Non-adaptive pooling strategies for detection of rare faulty items

We study non-adaptive pooling strategies for detection of rare faulty items. Given a binary sparse N-dimensional signal x, how to construct a sparse binary MxN pooling matrix F such that the signal can be reconstructed from the smallest possible number M of measurements y=Fx? We show that a very low number of measurements is possible for random spatially coupled design of pools F. Our design might find application in genetic screening or compressed genotyping. We show that our results are robust with respect to the uncertainty in the matrix F when some elements are mistaken.Comment: 5 page

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Compressed Genotyping

Significant volumes of knowledge have been accumulated in recent years linking subtle genetic variations to a wide variety of medical disorders from Cystic Fibrosis to mental retardation. Nevertheless, there are still great challenges in applying this knowledge routinely in the clinic, largely due to the relatively tedious and expensive process of DNA sequencing. Since the genetic polymorphisms that underlie these disorders are relatively rare in the human population, the presence or absence of a disease-linked polymorphism can be thought of as a sparse signal. Using methods and ideas from compressed sensing and group testing, we have developed a cost-effective genotyping protocol. In particular, we have adapted our scheme to a recently developed class of high throughput DNA sequencing technologies, and assembled a mathematical framework that has some important distinctions from 'traditional' compressed sensing ideas in order to address different biological and technical constraints.Comment: Submitted to IEEE Transaction on Information Theory - Special Issue on Molecular Biology and Neuroscienc

Learning Multimodal Structures in Computer Vision

A phenomenon or event can be received from various kinds of detectors or under different conditions. Each such acquisition framework is a modality of the phenomenon. Due to the relation between the modalities of multimodal phenomena, a single modality cannot fully describe the event of interest. Since several modalities report on the same event introduces new challenges comparing to the case of exploiting each modality separately. We are interested in designing new algorithmic tools to apply sensor fusion techniques in the particular signal representation of sparse coding which is a favorite methodology in signal processing, machine learning and statistics to represent data. This coding scheme is based on a machine learning technique and has been demonstrated to be capable of representing many modalities like natural images. We will consider situations where we are not only interested in support of the model to be sparse, but also to reflect a-priorily known knowledge about the application in hand. Our goal is to extract a discriminative representation of the multimodal data that leads to easily finding its essential characteristics in the subsequent analysis step, e.g., regression and classification. To be more precise, sparse coding is about representing signals as linear combinations of a small number of bases from a dictionary. The idea is to learn a dictionary that encodes intrinsic properties of the multimodal data in a decomposition coefficient vector that is favorable towards the maximal discriminatory power. We carefully design a multimodal representation framework to learn discriminative feature representations by fully exploiting, the modality-shared which is the information shared by various modalities, and modality-specific which is the information content of each modality individually. Plus, it automatically learns the weights for various feature components in a data-driven scheme. In other words, the physical interpretation of our learning framework is to fully exploit the correlated characteristics of the available modalities, while at the same time leverage the modality-specific character of each modality and change their corresponding weights for different parts of the feature in recognition

