Improving Reachability and Navigability in Recommender Systems

In this paper, we investigate recommender systems from a network perspective and investigate recommendation networks, where nodes are items (e.g., movies) and edges are constructed from top-N recommendations (e.g., related movies). In particular, we focus on evaluating the reachability and navigability of recommendation networks and investigate the following questions: (i) How well do recommendation networks support navigation and exploratory search? (ii) What is the influence of parameters, in particular different recommendation algorithms and the number of recommendations shown, on reachability and navigability? and (iii) How can reachability and navigability be improved in these networks? We tackle these questions by first evaluating the reachability of recommendation networks by investigating their structural properties. Second, we evaluate navigability by simulating three different models of information seeking scenarios. We find that with standard algorithms, recommender systems are not well suited to navigation and exploration and propose methods to modify recommendations to improve this. Our work extends from one-click-based evaluations of recommender systems towards multi-click analysis (i.e., sequences of dependent clicks) and presents a general, comprehensive approach to evaluating navigability of arbitrary recommendation networks

Graph-RAT: Combining data sources in music recommendation systems

The complexity of music recommendation systems has increased rapidly in recent years, drawing upon different sources of information: content analysis, web-mining, social tagging, etc. Unfortunately, the tools to scientifically evaluate such integrated systems are not readily available; nor are the base algorithms available. This article describes Graph-RAT (Graph-based Relational Analysis Toolkit), an open source toolkit that provides a framework for developing and evaluating novel hybrid systems. While this toolkit is designed for music recommendation, it has applications outside its discipline as well. An experiment—indicative of the sort of procedure that can be configured using the toolkit—is provided to illustrate its usefulness

Low-Rank Matrices on Graphs: Generalized Recovery & Applications

Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined recovery problem. Under certain circumstances, state-of-the-art algorithms provide an exact recovery for linear low-rank structures but at the expense of highly inscalable algorithms which use nuclear norm. However, the case of non-linear structures remains unresolved. We revisit the problem of low-rank recovery from a totally different perspective, involving graphs which encode pairwise similarity between the data samples and features. Surprisingly, our analysis confirms that it is possible to recover many approximate linear and non-linear low-rank structures with recovery guarantees with a set of highly scalable and efficient algorithms. We call such data matrices as \textit{Low-Rank matrices on graphs} and show that many real world datasets satisfy this assumption approximately due to underlying stationarity. Our detailed theoretical and experimental analysis unveils the power of the simple, yet very novel recovery framework \textit{Fast Robust PCA on Graphs

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

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