arXiv subjects

Hamid Krim

Publications and source records attributed to Hamid Krim.

51 records · Page 3Linked to original sources

arXiv2017

Information diffusion in interconnected heterogeneous networks

In this paper, we are interested in modeling the diffusion of information in a multilayer network using thermodynamic diffusion approach. State of each agent is viewed as a topic mixture represented by a distribution over multiple topics. We have observed and learned diffusion-related thermodynamical patterns in the training data set, and we have used the estimated diffusion structure to predict the future states of the agents. A priori knowledge of a fraction of the state of all agents changes the problem to be a Kalman predictor problem that refines the predicted system state using the error in estimation of the agents. A real world Twitter data set is then used to evaluate and validate our information diffusion model.

cs.SI↗

arXiv2017

First Study on Data Readiness Level

We introduce the idea of Data Readiness Level (DRL) to measure the relative richness of data to answer specific questions often encountered by data scientists. We first approach the problem in its full generality explaining its desired mathematical properties and applications and then we propose and study two DRL metrics. Specifically, we define DRL as a function of at least four properties of data: Noisiness, Believability, Relevance, and Coherence. The information-theoretic based metrics, Cosine Similarity and Document Disparity, are proposed as indicators of Relevance and Coherence for a piece of data. The proposed metrics are validated through a text-based experiment using Twitter data.

cs.IR↗

arXiv2016

Effective Connectivity-Based Neural Decoding: A Causal Interaction-Driven Approach

We propose a geometric model-free causality measurebased on multivariate delay embedding that can efficiently detect linear and nonlinear causal interactions between time series with no prior information. We then exploit the proposed causal interaction measure in real MEG data analysis. The results are used to construct effective connectivity maps of brain activity to decode different categories of visual stimuli. Moreover, we discovered that the MEG-based effective connectivity maps as a response to structured images exhibit more geometric patterns, as disclosed by analyzing the evolution of toplogical structures of the underlying networks using persistent homology. Extensive simulation and experimental result have been carried out to substantiate the capabilities of the proposed approach.

cs.NE↗

arXiv2016

Information Diffusion of Topic Propagation in Social Media

Real-world social and/or operational networks consist of agents with associated states, whose connectivity forms complex topologies. This complexity is further compounded by interconnected information layers, consisting, for instance, documents/resources of the agents which mutually share topical similarities. Our goal in this work is to predict the specific states of the agents, as their observed resources evolve in time and get updated. The information diffusion among the agents and the publications themselves effectively result in a dynamic process which we capture by an interconnected system of networks (i.e. layered). More specifically, we use a notion of a supra-Laplacian matrix to address such a generalized diffusion of an interconnected network starting with the classical "graph Laplacian". The auxiliary and external input update is modeled by a multidimensional Brownian process, yielding two contributions to the variations in the states of the agents: one that is due to the intrinsic interactions in the network system, and the other due to the external inputs or innovations. A variation on this theme, a priori knowledge of a fraction of the agents' states is shown to lead to a Kalman predictor problem. This helps us refine the predicted states exploiting the error in estimating the states of agents. Three real-world datasets are used to evaluate and validate the information diffusion process in this novel layered network approach. Our results demonstrate a lower prediction error when using the interconnected network rather than the single connectivity layer between the agents. The prediction error is further improved by using the estimated diffusion connection and by applying the Kalman approach with partial observations.

cs.SI↗

arXiv2015

Node Dominance: Revealing Community and Core-Periphery Structure in Social Networks

This study relates the local property of node dominance to local and global properties of a network. Iterative removal of dominated nodes yields a distributed algorithm for computing a core-periphery decomposition of a social network, where nodes in the network core are seen to be essential in terms of network flow and global structure. Additionally, the connected components in the periphery give information about the community structure of the network, aiding in community detection. A number of explicit results are derived, relating the core and periphery to network flow, community structure and global network structure, which are corroborated by observational results. The method is illustrated using a real world network (DBLP co-authorship network), with ground-truth communities.

cs.SI↗

arXiv2014

Coordinate-Free Quantification of Coverage in Dynamic Sensor Networks

We present a novel set of methods for analyzing coverage properties in dynamic sensor networks. The dynamic sensor network under consideration is studied through a series of snapshots, and is represented by a sequence of simplicial complexes, built from the communication graph at each time point. A method from computational topology called zigzag persistent homology takes this sequence of simplicial complexes as input, and returns a `barcode' containing the birth and death times of homological features in this sequence. We derive useful statistics from this output for analyzing time-varying coverage properties. Further, we propose a method which returns specific representative cycles for these homological features, at each point along the birth-death intervals. These representative cycles are then used to track coverage holes in the network, and obtain size estimates for individual holes at each time point. A weighted barcode, incorporating the size information, is then used as a visual and quantitative descriptor of the dynamic network coverage.

cs.CG↗

arXiv2014

Adaptive tracking of representative cycles in regular and zigzag persistent homology

