Community detection for correlation matrices

A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that tends to be intrinsically biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anti-correlated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested sub-communities with `hard' cores and `soft' peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy, detect `soft stocks' that alternate between communities, and discuss implications for portfolio optimization and risk management.Comment: Final version, accepted for publication on PR

Adaptive multiresolution search: How to beat brute force?

AbstractMultiresolution and wavelet-based search methods are suited to problems for which acceptable solutions are in regions of high average local fitness. In this paper, two different approaches are presented. In the Markov-based approach, the sampling resolution is chosen adaptively depending on the fitness of the last sample(s). The advantage of this method, behind its simplicity, is that it allows the computation of the discovery probability of a target sample for quite large search spaces. This permits to “reverse-engineer” search-and-optimization problems. Starting from some prototypic examples of fitness functions the discovery rate can be computed as a function of the free parameters. The second approach is a wavelet-based multiresolution search using a memory to store local average values of the fitness functions. The sampling density probability is chosen per design proportional to a low-resolution approximation of the fitness function. High average fitness regions are sampled more often, and at a higher resolution, than low average fitness regions. If splines are used as scaling mother functions, a fuzzy description of the search strategy can be given within the framework of the Takagi–Sugeno model

Statistical Mechanics of the Community Detection Problem: Theory and Application

We study phase transitions in spin glass type systems and in related computational problems. In the current work, we focus on the community detection problem when cast in terms of a general Potts spin glass type problem. We report on phase transitions between solvable and unsolvable regimes. Solvable region may further split into easy and hard phases. Spin glass type phase transitions appear at both low and high temperatures. Low temperature transitions correspond to an order by disorder type effect wherein fluctuations render the system ordered or solvable. Separate transitions appear at higher temperatures into a disordered: or an unsolvable) phases. Different sorts of randomness lead to disparate behaviors. We illustrate the spin glass character of both transitions and report on memory effects. We further relate Potts type spin systems to mechanical analogs and suggest how chaotic-type behavior in general thermodynamic systems can indeed naturally arise in hard-computational problems and spin-glasses. In this work, we also examine large networks: with a power law distribution in cluster size) that have a large number of communities. We infer that large systems at a constant ratio of q to the number of nodes N asymptotically tend toward insolvability in the limit of large N for any positive temperature. We further employ multivariate Tutte polynomials to show that increasing q emulates increasing T for a general Potts model, leading to a similar stability region at low T. We further apply the replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of community detection and its phase diagram. The problem is cast as identifying tightly bound clusters against a background. Within our multiresolution approach, we compute information theory based correlations among multiple solutions of the same graph over a range of resolutions. Significant multiresolution structures are identified by replica correlations as manifest in information overlaps. With the aid of these correlations as well as thermodynamic measures, the phase diagram of the corresponding Potts model is analyzed both at zero and finite temperatures. Optimal parameters corresponding to a sensible unsupervised segmentation correspond to the easy phase of the Potts model. Our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflage images

Histopathological image analysis : a review

Over the past decade, dramatic increases in computational power and improvement in image analysis algorithms have allowed the development of powerful computer-assisted analytical approaches to radiological data. With the recent advent of whole slide digital scanners, tissue histopathology slides can now be digitized and stored in digital image form. Consequently, digitized tissue histopathology has now become amenable to the application of computerized image analysis and machine learning techniques. Analogous to the role of computer-assisted diagnosis (CAD) algorithms in medical imaging to complement the opinion of a radiologist, CAD algorithms have begun to be developed for disease detection, diagnosis, and prognosis prediction to complement the opinion of the pathologist. In this paper, we review the recent state of the art CAD technology for digitized histopathology. This paper also briefly describes the development and application of novel image analysis technology for a few specific histopathology related problems being pursued in the United States and Europe

MRF-based image segmentation using Ant Colony System

In this paper, we propose a novel method for image segmentation that we call ACS-MRF method. ACS-MRF is a hybrid ant colony system coupled with a local search. We show how a colony of cooperating ants are able to estimate the labels field and minimize the MAP estimate. Cooperation between ants is performed by exchanging information through pheromone updating. The obtained results show the efficiency of the new algorithm, which is able to compete with other stochastic optimization methods like Simulated annealing and Genetic algorithm in terms of solution quality

