R\'enyi Information Measures for Spectral Change Detection

Change detection within an audio stream is an important task in several domains, such as classification and segmentation of a sound or of a music piece, as well as indexing of broadcast news or surveillance applications. In this paper we propose two novel methods for spectral change detection without any assumption about the input sound: they are both based on the evaluation of information measures applied to a time- frequency representation of the signal, and in particular to the spectrogram. The class of measures we consider, the R\'enyi entropies, are obtained by extending the Shannon entropy definition: a biasing of the spectrogram coefficients is realized through the dependence of such measures on a parameter, which allows refined results compared to those obtained with standard divergences. These methods provide a low computational cost and are well-suited as a support for higher level analysis, segmentation and classification algorithms.Comment: 2011 IEEE Conference on Acoustics, Speech and Signal Processin

On the Analysis of a Label Propagation Algorithm for Community Detection

This paper initiates formal analysis of a simple, distributed algorithm for community detection on networks. We analyze an algorithm that we call \textsc{Max-LPA}, both in terms of its convergence time and in terms of the "quality" of the communities detected. \textsc{Max-LPA} is an instance of a class of community detection algorithms called \textit{label propagation} algorithms. As far as we know, most analysis of label propagation algorithms thus far has been empirical in nature and in this paper we seek a theoretical understanding of label propagation algorithms. In our main result, we define a clustered version of \er random graphs with clusters $V_1, V_2,..., V_k$ where the probability $p$, of an edge connecting nodes within a cluster $V_i$ is higher than $p'$, the probability of an edge connecting nodes in distinct clusters. We show that even with fairly general restrictions on $p$ and $p'$ ($p = \Omega(\frac{1}{n^{1/4-\epsilon}})$ for any $\epsilon > 0$, $p' = O(p^2)$, where $n$ is the number of nodes), \textsc{Max-LPA} detects the clusters $V_1, V_2,..., V_n$ in just two rounds. Based on this and on empirical results, we conjecture that \textsc{Max-LPA} can correctly and quickly identify communities on clustered \er graphs even when the clusters are much sparser, i.e., with $p = \frac{c\log n}{n}$ for some $c > 1$.Comment: 17 pages. Submitted to ICDCN 201