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

Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring

Density-sensitive semisupervised inference

Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$ of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of $P_X$. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a minimax framework for analyzing semisupervised methods. In particular, we study methods based on metrics that are sensitive to the distribution $P_X$. Our model includes a parameter $\alpha$ that controls the strength of the semisupervised assumption. We then use the data to adapt to $\alpha$.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1092 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Doctor of Philosophy

dissertationThe goal of machine learning is to develop efficient algorithms that use training data to create models that generalize well to unseen data. Learning algorithms can use labeled data, unlabeled data or both. Supervised learning algorithms learn a model using labeled data only. Unsupervised learning methods learn the internal structure of a dataset using only unlabeled data. Lastly, semisupervised learning is the task of finding a model using both labeled and unlabeled data. In this research work, we contribute to both supervised and semisupervised learning. We contribute to supervised learning by proposing an efficient high-dimensional space coverage scheme which is based on the disjunctive normal form. We use conjunctions of a set of half-spaces to create a set of convex polytopes. Disjunction of these polytopes can provide desirable coverage of space. Unlike traditional methods based on neural networks, we do not initialize the model parameters randomly. As a result, our model minimizes the risk of poor local minima and higher learning rates can be used which leads to faster convergence. We contribute to semisupervised learning by proposing 2 unsupervised loss functions that form the basis of a novel semisupervised learning method. The first loss function is called Mutual-Exclusivity. The motivation of this method is the observation that an optimal decision boundary lies between the manifolds of different classes where there are no or very few samples. Decision boundaries can be pushed away from training samples by maximizing their margin and it is not necessary to know the class labels of the samples to maximize the margin. The second loss is named Transformation/Stability and is based on the fact that the prediction of a classifier for a data sample should not change with respect to transformations and perturbations applied to that data sample. In addition, internal variations of a learning system should have little to no effect on the output. The proposed loss minimizes the variation in the prediction of the network for a specific data sample. We also show that the same technique can be used to improve the robustness of a learning model with respect to adversarial examples

LASS: a simple assignment model with Laplacian smoothing

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity matrix, which encourages similar items to have similar assignments. We propose a simple quadratic programming model that captures this intuition. We give necessary conditions for its solution to be unique, define an out-of-sample mapping, and derive a simple, effective training algorithm based on the alternating direction method of multipliers. The model predicts reasonable assignments from even a few similarity values, and can be seen as a generalization of semisupervised learning. It is particularly useful when items naturally belong to multiple categories, as for example when annotating documents with keywords or pictures with tags, with partially tagged items, or when the categories have complex interrelations (e.g. hierarchical) that are unknown.Comment: 20 pages, 4 figures. A shorter version appears in AAAI 201

Applicability of semi-supervised learning assumptions for gene ontology terms prediction

Gene Ontology (GO) is one of the most important resources in bioinformatics, aiming to provide a unified framework for the biological annotation of genes and proteins across all species. Predicting GO terms is an essential task for bioinformatics, but the number of available labelled proteins is in several cases insufficient for training reliable machine learning classifiers. Semi-supervised learning methods arise as a powerful solution that explodes the information contained in unlabelled data in order to improve the estimations of traditional supervised approaches. However, semi-supervised learning methods have to make strong assumptions about the nature of the training data and thus, the performance of the predictor is highly dependent on these assumptions. This paper presents an analysis of the applicability of semi-supervised learning assumptions over the specific task of GO terms prediction, focused on providing judgment elements that allow choosing the most suitable tools for specific GO terms. The results show that semi-supervised approaches significantly outperform the traditional supervised methods and that the highest performances are reached when applying the cluster assumption. Besides, it is experimentally demonstrated that cluster and manifold assumptions are complimentary to each other and an analysis of which GO terms can be more prone to be correctly predicted with each assumption, is provided.Postprint (published version