Multiresolution neural networks for image edge detection and restoration

One of the methods for building an automatic visual system is to borrow the properties of the human visual system (HVS). Artificial neural networks are based on this doctrine and they have been applied to image processing and computer vision. This work focused on the plausibility of using a class of Hopfield neural networks for edge detection and image restoration. To this end, a quadratic energy minimization framework is presented. Central to this framework are relaxation operations, which can be implemented using the class of Hopfield neural networks. The role of the uncertainty principle in vision is described, which imposes a limit on the simultaneous localisation in both class and position space. It is shown how a multiresolution approach allows the trade off between position and class resolution and ensures both robustness in noise and efficiency of computation. As edge detection and image restoration are ill-posed, some a priori knowledge is needed to regularize these problems. A multiresolution network is proposed to tackle the uncertainty problem and the regularization of these ill-posed image processing problems. For edge detection, orientation information is used to construct a compatibility function for the strength of the links of the proposed Hopfield neural network. Edge detection 'results are presented for a number of synthetic and natural images which show that the iterative network gives robust results at low signal-to-noise ratios (0 dB) and is at least as good as many previous methods at capturing complex region shapes. For restoration, mean square error is used as the quadratic energy function of the Hopfield neural network. The results of the edge detection are used for adaptive restoration. Also shown are the results of restoration using the proposed iterative network framework

AUTOMATIC 3D DEFORMED MIDSAGITTAL SURFACE LOCALIZATION BY CONSTRAINED MONTE CARLO OPTIMIZATION

AUTOMATIC 3D DEFORMED MIDSAGITTAL SURFACE LOCALIZATION BY CONSTRAINED MONTE CARLO OPTIMIZATIO

Query of image content using Wavelets and Gibbs-Markov Random Fields

The central theme of this thesis is the application of Wavelets and Random Processes to content-based image query (on texture patterns, in particular). Given a query image, a content-based search extracts a certain representative measure (or signature) from the query image and likewise for all the target images in the search archive. A good representative measure is one that provides us with the ability to differentiate easily between different patterns. A distance measure is computed between the query properties and the properties of each of the target images. The lowest distance measure gives us the best target match for the particular query. Typically, the measure extraction on the target archive is performed as a pre-processing step. The thesis features two different methods of measure extraction. The first one is a wavelet based measure extraction method. It builds upon a previously documented method, but adds subtle modifications to it so that it now lends much much more effectiveness to pattern matching on texture patterns and on images of unequal sizes. The modified algorithm as well as the mathematics behind it is presented. The second method uses a Markov Random Field to model the texture properties of regions within an image. The parameters of the model serve as the texture measure or signature. Wavelet-based multiresolution is then used to speed up the search. The theory of Markov Random Fields, their equivalence with Gibbs Random Fields, the Hammerseley-Clifford theorem and parameter estimation techniques are presented. In addition to pattern matching these texture signatures have also be used for controlled image smoothing and texture generation. The results from both methods are encouraging. One hopes that these methods find widespread use in image query applications

Registration of Brain MRI/PET Images Based on Adaptive Combination of Intensity and Gradient Field Mutual Information

Traditional mutual information (MI) function aligns two multimodality images with intensity information, lacking spatial information, so that it usually presents many local maxima that can lead to inaccurate registration. Our paper proposes an algorithm of adaptive combination of intensity and gradient field mutual information (ACMI). Gradient code maps (GCM) are constructed by coding gradient field information of corresponding original images. The gradient field MI, calculated from GCMs, can provide complementary properties to intensity MI. ACMI combines intensity MI and gradient field MI with a nonlinear weight function, which can automatically adjust the proportion between two types MI in combination to improve registration. Experimental results demonstrate that ACMI outperforms the traditional MI and it is much less sensitive to reduced resolution or overlap of images