Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space

This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals. More specifically, we discuss how the underlying notion of a `smooth signal' inherited from (the typically considered variants of) the graph Laplacian are not suitable when dealing with edge signals that encode a notion of flow. To overcome this limitation we introduce a class of filters based on the Edge-Laplacian, a special case of the Hodge-Laplacian for simplicial complexes of order one. We demonstrate how this Edge-Laplacian leads to low-pass filters that enforce (approximate) flow-conservation in the processed signals. Moreover, we show how these new filters can be combined with more classical Laplacian-based processing methods on the line-graph. Finally, we illustrate the developed tools by denoising synthetic traffic flows on the London street network.Comment: 5 pages, 2 figur

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

The Development of Parallel Adaptive Sampling Algorithms for Analyzing Biological Networks

The availability of biological data in massive scales continues to represent unlimited opportunities as well as great challenges in bioinformatics research. Developing innovative data mining techniques and efficient parallel computational methods to implement them will be crucial in extracting useful knowledge from this raw unprocessed data, such as in discovering significant cellular subsystems from gene correlation networks. In this paper, we present a scalable combinatorial sampling technique, based on identifying maximum chordal subgraphs, that reduces noise from biological correlation networks, thereby making it possible to find biologically relevant clusters from the filtered network. We show how selecting the appropriate filter is crucial in maintaining the key structures from the original networks and uncovering new ones after removing noisy relationships. We also conduct one of the first comparisons in two important sensitivity criteria— the perturbation due to the vertex numbers of the network and perturbations due to data distribution. We demonstrate that our chordal-graph based filter is effective across many different vertex permutations, as is our parallel implementation of the sampling algorithm

A multi-view approach to cDNA micro-array analysis

The official published version can be obtained from the link below.Microarray has emerged as a powerful technology that enables biologists to study thousands of genes simultaneously, therefore, to obtain a better understanding of the gene interaction and regulation mechanisms. This paper is concerned with improving the processes involved in the analysis of microarray image data. The main focus is to clarify an image's feature space in an unsupervised manner. In this paper, the Image Transformation Engine (ITE), combined with different filters, is investigated. The proposed methods are applied to a set of real-world cDNA images. The MatCNN toolbox is used during the segmentation process. Quantitative comparisons between different filters are carried out. It is shown that the CLD filter is the best one to be applied with the ITE.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the National Science Foundation of China under Innovative Grant 70621001, Chinese Academy of Sciences under Innovative Group Overseas Partnership Grant, the BHP Billiton Cooperation of Australia Grant, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050 and the Alexander von Humboldt Foundation of Germany