Random Walks: A Review of Algorithms and Applications

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science. Furthermore, in quantum mechanics, quantum walks can be regarded as quantum analogues of classical random walks. Classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding. In this paper, we aim to provide a comprehensive review of classical random walks and quantum walks. We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms. We also compare the algorithms based on quantum walks and classical random walks from the perspective of time complexity. Then we introduce their applications in the field of computer science. Finally we discuss the open issues from the perspectives of efficiency, main-memory volume, and computing time of existing algorithms. This study aims to contribute to this growing area of research by exploring random walks and quantum walks together.Comment: 13 pages, 4 figure

RANDOM WALK APPLIED TO HETEROGENOUS DRUG-TARGET NETWORKS FOR PREDICTING BIOLOGICAL OUTCOMES

Thesis (Ph.D.) - Indiana University, Informatics and Computing, 2016Prediction of unknown drug target interactions from bioassay data is critical not only for the understanding of various interactions but also crucial for the development of new drugs and repurposing of old ones. Conventional methods for prediction of such interactions can be divided into 2D based and 3D based methods. 3D methods are more CPU expensive and require more manual interpretation whereas 2D methods are actually fast methods like machine learning and similarity search which use chemical fingerprints. One of the problems of using traditional machine learning based method to predict drug-target pairs is that it requires a labeled information of true and false interactions. One of the major problems of supervised learning methods is selection on negative samples. Unknown drug target interactions are regarded as false interactions, which may influence the predictive accuracy of the model. To overcome this problem network based methods has become an effective tool in predicting the drug target interactions overcoming the negative sampling problem. In this dissertation study, I will describe traditional machine learning methods and 3D methods of pharmacophore modeling for drug target prediction and will show how these methods work in a drug discovery scenario. I will then introduce a new framework for drug target prediction based on bipartite networks of drug target relations known as Random Walk with Restart (RWR). RWR integrates various networks including drug– drug similarity networks, protein-protein similarity networks and drug- target interaction networks into a heterogeneous network that is capable of predicting novel drug-target relations. I will describe how chemical features for measuring drug-drug similarity do not affect performance in predicting interactions and further show the performance of RWR using an external dataset from ChEMBL database. I will describe about further implementations of RWR approach into multilayered networks consisting of biological data like diseases, tissue based gene expression data, protein- complexes and metabolic pathways to predict associations between human diseases and metabolic pathways which are very crucial in drug discovery. I have further developed a software tool package netpredictor in R (standalone and the web) for unipartite and bipartite networks and implemented network-based predictive algorithms and network properties for drug-target prediction. This package will be described

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Graph based Anomaly Detection and Description: A Survey

Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured graph data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we give a general framework for the algorithms categorized under various settings: unsupervised vs. (semi-)supervised approaches, for static vs. dynamic graphs, for attributed vs. plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly attribution and highlight the major techniques that facilitate digging out the root cause, or the ‘why’, of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field

Learning on Graphs with Partially Absorbing Random Walks: Theory and Practice

Learning on graphs has been studied for decades with abundant models proposed, yet many of their behaviors and relations remain unclear. This thesis fills this gap by introducing a novel second-order Markov chain, called partially absorbing random walks (ParWalk). Different from ordinary random walk, ParWalk is absorbed at the current state $i$ with probability $p_i$, and follows a random edge out with probability $1-p_i$. The partial absorption results in absorption probability between any two vertices, which turns out to encompass various popular models including PageRank, hitting times, label propagation, and regularized Laplacian kernels. The unified treatment reveals the distinguishing characteristics of these models arising from different contexts, and allows comparing them and transferring findings from one paradigm to another. The key for learning on graphs is capitalizing on the cluster structure of the underlying graph. The absorption probabilities of ParWalk, turn out to be highly effective in capturing the cluster structure. Given a query vertex $q$ in a cluster $\mathcal{S}$, we show that when the absorbing capacity ($p_i$) of each vertex on the graph is small, the probabilities of ParWalk to be absorbed at $q$ have small variations in region of high conductance (within clusters), but have large gaps in region of low conductance (between clusters). And the less absorbent the vertices of $\mathcal{S}$ are, the better the absorption probabilities can represent the local cluster $\mathcal{S}$. Our theory induces principles for designing reliable similarity measures and provides justification to a number of popular ones such as hitting times and the pseudo-inverse of graph Laplacian. Furthermore, it reveals their new important properties. For example, we are the first to show that hitting times is better in retrieving sparse clusters, while the pseudo-inverse of graph Laplacian is better for dense ones. The theoretical insights instilled from ParWalk guide us in developing robust algorithms for various applications including local clustering, semi-supervised learning, and ranking. For local clustering, we propose a new method for salient object segmentation. By taking a noisy saliency map as the probability distribution of query vertices, we compute the absorption probabilities of ParWalk to the queries, producing a high-quality refined saliency map where the objects can be easily segmented. For semi-supervised learning, we propose a new algorithm for label propagation. The algorithm is justified by our theoretical analysis and guaranteed to be superior than many existing ones. For ranking, we design a new similarity measure using ParWalk, which combines the strengths of both hitting times and the pseudo-inverse of graph Laplacian. The hybrid similarity measure can well adapt to complex data of diverse density, thus performs superiorly overall. For all these learning tasks, our methods achieve substantial improvements over the state-of-the-art on extensive benchmark datasets

