Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. The first algorithm, called Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image super-resolution, deblurring and denoising applications and shown to outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Low-shot learning with large-scale diffusion

This paper considers the problem of inferring image labels from images when only a few annotated examples are available at training time. This setup is often referred to as low-shot learning, where a standard approach is to re-train the last few layers of a convolutional neural network learned on separate classes for which training examples are abundant. We consider a semi-supervised setting based on a large collection of images to support label propagation. This is possible by leveraging the recent advances on large-scale similarity graph construction. We show that despite its conceptual simplicity, scaling label propagation up to hundred millions of images leads to state of the art accuracy in the low-shot learning regime

Contribution to Graph-based Manifold Learning with Application to Image Categorization.

122 pLos algoritmos de aprendizaje de variedades basados en grafos (Graph,based manifold) son técnicas que han demostrado ser potentes herramientas para la extracción de características y la reducción de la dimensionalidad en los campos de reconomiento de patrones, visión por computador y aprendizaje automático. Estos algoritmos utilizan información basada en las similitudes de pares de muestras y del grafo ponderado resultante para revelar la estructura geométrica intrínseca de la variedad

Contribution to Graph-based Manifold Learning with Application to Image Categorization.

122 pLos algoritmos de aprendizaje de variedades basados en grafos (Graph,based manifold) son técnicas que han demostrado ser potentes herramientas para la extracción de características y la reducción de la dimensionalidad en los campos de reconomiento de patrones, visión por computador y aprendizaje automático. Estos algoritmos utilizan información basada en las similitudes de pares de muestras y del grafo ponderado resultante para revelar la estructura geométrica intrínseca de la variedad

Inferring a Transcriptional Regulatory Network from Gene Expression Data Using Nonlinear Manifold Embedding

Transcriptional networks consist of multiple regulatory layers corresponding to the activity of global regulators, specialized repressors and activators of transcription as well as proteins and enzymes shaping the DNA template. Such intrinsic multi-dimensionality makes uncovering connectivity patterns difficult and unreliable and it calls for adoption of methodologies commensurate with the underlying organization of the data source. Here we present a new computational method that predicts interactions between transcription factors and target genes using a compendium of microarray gene expression data and the knowledge of known interactions between genes and transcription factors. The proposed method called Kernel Embedding of REgulatory Networks (KEREN) is based on the concept of gene-regulon association and it captures hidden geometric patterns of the network via manifold embedding. We applied KEREN to reconstruct gene regulatory interactions in the model bacteria E.coli on a genome-wide scale. Our method not only yields accurate prediction of verifiable interactions, which outperforms on certain metrics comparable methodologies, but also demonstrates the utility of a geometric approach to the analysis of high-dimensional biological data. We also describe the general application of kernel embedding techniques to some other function and network discovery algorithms

Physics based supervised and unsupervised learning of graph structure

Graphs are central tools to aid our understanding of biological, physical, and social systems. Graphs also play a key role in representing and understanding the visual world around us, 3D-shapes and 2D-images alike. In this dissertation, I propose the use of physical or natural phenomenon to understand graph structure. I investigate four phenomenon or laws in nature: (1) Brownian motion, (2) Gauss\u27s law, (3) feedback loops, and (3) neural synapses, to discover patterns in graphs