps (SSSE) was designed as a semisupervised enhancement to the LE algorithm by augmenting the Laplacian matrix with a user-defined potential function. However, the user-defined enhancement has yet to be explored in the LPP framework. The first part of this thesis proposes to use the Spatial-Spectral potential within the LPP algorithm, creating a new algorithm we call the Schroedinger Eigenmap Projections (SEP). Through experiments on publicly available data with expert-labeled ground truth, we perform experiments to compare the performance of the SEP algorithm with respect to the LPP algorithm. The second part of this thesis proposes incorporating the Spatial Spectral potential from SSSE into the SSMA framework. Using two multi-angled HSI’s, we explore the impact of incorporating this potential into SSMA

Hyperspectral image representation and processing with binary partition trees

The optimal exploitation of the information provided by hyperspectral images requires the development of advanced image processing tools. Therefore, under the title Hyperspectral image representation and Processing with Binary Partition Trees, this PhD thesis proposes the construction and the processing of a new region-based hierarchical hyperspectral image representation: the Binary Partition Tree (BPT). This hierarchical region-based representation can be interpreted as a set of hierarchical regions stored in a tree structure. Hence, the Binary Partition Tree succeeds in presenting: (i) the decomposition of the image in terms of coherent regions and (ii) the inclusion relations of the regions in the scene. Based on region-merging techniques, the construction of BPT is investigated in this work by studying hyperspectral region models and the associated similarity metrics. As a matter of fact, the very high dimensionality and the complexity of the data require the definition of specific region models and similarity measures. Once the BPT is constructed, the fixed tree structure allows implementing efficient and advanced application-dependent techniques on it. The application-dependent processing of BPT is generally implemented through a specific pruning of the tree. Accordingly, some pruning techniques are proposed and discussed according to different applications. This Ph.D is focused in particular on segmentation, object detection and classification of hyperspectral imagery. Experimental results on various hyperspectral data sets demonstrate the interest and the good performances of the BPT representatio

Visualization of hyperspectral images on parallel and distributed platform: Apache Spark

The field of hyperspectral image storage and processing has undergone a remarkable evolution in recent years. The visualization of these images represents a challenge as the number of bands exceeds three bands, since direct visualization using the trivial system red, green and blue (RGB) or hue, saturation and lightness (HSL) is not feasible. One potential solution to resolve this problem is the reduction of the dimensionality of the image to three dimensions and thereafter assigning each dimension to a color. Conventional tools and algorithms have become incapable of producing results within a reasonable time. In this paper, we present a new distributed method of visualization of hyperspectral image based on the principal component analysis (PCA) and implemented in a distributed parallel environment (Apache Spark). The visualization of the big hyperspectral images with the proposed method is made in a smaller time and with the same performance as the classical method of visualization