Spectral Detection on Sparse Hypergraphs

We consider the problem of the assignment of nodes into communities from a set of hyperedges, where every hyperedge is a noisy observation of the community assignment of the adjacent nodes. We focus in particular on the sparse regime where the number of edges is of the same order as the number of vertices. We propose a spectral method based on a generalization of the non-backtracking Hashimoto matrix into hypergraphs. We analyze its performance on a planted generative model and compare it with other spectral methods and with Bayesian belief propagation (which was conjectured to be asymptotically optimal for this model). We conclude that the proposed spectral method detects communities whenever belief propagation does, while having the important advantages to be simpler, entirely nonparametric, and to be able to learn the rule according to which the hyperedges were generated without prior information.Comment: 8 pages, 5 figure

Lidar waveform based analysis of depth images constructed using sparse single-photon data

This paper presents a new Bayesian model and algorithm used for depth and intensity profiling using full waveforms from the time-correlated single photon counting (TCSPC) measurement in the limit of very low photon counts. The model proposed represents each Lidar waveform as a combination of a known impulse response, weighted by the target intensity, and an unknown constant background, corrupted by Poisson noise. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters and their constraints. In particular, a gamma Markov random field (MRF) is used to model the joint distribution of the target intensity, and a second MRF is used to model the distribution of the target depth, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to compute the Bayesian estimates of interest and perform Bayesian inference. This algorithm is equipped with a stochastic optimization adaptation mechanism that automatically adjusts the parameters of the MRFs by maximum marginal likelihood estimation. Finally, the benefits of the proposed methodology are demonstrated through a serie of experiments using real data

Unsupervised learning for long-term autonomy

This thesis investigates methods to enable a robot to build and maintain an environment model in an automatic manner. Such capabilities are especially important in long-term autonomy, where robots operate for extended periods of time without human intervention. In such scenarios we can no longer assume that the environment and the models will remain static. Rather changes are expected and the robot needs to adapt to the new, unseen, circumstances automatically. The approach described in this thesis is based on clustering the robot’s sensing information. This provides a compact representation of the data which can be updated as more information becomes available. The work builds on affinity propagation (Frey and Dueck, 2007), a recent clustering method which obtains high quality clusters while only requiring similarities between pairs of points, and importantly, selecting the number of clusters automatically. This is essential for real autonomy as we typically do not know “a priori” how many clusters best represent the data. The contributions of this thesis a three fold. First a self-supervised method capable of learning a visual appearance model in long-term autonomy settings is presented. Secondly, affinity propagation is extended to handle multiple sensor modalities, often occurring in robotics, in a principle way. Third, a method for joint clustering and outlier selection is proposed which selects a user defined number of outlier while clustering the data. This is solved using an extension of affinity propagation as well as a Lagrangian duality approach which provides guarantees on the optimality of the solution

Disentangled Autoencoder for Cross-Stain Feature Extraction in Pathology Image Analysis

A novel deep autoencoder architecture is proposed for the analysis of histopathology images. Its purpose is to produce a disentangled latent representation in which the structure and colour information are confined to different subspaces so that stain-independent models may be learned. For this, we introduce two constraints on the representation which are implemented as a classifier and an adversarial discriminator. We show how they can be used for learning a latent representation across haematoxylin-eosin and a number of immune stains. Finally, we demonstrate the utility of the proposed representation in the context of matching image patches for registration applications and for learning a bag of visual words for whole slide image summarization

Algebraic graph theory in the analysis of frequency assignment problems

Frequency Assignment Problems (FAPs) arise when transmitters need to be allocated frequencies with the aim of minimizing interference, whilst maintaining an efficient use of the radio spectrum. In this thesis FAPs are seen as generalised graph colouring problems, where transmitters are represented by vertices, and their interactions by weighted edges. Solving FAPs often relies on known structural properties to facilitate algorithms. When no structural information is available explicitly, obtaining it from numerical data is difficult. This lack of structural information is a key underlying motivation for the research work in this thesis. If there are TV transmitters to be assigned, we assume as given an N x N "influence matrix" W with entries Wij representing influence between transmitters i and j. From this matrix we derive the Laplacian matrix L = D—W, where D is a diagonal matrix whose entries da are the sum of all influences working in transmitter i. The focus of this thesis is the study of mathematical properties of the matrix L. We généralisé certain properties of the Laplacian eigenvalues and eigenvectors that hold for simple graphs. We also observe and discuss changes in the shape of the Laplacian eigenvalue spectrum due to modifications of a FAP. We include a number of computational experiments and generated simulated examples of FAPs for which we explicitly calculate eigenvalues and eigenvectors in order to test the developed theoretical results. We find that the Laplacians prove useful in identifying certain types of problems, providing structured approach to reducing the original FAP to smaller size subproblems, hence assisting existing heuristic algorithms for solving frequency assignments. In that sense we conclude that analysis of the Laplacians is a useful tool for better understanding of FAPs