Persistent homology and zigzag persistent homology are techniques which track the homology over a sequence of spaces, outputting a set of intervals corresponding to birth and death times of homological features in the sequence. This paper presents a method for choosing a homology class to correspond to each of the intervals at each time point. For each homology class a specific representative cycle is stored, with the choice of homology class and representative cycle being both geometrically relevant and compatible with the birth-death interval decomposition. After describing the method in detail and proving its correctness, we illustrate the utility of the method by applying it to the study of coverage holes in time-varying sensor networks.

cs.CG↗

arXiv2014

Robust Detection of Periodic Patterns in Gene Expression Microarray Data using Topological Signal Analysis

In this paper, we present a new approach for analyzing gene expression data that builds on topological characteristics of time series. Our goal is to identify cell cycle regulated genes in micro array dataset. We construct a point cloud out of time series using delay coordinate embeddings. Persistent homology is utilized to analyse the topology of the point cloud for detection of periodicity. This novel technique is accurate and robust to noise, missing data points and varying sampling intervals. Our experiments using Yeast Saccharomyces cerevisiae dataset substantiate the capabilities of the proposed method.

q-bio.QM↗

arXiv2014

Robust Subspace Recovery via Bi-Sparsity Pursuit

Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying structure may be affected by sparse errors and/or outliers. In this paper, we propose a bi-sparse model as a framework to analyze this problem and provide a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We further show the effectiveness of our method by experiments on both synthetic data and real-world vision data.

cs.CV↗

arXiv2014

Persistent Homology of Delay Embeddings

The objective of this study is to detect and quantify the periodic behavior of the signals using topological methods. We propose to use delay-coordinate embeddings as a tool to measure the periodicity of signals. Moreover, we use persistent homology for analyzing the structure of point clouds of delay-coordinate embeddings. A method for finding the appropriate value of delay is proposed based on the autocorrelation function of the signals. We apply this topological approach to wheeze signals by introducing a model based on their harmonic characteristics. Wheeze detection is performed using the first Betti numbers of a few number of landmarks chosen from embeddings of the signals.

math.AT↗

arXiv2014

Analysis and Control of Beliefs in Social Networks

In this paper, we investigate the problem of how beliefs diffuse among members of social networks. We propose an information flow model (IFM) of belief that captures how interactions among members affect the diffusion and eventual convergence of a belief. The IFM model includes a generalized Markov Graph (GMG) model as a social network model, which reveals that the diffusion of beliefs depends heavily on two characteristics of the social network characteristics, namely degree centralities and clustering coefficients. We apply the IFM to both converged belief estimation and belief control strategy optimization. The model is compared with an IFM including the Barabasi-Albert model, and is evaluated via experiments with published real social network data.

cs.SI↗

arXiv2013

Distributed computation of homology using harmonics

We present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a basis for algebraic 1-cycles, and then use harmonics to efficiently identify the contractible and homologous cycles. The computational complexity of the algorithm is $O(|P|^ω)$, where $|P|$ is much smaller than the number of edges, and $ω$ is the complexity order of matrix multiplication. For geometric graphs, we show using simulations that $|P|$ is very close to the first Betti number.

math.AT↗

arXiv2013

Distributed boundary tracking using alpha and Delaunay-Cech shapes

For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $α-$shape of $S$. $α-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for the shape of $S$. We assume that the distances between pairs of points which are closer than a certain distance $r>0$ are provided, and we show constructively that this information is sufficient to compute the alpha shapes for a range of parameters, where the range depends on $r$. Such distributed algorithms are very useful in domains such as sensor networks, where each point represents a sensing node, the location of which is not necessarily known. We also introduce a new geometric object called the Delaunay-Čech shape, which is geometrically more appropriate than an $α-$shape for some cases, and show that it is topologically equivalent to $α-$shapes.

cs.CG↗

arXiv2011

A Invertible Dimension Reduction of Curves on a Manifold

In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential geometry tools such as moving frame and parallel transportation are successfully adapted into the dimension reduction problem of high dimensional curves. Intuitively, instead of searching for a global flat subspace for curve embedding, we deployed a sequence of local flat subspaces adaptive to the geometry of both of the curve and the manifold it lies on. In practice, the experimental results of the dimension reduction and reconstruction algorithms well illustrate the advantages of the proposed theoretical innovation.

cs.CV↗

arXiv2011

Topological Fidelity in Sensor Networks

Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection and Localization. We also note these solutions remain coordinate free as no priori localization information of the nodes is assumed. For the coverage hole problem, we follow a "divide and conquer approach", by strategically dissecting the network so that the overall topology is preserved, while efficiently pursuing the detection and localization of failures. The detection of holes, is enabled by first attributing a combinatorial object called a "Rips Complex" to each network segment, and by subsequently checking the existence/non-existence of holes by way of triviality of the first homology class of this complex. Our estimate exponentially approaches the location of potential holes with each iteration, yielding a very fast convergence coupled with optimal usage of valuable resources such as power and memory. We then show a simple extension of the above problem to address a well known problem in networks, namely the localization of a worm hole attack. We demonstrate the effectiveness of the presented algorithm with several substantiating examples.

cs.NI↗