Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods

Hyperspectral images show similar statistical properties to natural grayscale or color photographic images. However, the classification of hyperspectral images is more challenging because of the very high dimensionality of the pixels and the small number of labeled examples typically available for learning. These peculiarities lead to particular signal processing problems, mainly characterized by indetermination and complex manifolds. The framework of statistical learning has gained popularity in the last decade. New methods have been presented to account for the spatial homogeneity of images, to include user's interaction via active learning, to take advantage of the manifold structure with semisupervised learning, to extract and encode invariances, or to adapt classifiers and image representations to unseen yet similar scenes. This tutuorial reviews the main advances for hyperspectral remote sensing image classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201

Positive Definite Kernels in Machine Learning

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x,\cdot),x\in\mathcal{X}\}$ associated with a kernel $k$ defined on a space $\mathcal{X}$. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain data-types such as images, graphs or speech segments.Comment: draft. corrected a typo in figure

Domain Adaptation on Graphs by Learning Aligned Graph Bases

A common assumption in semi-supervised learning with graph models is that the class label function varies smoothly on the data graph, resulting in the rather strict prior that the label function has low-frequency content. Meanwhile, in many classification problems, the label function may vary abruptly in certain graph regions, resulting in high-frequency components. Although the semi-supervised estimation of class labels is an ill-posed problem in general, in several applications it is possible to find a source graph on which the label function has similar frequency content to that on the target graph where the actual classification problem is defined. In this paper, we propose a method for domain adaptation on graphs motivated by these observations. Our algorithm is based on learning the spectrum of the label function in a source graph with many labeled nodes, and transferring the information of the spectrum to the target graph with fewer labeled nodes. While the frequency content of the class label function can be identified through the graph Fourier transform, it is not easy to transfer the Fourier coefficients directly between the two graphs, since no one-to-one match exists between the Fourier basis vectors of independently constructed graphs in the domain adaptation setting. We solve this problem by learning a transformation between the Fourier bases of the two graphs that flexibly ``aligns'' them. The unknown class label function on the target graph is then reconstructed such that its spectrum matches that on the source graph while also ensuring the consistency with the available labels. The proposed method is tested in the classification of image, online product review, and social network data sets. Comparative experiments suggest that the proposed algorithm performs better than recent domain adaptation methods in the literature in most settings

Graph-based Semi-supervised Learning: Algorithms and Applications.

114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results

Line Based Multi-Range Asymmetric Conditional Random Field For Terrestrial Laser Scanning Data Classification

Terrestrial Laser Scanning (TLS) is a ground-based, active imaging method that rapidly acquires accurate, highly dense three-dimensional point cloud of object surfaces by laser range finding. For fully utilizing its benefits, developing a robust method to classify many objects of interests from huge amounts of laser point clouds is urgently required. However, classifying massive TLS data faces many challenges, such as complex urban scene, partial data acquisition from occlusion. To make an automatic, accurate and robust TLS data classification, we present a line-based multi-range asymmetric Conditional Random Field algorithm. The first contribution is to propose a line-base TLS data classification method. In this thesis, we are interested in seven classes: building, roof, pedestrian road (PR), tree, low man-made object (LMO), vehicle road (VR), and low vegetation (LV). The line-based classification is implemented in each scan profile, which follows the line profiling nature of laser scanning mechanism.Ten conventional local classifiers are tested, including popular generative and discriminative classifiers, and experimental results validate that the line-based method can achieve satisfying classification performance. However, local classifiers implement labeling task on individual line independently of its neighborhood, the inference of which often suffers from similar local appearance across different object classes. The second contribution is to propose a multi-range asymmetric Conditional Random Field (maCRF) model, which uses object context as post-classification to improve the performance of a local generative classifier. The maCRF incorporates appearance, local smoothness constraint, and global scene layout regularity together into a probabilistic graphical model. The local smoothness enforces that lines in a local area to have the same class label, while scene layout favours an asymmetric regularity of spatial arrangement between different object classes within long-range, which is considered both in vertical (above-bellow relation) and horizontal (front-behind) directions. The asymmetric regularity allows capturing directional spatial arrangement between pairwise objects (e.g. it allows ground is lower than building, not vice-versa). The third contribution is to extend the maCRF model by adding across scan profile context, which is called Across scan profile Multi-range Asymmetric Conditional Random Field (amaCRF) model. Due to the sweeping nature of laser scanning, the sequentially acquired TLS data has strong spatial dependency, and the across scan profile context can provide more contextual information. The final contribution is to propose a sequential classification strategy. Along the sweeping direction of laser scanning, amaCRF models were sequentially constructed. By dynamically updating posterior probability of common scan profiles, contextual information propagates through adjacent scan profiles