arXiv subjects

Duan-Shin Lee

Publications and source records attributed to Duan-Shin Lee.

22 records · Page 2Linked to original sources

arXiv2017

K-sets+: a Linear-time Clustering Algorithm for Data Points with a Sparse Similarity Measure

In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the K-sets+ algorithm converges in a finite number of iterations and it retains the same performance guarantee as the K-sets algorithm for clustering data points in a metric space. We then extend the applicability of the K-sets+ algorithm from data points in a semi-metric space to data points that only have a symmetric similarity measure. Such an extension leads to great reduction of computational complexity. In particular, for an n * n similarity matrix with m nonzero elements in the matrix, the computational complexity of the K-sets+ algorithm is O((Kn + m)I), where I is the number of iterations. The memory complexity to achieve that computational complexity is O(Kn + m). As such, both the computational complexity and the memory complexity are linear in n when the n * n similarity matrix is sparse, i.e., m = O(n). We also conduct various experiments to show the effectiveness of the K-sets+ algorithm by using a synthetic dataset from the stochastic block model and a real network from the WonderNetwork website.

cs.DS↗

arXiv2017

Community Detection in Signed Networks: an Error-Correcting Code Approach

In this paper, we consider the community detection problem in signed networks, where there are two types of edges: positive edges (friends) and negative edges (enemies). One renowned theorem of signed networks, known as Harary's theorem, states that structurally balanced signed networks are clusterable. By viewing each cycle in a signed network as a parity-check constraint, we show that the community detection problem in a signed network with two communities is equivalent to the decoding problem for a parity-check code. We also show how one can use two renowned decoding algorithms in error- correcting codes for community detection in signed networks: the bit-flipping algorithm, and the belief propagation algorithm. In addition to these two algorithms, we also propose a new community detection algorithm, called the Hamming distance algorithm, that performs community detection by finding a codeword that minimizes the Hamming distance. We compare the performance of these three algorithms by conducting various experiments with known ground truth. Our experimental results show that our Hamming distance algorithm outperforms the other two.

cs.SI↗

arXiv2015

A Probabilistic Framework for Structural Analysis in Directed Networks

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution to formerly define various notions, including centrality, relative centrality, community, and modularity. The main objective of this paper is to extend the probabilistic framework to directed networks, where the sampling bivariate distributions could be asymmetric. Our main finding is that we can relax the assumption from symmetric bivariate distributions to bivariate distributions that have the same marginal distributions. By using such a weaker assumption, we show that various notions for structural analysis in directed networks can also be defined in the same manner as before. However, since the bivariate distribution could be asymmetric, the community detection algorithms proposed in our previous work cannot be directly applied. For this, we show that one can construct another sampled graph with a symmetric bivariate distribution so that for any partition of the network, the modularity index remains the same as that of the original sampled graph. Based on this, we propose a hierarchical agglomerative algorithm that returns a partition of communities when the algorithm converges.

cs.SI↗

arXiv2010

Constructions of Optical Queues With a Limited Number of Recirculations--Part I: Greedy Constructions

In this two-part paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. We show that the constructions of certain types of optical queues, including linear compressors, linear decompressors, and 2-to-1 FIFO multiplexers, under a simple packet routing scheme and under the constraint of a limited number of recirculations can be transformed into equivalent integer representation problems under a corresponding constraint. Given $M$ and $k$, the problem of finding an \emph{optimal} construction, in the sense of maximizing the maximum delay (resp., buffer size), among our constructions of linear compressors/decompressors (resp., 2-to-1 FIFO multiplexers) is equivalent to the problem of finding an optimal sequence ${\dbf^*}_1^M$ in $\Acal_M$ (resp., $\Bcal_M$) such that $B({\dbf^*}_1^M;k)=\max_{\dbf_1^M\in \Acal_M}B(\dbf_1^M;k)$ (resp., $B({\dbf^*}_1^M;k)=\max_{\dbf_1^M\in \Bcal_M}B(\dbf_1^M;k)$), where $\Acal_M$ (resp., $\Bcal_M$) is the set of all sequences of fiber delays allowed in our constructions of linear compressors/decompressors (resp., 2-to-1 FIFO multiplexers). In Part I, we propose a class of \emph{greedy} constructions of linear compressors/decompressors and 2-to-1 FIFO multiplexers by specifying a class $\Gcal_{M,k}$ of sequences such that $\Gcal_{M,k}\subseteq \Bcal_M\subseteq \Acal_M$ and each sequence in $\Gcal_{M,k}$ is obtained recursively in a greedy manner. We then show that every optimal construction must be a greedy construction. In Part II, we further show that there are at most two optimal constructions and give a simple algorithm to obtain the optimal construction(s).

cs.IT↗