Texture-boundary detection in real-time

Boundary detection is an essential first-step for many computer vision applications. In practice, boundary detection is difficult because most images contain texture. Normally, texture-boundary detectors are complex, and so cannot run in real-time. On the other hand, the few texture boundary detectors that do run in real-time leave much to be desired in terms of quality. This thesis proposes two real-time texture-boundary detectors – the Variance Ridge Detector and the Texton Ridge Detector – both of which can detect high-quality texture-boundaries in real-time. The Variance Ridge Detector is able to run at 47 frames per second on 320 by 240 images, while scoring an F-measure of 0.62 (out of a theoretical maximum of 0.79) on the Berkeley segmentation dataset. The Texton Ridge Detector runs at 10 frames per second but produces slightly better results, with an F-measure score of 0.63. These objective measurements show that the two proposed texture-boundary detectors outperform all other texture-boundary detectors on either quality or speed. As boundary detection is so widely-used, this development could induce improvements to many real-time computer vision applications

Learning-Based Approaches for Graph Problems: A Survey

Over the years, many graph problems specifically those in NP-complete are studied by a wide range of researchers. Some famous examples include graph colouring, travelling salesman problem and subgraph isomorphism. Most of these problems are typically addressed by exact algorithms, approximate algorithms and heuristics. There are however some drawback for each of these methods. Recent studies have employed learning-based frameworks such as machine learning techniques in solving these problems, given that they are useful in discovering new patterns in structured data that can be represented using graphs. This research direction has successfully attracted a considerable amount of attention. In this survey, we provide a systematic review mainly on classic graph problems in which learning-based approaches have been proposed in addressing the problems. We discuss the overview of each framework, and provide analyses based on the design and performance of the framework. Some potential research questions are also suggested. Ultimately, this survey gives a clearer insight and can be used as a stepping stone to the research community in studying problems in this field.Comment: v1: 41 pages; v2: 40 page

Visual Tracking in Robotic Minimally Invasive Surgery

Intra-operative imaging and robotics are some of the technologies driving forward better and more effective minimally invasive surgical procedures. To advance surgical practice and capabilities further, one of the key requirements for computationally enhanced interventions is to know how instruments and tissues move during the operation. While endoscopic video captures motion, the complex appearance dynamic effects of surgical scenes are challenging for computer vision algorithms to handle with robustness. Tackling both tissue and instrument motion estimation, this thesis proposes a combined non-rigid surface deformation estimation method to track tissue surfaces robustly and in conditions with poor illumination. For instrument tracking, a keypoint based 2D tracker that relies on the Generalized Hough Transform is developed to initialize a 3D tracker in order to robustly track surgical instruments through long sequences that contain complex motions. To handle appearance changes and occlusion a patch-based adaptive weighting with segmentation and scale tracking framework is developed. It takes a tracking-by-detection approach and a segmentation model is used to assigns weights to template patches in order to suppress back- ground information. The performance of the method is thoroughly evaluated showing that without any offline-training, the tracker works well even in complex environments. Finally, the thesis proposes a novel 2D articulated instrument pose estimation framework, which includes detection-regression fully convolutional network and a multiple instrument parsing component. The framework achieves compelling performance and illustrates interesting properties includ- ing transfer between different instrument types and between ex vivo and in vivo data. In summary, the thesis advances the state-of-the art in visual tracking for surgical applications for both tissue and instrument motion estimation. It contributes to developing the technological capability of full surgical scene understanding from endoscopic video