arXiv subjects

Kun He

Publications and source records attributed to Kun He.

205 records · Page 12Linked to original sources

arXiv2015

Detecting Overlapping Communities from Local Spectral Subspaces

Based on the definition of local spectral subspace, we propose a novel approach called LOSP for local overlapping community detection. Instead of using the invariant subspace spanned by the dominant eigenvectors of the entire network, we run the power method for a few steps to approximate the leading eigenvectors that depict the embedding of the local neighborhood structure around seeds of interest. We then seek a sparse approximate indicator vector in the local spectral subspace spanned by these vectors such that the seeds are in its support. We evaluate LOSP on five large real world networks across various domains with labeled ground-truth communities and compare the results with the state-of-the-art community detection approaches. LOSP identifies the members of a target community with high accuracy from very few seed members, and outperforms the local Heat Kernel or PageRank diffusions as well as the global baselines. Two candidate definitions of the local spectral subspace are analyzed, and different community scoring functions for determining the community boundary, including two new metrics, are thoroughly evaluated. The structural properties of different seed sets and the impact of the seed set size are discussed. We observe low degree seeds behave better, and LOSP is robust even when started from a single random seed. Using LOSP as a subroutine and starting from each ego connected component, we try the harder yet significant task of identifying all communities a single vertex is in. Experiments show that the proposed method achieves high F1 measures on the detected multiple local overlapping communities containing the seed vertex.

cs.SI↗

arXiv2015

Overlapping Community Detection via Local Spectral Clustering

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure in large networks. A growing body of work has been adopting local expansion methods in order to identify the community members from a few exemplary seed members. In this paper, we propose a novel approach for finding overlapping communities called LEMON (Local Expansion via Minimum One Norm). The algorithm finds the community by seeking a sparse vector in the span of the local spectra such that the seeds are in its support. We show that LEMON can achieve the highest detection accuracy among state-of-the-art proposals. The running time depends on the size of the community rather than that of the entire graph. The algorithm is easy to implement, and is highly parallelizable. We further provide theoretical analysis on the local spectral properties, bounding the measure of tightness of extracted community in terms of the eigenvalues of graph Laplacian. Moreover, given that networks are not all similar in nature, a comprehensive analysis on how the local expansion approach is suited for uncovering communities in different networks is still lacking. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the seed set quality and quantity would affect the performance are provided.

cs.SI↗

arXiv2015

Uncovering the Small Community Structure in Large Networks: A Local Spectral Approach

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify the community from a few exemplary seed members. In this paper, we propose a novel approach for finding overlapping communities called LEMON (Local Expansion via Minimum One Norm). Different from PageRank-like diffusion methods, LEMON finds the community by seeking a sparse vector in the span of the local spectra such that the seeds are in its support. We show that LEMON can achieve the highest detection accuracy among state-of-the-art proposals. The running time depends on the size of the community rather than that of the entire graph. The algorithm is easy to implement, and is highly parallelizable. Moreover, given that networks are not all similar in nature, a comprehensive analysis on how the local expansion approach is suited for uncovering communities in different networks is still lacking. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the quality and quantity of the seed set would affect the performance are provided.

cs.SI↗

arXiv2015

Revealing Multiple Layers of Hidden Community Structure in Networks

We introduce a new conception of community structure, which we refer to as hidden community structure. Hidden community structure refers to a specific type of overlapping community structure, in which the detection of weak, but meaningful, communities is hindered by the presence of stronger communities. We present Hidden Community Detection HICODE, an algorithm template that identifies both the strong, dominant community structure as well as the weaker, hidden community structure in networks. HICODE begins by first applying an existing community detection algorithm to a network, and then removing the structure of the detected communities from the network. In this way, the structure of the weaker communities becomes visible. Through application of HICODE, we demonstrate that a wide variety of real networks from different domains contain many communities that, though meaningful, are not detected by any of the popular community detection algorithms that we consider. Additionally, on both real and synthetic networks containing a hidden ground-truth community structure, HICODE uncovers this structure better than any baseline algorithms that we compared against. For example, on a real network of undergraduate students that can be partitioned either by `Dorm' (residence hall) or `Year', we see that HICODE uncovers the weaker `Year' communities with a JCRecall score (a recall-based metric that we define in the text) of over 0.7, while the baseline algorithms achieve scores below 0.2.

cs.SI↗

arXiv2015

A theoretical foundation of the target-decoy search strategy for false discovery rate control in proteomics

Motivation: Target-decoy search (TDS) is currently the most popular strategy for estimating and controlling the false discovery rate (FDR) of peptide identifications in mass spectrometry-based shotgun proteomics. While this strategy is very useful in practice and has been intensively studied empirically, its theoretical foundation has not yet been well established. Result: In this work, we systematically analyze the TDS strategy in a rigorous statistical sense. We prove that the commonly used concatenated TDS provides a conservative estimate of the FDR for any given score threshold, but it cannot rigorously control the FDR. We prove that with a slight modification to the commonly used formula for FDR estimation, the peptide-level FDR can be rigorously controlled based on the concatenated TDS. We show that the spectrum-level FDR control is difficult. We verify the theoretical conclusions with real mass spectrometry data.

stat.AP↗

arXiv2014

An iterative merging placement algorithm for the fixed-outline floorplanning

Given a set of rectangular modules with fixed area and variable dimensions, and a fixed rectangular circuit. The placement of Fixed-Outline Floorplanning with Soft Modules (FOFSM) aims to determine the dimensions and position of each module on the circuit. We present a two-stage Iterative Merging Placement (IMP) algorithm for the FOFSM with zero deadspace constraint. The first stage iteratively merges two modules with the least area into a composite module to achieve a final composite module, and builds up a slicing tree in a bottom-up hierarchy. The second stage recursively determines the relative relationship (left-right or top-bottom) of the sibling modules in the slicing tree in a top-down hierarchy, and the dimensions and position of each leaf module are determined automatically. Compared with zero-dead-space (ZDS) algorithm, the only algorithm guarantees a feasible layout under some condition, we prove that the proposed IMP could construct a feasible layout under a more relaxed condition. Besides, IMP is more scalable in handling FOFSM considering the wirelength or without the zero deadspace constraint.

cs.DS↗

arXiv2011

Analysis on the computability over the efficient utilization problem of the four-dimensional space-time

This paper formally proposes a problem about the efficient utilization of the four dimensional space-time. Given a cuboid container, a finite number of rigid cuboid items, and the time length that each item should be continuous baked in the container, the problem asks to arrange the starting time for each item being placed into the container and to arrange the position and orientation for each item at each instant during its continuous baking period such that the total time length the container be utilized is as short as possible. Here all side dimensions of the container and of the items are positive real numbers arbitrarily given. Differs from the classical packing problems, the position and orientation of each item in the container could be changed over time. Therefore, according to above mathematical model, the four-dimensional space-time can be utilized more truly and more fully. This paper then proves that there exists an exact algorithm that could solve the problem by finite operations, so we say this problem is weak computable. Based on the understanding of this computability proof, it is expected to design effective approximate algorithms in the near future. A piggyback work completed is a strict proof on the weak computability over general and natural case of the three-dimensional cuboid packing decision problem that all parameters are positive real numbers.

cs.CC↗