NON-LINEAR AND SPARSE REPRESENTATIONS FOR MULTI-MODAL RECOGNITION

In the first part of this dissertation, we address the problem of representing 2D and 3D shapes. In particular, we introduce a novel implicit shape representation based on Support Vector Machine (SVM) theory. Each shape is represented by an analytic decision function obtained by training an SVM, with a Radial Basis Function (RBF) kernel, so that the interior shape points are given higher values. This empowers support vector shape (SVS) with multifold advantages. First, the representation uses a sparse subset of feature points determined by the support vectors, which significantly improves the discriminative power against noise, fragmentation and other artifacts that often come with the data. Second, the use of the RBF kernel provides scale, rotation, and translation invariant features, and allows a shape to be represented accurately regardless of its complexity. Finally, the decision function can be used to select reliable feature points. These features are described using gradients computed from highly consistent decision functions instead of conventional edges. Our experiments on 2D and 3D shapes demonstrate promising results. The availability of inexpensive 3D sensors like Kinect necessitates the design of new representation for this type of data. We present a 3D feature descriptor that represents local topologies within a set of folded concentric rings by distances from local points to a projection plane. This feature, called as Concentric Ring Signature (CORS), possesses similar computational advantages to point signatures yet provides more accurate matches. CORS produces compact and discriminative descriptors, which makes it more robust to noise and occlusions. It is also well-known to computer vision researchers that there is no universal representation that is optimal for all types of data or tasks. Sparsity has proved to be a good criterion for working with natural images. This motivates us to develop efficient sparse and non-linear learning techniques for automatically extracting useful information from visual data. Specifically, we present dictionary learning methods for sparse and redundant representations in a high-dimensional feature space. Using the kernel method, we describe how the well-known dictionary learning approaches such as the method of optimal directions and KSVD can be made non-linear. We analyse their kernel constructions and demonstrate their effectiveness through several experiments on classification problems. It is shown that non-linear dictionary learning approaches can provide significantly better discrimination compared to their linear counterparts and kernel PCA, especially when the data is corrupted by different types of degradations. Visual descriptors are often high dimensional. This results in high computational complexity for sparse learning algorithms. Motivated by this observation, we introduce a novel framework, called sparse embedding (SE), for simultaneous dimensionality reduction and dictionary learning. We formulate an optimization problem for learning a transformation from the original signal domain to a lower-dimensional one in a way that preserves the sparse structure of data. We propose an efficient optimization algorithm and present its non-linear extension based on the kernel methods. One of the key features of our method is that it is computationally efficient as the learning is done in the lower-dimensional space and it discards the irrelevant part of the signal that derails the dictionary learning process. Various experiments show that our method is able to capture the meaningful structure of data and can perform significantly better than many competitive algorithms on signal recovery and object classification tasks. In many practical applications, we are often confronted with the situation where the data that we use to train our models are different from that presented during the testing. In the final part of this dissertation, we present a novel framework for domain adaptation using a sparse and hierarchical network (DASH-N), which makes use of the old data to improve the performance of a system operating on a new domain. Our network jointly learns a hierarchy of features together with transformations that rectify the mismatch between different domains. The building block of DASH-N is the latent sparse representation. It employs a dimensionality reduction step that can prevent the data dimension from increasing too fast as traversing deeper into the hierarchy. Experimental results show that our method consistently outperforms the current state-of-the-art by a significant margin. Moreover, we found that a multi-layer {DASH-N} has an edge over the single-layer DASH-N

