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

Discrete Visual Perception

International audienceComputational vision and biomedical image have made tremendous progress of the past decade. This is mostly due the development of efficient learning and inference algorithms which allow better, faster and richer modeling of visual perception tasks. Graph-based representations are among the most prominent tools to address such perception through the casting of perception as a graph optimization problem. In this paper, we briefly introduce the interest of such representations, discuss their strength and limitations and present their application to address a variety of problems in computer vision and biomedical image analysis

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

Expectation-Maximization Binary Clustering for Behavioural Annotation

We present a variant of the well sounded Expectation-Maximization Clustering algorithm that is constrained to generate partitions of the input space into high and low values. The motivation of splitting input variables into high and low values is to favour the semantic interpretation of the final clustering. The Expectation-Maximization binary Clustering is specially useful when a bimodal conditional distribution of the variables is expected or at least when a binary discretization of the input space is deemed meaningful. Furthermore, the algorithm deals with the reliability of the input data such that the larger their uncertainty the less their role in the final clustering. We show here its suitability for behavioural annotation of movement trajectories. However, it can be considered as a general purpose algorithm for the clustering or segmentation of multivariate data or temporal series.Comment: 34 pages main text including 11 (full page) figure

Analysis of infrared polarisation signatures for vehicle detection

Thermal radiation emitted from objects within a scene tends to be partially polarised in a direction parallel to the surface normal, to an extent governed by properties of the surface material. This thesis investigates whether vehicle detection algorithms can be improved by the additional measurement of polarisation state as well as intensity in the long wave infrared. Knowledge about the polarimetric properties of scenes guides the development of histogram based and cluster based descriptors which are used in a traditional classification framework. The best performing histogram based method, the Polarimetric Histogram, which forms a descriptor based on the polarimetric vehicle signature is shown to outperform the standard Histogram of Oriented Gradients descriptor which uses intensity imagery alone. These descriptors then lead to a novel clustering algorithm which, at a false positive rate of 10−2 is shown to improve upon the Polarimetric Histogram descriptor, increasing the true positive rate from 0.19 to 0.63. In addition, a multi-modal detection framework which combines thermal intensity hotspot and polarimetric hotspot detections with a local motion detector is presented. Through the combination of these detectors, the false positive rate is shown to be reduced when compared to the result of individual detectors in isolation

Behaviour Profiling using Wearable Sensors for Pervasive Healthcare

In recent years, sensor technology has advanced in terms of hardware sophistication and miniaturisation. This has led to the incorporation of unobtrusive, low-power sensors into networks centred on human participants, called Body Sensor Networks. Amongst the most important applications of these networks is their use in healthcare and healthy living. The technology has the possibility of decreasing burden on the healthcare systems by providing care at home, enabling early detection of symptoms, monitoring recovery remotely, and avoiding serious chronic illnesses by promoting healthy living through objective feedback. In this thesis, machine learning and data mining techniques are developed to estimate medically relevant parameters from a participant‘s activity and behaviour parameters, derived from simple, body-worn sensors. The first abstraction from raw sensor data is the recognition and analysis of activity. Machine learning analysis is applied to a study of activity profiling to detect impaired limb and torso mobility. One of the advances in this thesis to activity recognition research is in the application of machine learning to the analysis of 'transitional activities': transient activity that occurs as people change their activity. A framework is proposed for the detection and analysis of transitional activities. To demonstrate the utility of transition analysis, we apply the algorithms to a study of participants undergoing and recovering from surgery. We demonstrate that it is possible to see meaningful changes in the transitional activity as the participants recover. Assuming long-term monitoring, we expect a large historical database of activity to quickly accumulate. We develop algorithms to mine temporal associations to activity patterns. This gives an outline of the user‘s routine. Methods for visual and quantitative analysis of routine using this summary data structure are proposed and validated. The activity and routine mining methodologies developed for specialised sensors are adapted to a smartphone application, enabling large-scale use. Validation of the algorithms is performed using datasets collected in laboratory settings, and free living scenarios. Finally, future research directions and potential improvements to the techniques developed in this thesis are outlined

A Large Scale Inertial Aided Visual Simultaneous Localization And Mapping (SLAM) System For Small Mobile Platforms

In this dissertation we present a robust simultaneous mapping and localization scheme that can be deployed on a computationally limited, small unmanned aerial system. This is achieved by developing a key frame based algorithm that leverages the multiprocessing capacity of modern low power mobile processors. The novelty of the algorithm lies in the design to make it robust against rapid exploration while keeping the computational time to a minimum. A novel algorithm is developed where the time critical components of the localization and mapping system are computed in parallel utilizing the multiple cores of the processor. The algorithm uses a scale and rotation invariant state of the art binary descriptor for landmark description making it suitable for compact large scale map representation and robust tracking. This descriptor is also used in loop closure detection making the algorithm efficient by eliminating any need for separate descriptors in a Bag of Words scheme. Effectiveness of the algorithm is demonstrated by performance evaluation in indoor and large scale outdoor dataset. We demonstrate the efficiency and robustness of the algorithm by successful six degree of freedom (6 DOF) pose estimation in challenging indoor and outdoor environment. Performance of the algorithm is validated on a quadcopter with onboard computation