Scaling Analysis of Affinity Propagation

We analyze and exploit some scaling properties of the Affinity Propagation (AP) clustering algorithm proposed by Frey and Dueck (2007). First we observe that a divide and conquer strategy, used on a large data set hierarchically reduces the complexity ${\cal O}(N^2)$ to ${\cal O}(N^{(h+2)/(h+1)})$, for a data-set of size $N$ and a depth $h$ of the hierarchical strategy. For a data-set embedded in a $d$-dimensional space, we show that this is obtained without notably damaging the precision except in dimension $d=2$. In fact, for $d$ larger than 2 the relative loss in precision scales like $N^{(2-d)/(h+1)d}$. Finally, under some conditions we observe that there is a value $s^*$ of the penalty coefficient, a free parameter used to fix the number of clusters, which separates a fragmentation phase (for $s<s^*$) from a coalescent one (for $s>s^*$) of the underlying hidden cluster structure. At this precise point holds a self-similarity property which can be exploited by the hierarchical strategy to actually locate its position. From this observation, a strategy based on \AP can be defined to find out how many clusters are present in a given dataset.Comment: 28 pages, 14 figures, Inria research repor

Point-wise mutual information-based video segmentation with high temporal consistency

In this paper, we tackle the problem of temporally consistent boundary detection and hierarchical segmentation in videos. While finding the best high-level reasoning of region assignments in videos is the focus of much recent research, temporal consistency in boundary detection has so far only rarely been tackled. We argue that temporally consistent boundaries are a key component to temporally consistent region assignment. The proposed method is based on the point-wise mutual information (PMI) of spatio-temporal voxels. Temporal consistency is established by an evaluation of PMI-based point affinities in the spectral domain over space and time. Thus, the proposed method is independent of any optical flow computation or previously learned motion models. The proposed low-level video segmentation method outperforms the learning-based state of the art in terms of standard region metrics

Extracting user spatio-temporal profiles from location based social networks

Report de RecercaLocation Based Social Networks (LBSN) like Twitter or Instagram are a good source for user spatio-temporal behavior. These social network provide a low rate sampling of user's location information during large intervals of time that can be used to discover complex behaviors, including mobility profiles, points of interest or unusual events. This information is important for different domains like mobility route planning, touristic recommendation systems or city planning. Other approaches have used the data from LSBN to categorize areas of a city depending on the categories of the places that people visit or to discover user behavioral patterns from their visits. The aim of this paper is to analyze how the spatio-temporal behavior of a large number of users in a well limited geographical area can be segmented in different profiles. These behavioral profiles are obtained by means of clustering algorithms that show the different behaviors that people have when living and visiting a city. The data analyzed was obtained from the public data feeds of Twitter and Instagram inside the area of the city of Barcelona for a period of several months. The analysis of these data shows that these kind of algorithms can be successfully applied to data from any city (or any general area) to discover useful profiles that can be described on terms of the city singular places and areas and their temporal relationships. These profiles can be used as a basis for making decisions in different application domains, specially those related with mobility inside and outside a city.Preprin

Passive characterization of sopcast usage in residential ISPs

Abstract—In this paper we present an extensive analysis of traffic generated by SopCast users and collected from operative networks of three national ISPs in Europe. After more than a year of continuous monitoring, we present results about the popularity of SopCast which is the largely preferred application in the studied networks. We focus on analysis of (i) application and bandwidth usage at different time scales, (ii) peer lifetime, arrival and departure processes, (iii) peer localization in the world. Results provide useful insights into users ’ behavior, including their attitude towards P2P-TV application usage and the conse-quent generated load on the network, that is quite variable based on the access technology and geographical location. Our findings are interesting to Researchers interested in the investigation of users ’ attitude towards P2P-TV services, to foresee new trends in the future usage of the Internet, and to augment the design of their application. I