Graph-based techniques for compression and reconstruction of sparse sources

The main goal of this thesis is to develop lossless compression schemes for analog and binary sources. All the considered compression schemes have as common feature that the encoder can be represented by a graph, so they can be studied employing tools from modern coding theory. In particular, this thesis is focused on two compression problems: the group testing and the noiseless compressed sensing problems. Although both problems may seem unrelated, in the thesis they are shown to be very close. Furthermore, group testing has the same mathematical formulation as non-linear binary source compression schemes that use the OR operator. In this thesis, the similarities between these problems are exploited. The group testing problem is aimed at identifying the defective subjects of a population with as few tests as possible. Group testing schemes can be divided into two groups: adaptive and non-adaptive group testing schemes. The former schemes generate tests sequentially and exploit the partial decoding results to attempt to reduce the overall number of tests required to label all members of the population, whereas non-adaptive schemes perform all the test in parallel and attempt to label as many subjects as possible. Our contributions to the group testing problem are both theoretical and practical. We propose a novel adaptive scheme aimed to efficiently perform the testing process. Furthermore, we develop tools to predict the performance of both adaptive and non-adaptive schemes when the number of subjects to be tested is large. These tools allow to characterize the performance of adaptive and non-adaptive group testing schemes without simulating them. The goal of the noiseless compressed sensing problem is to retrieve a signal from its lineal projection version in a lower-dimensional space. This can be done only whenever the amount of null components of the original signal is large enough. Compressed sensing deals with the design of sampling schemes and reconstruction algorithms that manage to reconstruct the original signal vector with as few samples as possible. In this thesis we pose the compressed sensing problem within a probabilistic framework, as opposed to the classical compression sensing formulation. Recent results in the state of the art show that this approach is more efficient than the classical one. Our contributions to noiseless compressed sensing are both theoretical and practical. We deduce a necessary and sufficient matrix design condition to guarantee that the reconstruction is lossless. Regarding the design of practical schemes, we propose two novel reconstruction algorithms based on message passing over the sparse representation of the matrix, one of them with very low computational complexity.El objetivo principal de la tesis es el desarrollo de esquemas de compresión sin pérdidas para fuentes analógicas y binarias. Los esquemas analizados tienen en común la representación del compresor mediante un grafo; esto ha permitido emplear en su estudio las herramientas de codificación modernas. Más concretamente la tesis estudia dos problemas de compresión en particular: el diseño de experimentos de testeo comprimido de poblaciones (de sangre, de presencia de elementos contaminantes, secuenciado de ADN, etcétera) y el muestreo comprimido de señales reales en ausencia de ruido. A pesar de que a primera vista parezcan problemas totalmente diferentes, en la tesis mostramos que están muy relacionados. Adicionalmente, el problema de testeo comprimido de poblaciones tiene una formulación matemática idéntica a los códigos de compresión binarios no lineales basados en puertas OR. En la tesis se explotan las similitudes entre todos estos problemas. Existen dos aproximaciones al testeo de poblaciones: el testeo adaptativo y el no adaptativo. El primero realiza los test de forma secuencial y explota los resultados parciales de estos para intentar reducir el número total de test necesarios, mientras que el segundo hace todos los test en bloque e intenta extraer el máximo de datos posibles de los test. Nuestras contribuciones al problema de testeo comprimido han sido tanto teóricas como prácticas. Hemos propuesto un nuevo esquema adaptativo para realizar eficientemente el proceso de testeo. Además hemos desarrollado herramientas que permiten predecir el comportamiento tanto de los esquemas adaptativos como de los esquemas no adaptativos cuando el número de sujetos a testear es elevado. Estas herramientas permiten anticipar las prestaciones de los esquemas de testeo sin necesidad de simularlos. El objetivo del muestreo comprimido es recuperar una señal a partir de su proyección lineal en un espacio de menor dimensión. Esto sólo es posible si se asume que la señal original tiene muchas componentes que son cero. El problema versa sobre el diseño de matrices y algoritmos de reconstrucción que permitan implementar esquemas de muestreo y reconstrucción con un número mínimo de muestras. A diferencia de la formulación clásica de muestreo comprimido, en esta tesis se ha empleado un modelado probabilístico de la señal. Referencias recientes en la literatura demuestran que este enfoque permite conseguir esquemas de compresión y descompresión más eficientes. Nuestras contribuciones en el campo de muestreo comprimido de fuentes analógicas dispersas han sido también teóricas y prácticas. Por un lado, la deducción de la condición necesaria y suficiente que debe garantizar la matriz de muestreo para garantizar que se puede reconstruir unívocamente la secuencia de fuente. Por otro lado, hemos propuesto dos algoritmos, uno de ellos de baja complejidad computacional, que permiten reconstruir la señal original basados en paso de mensajes entre los nodos de la representación gráfica de la matriz de proyección.Postprint (published version

Sparse feature learning for image analysis in segmentation, classification, and disease diagnosis.

The success of machine learning algorithms generally depends on intermediate data representation, called features that disentangle the hidden factors of variation in data. Moreover, machine learning models are required to be generalized, in order to reduce the specificity or bias toward the training dataset. Unsupervised feature learning is useful in taking advantage of large amount of unlabeled data, which is available to capture these variations. However, learned features are required to capture variational patterns in data space. In this dissertation, unsupervised feature learning with sparsity is investigated for sparse and local feature extraction with application to lung segmentation, interpretable deep models, and Alzheimer\u27s disease classification. Nonnegative Matrix Factorization, Autoencoder and 3D Convolutional Autoencoder are used as architectures or models for unsupervised feature learning. They are investigated along with nonnegativity, sparsity and part-based representation constraints for generalized and transferable feature extraction

Applied Harmonic Analysis and Data Processing

Massive data sets have their own architecture. Each data source has an inherent structure, which we should attempt to detect in order to utilize it for applications, such as denoising, clustering, anomaly detection, knowledge extraction, or classification. Harmonic analysis revolves around creating new structures for decomposition, rearrangement and reconstruction of operators and functions—in other words inventing and exploring new architectures for information and inference. Two previous very successful workshops on applied harmonic analysis and sparse approximation have taken place in 2012 and in 2015. This workshop was the an evolution and continuation of these workshops and intended to bring together world leading experts in applied harmonic analysis, data analysis, optimization, statistics, and machine learning to report on recent developments, and to foster new developments and collaborations