arXiv subjects

Min Xu

Publications and source records attributed to Min Xu.

261 records · Page 15Linked to original sources

arXiv2012

Efficient Active Algorithms for Hierarchical Clustering

Advances in sensing technologies and the growth of the internet have resulted in an explosion in the size of modern datasets, while storage and processing power continue to lag behind. This motivates the need for algorithms that are efficient, both in terms of the number of measurements needed and running time. To combat the challenges associated with large datasets, we propose a general framework for active hierarchical clustering that repeatedly runs an off-the-shelf clustering algorithm on small subsets of the data and comes with guarantees on performance, measurement complexity and runtime complexity. We instantiate this framework with a simple spectral clustering algorithm and provide concrete results on its performance, showing that, under some assumptions, this algorithm recovers all clusters of size ?(log n) using O(n log^2 n) similarities and runs in O(n log^3 n) time for a dataset of n objects. Through extensive experimentation we also demonstrate that this framework is practically alluring.

cs.LG↗

arXiv2012

The Forwarding Indices of Graphs -- a Survey

A routing $R$ of a given connected graph $G$ of order $n$ is a collection of $n(n-1)$ simple paths connecting every ordered pair of vertices of $G$. The vertex-forwarding index $ξ(G,R)$ of $G$ with respect to $R$ is defined as the maximum number of paths in $R$ passing through any vertex of $G$. The vertex-forwarding index $ξ(G)$ of $G$ is defined as the minimum $ξ(G,R)$ over all routing $R$'s of $G$. Similarly, the edge-forwarding index $ π(G,R)$ of $G$ with respect to $R$ is the maximum number of paths in $R$ passing through any edge of $G$. The edge-forwarding index $π(G)$ of $G$ is the minimum $π(G,R)$ over all routing $R$'s of $G$. The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention in the past ten years and more. In this paper we survey some known results on these forwarding indices, further research problems and several conjectures.

math.CO↗

arXiv2011

On the metric dimension of line graphs

Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$. The \emph{metric dimension} $μ(G)$ of $G$ is the minimum cardinality of all the resolving sets of $G$. Cáceres et al. \cite{Ca2} computed the metric dimension of the line graphs of complete bipartite graphs. Recently, Bailey and Cameron \cite{Ba} computed the metric dimension of the line graphs of complete graphs. In this paper we study the metric dimension of the line graph $L(G)$ of $G$. In particular, we show that $μ(L(G))=|E(G)|-|V(G)|$ for a strongly connected digraph $G$ except for directed cycles, where $V(G)$ is the vertex set and $E(G)$ is the edge set of $G$. As a corollary, the metric dimension of de Brujin digraphs and Kautz digraphs is given. Moreover, we prove that $\lceil\log_2Δ(G)\rceil\leqμ(L(G))\leq |V(G)|-2$ for a simple connected graph $G$ with at least five vertices, where $Δ(G)$ is the maximum degree of $G$. Finally, we obtain the metric dimension of the line graph of a tree in terms of its parameters.

math.CO↗

arXiv2011

High-dimensional covariance estimation based on Gaussian graphical models

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse undirected graphical model structure via thresholding of each among many $\ell_1$-norm penalized regression functions; we then estimate the covariance matrix and its inverse using the maximum likelihood estimator. We show that under suitable conditions, this approach yields consistent estimation in terms of graphical structure and fast convergence rates with respect to the operator and Frobenius norm for the covariance matrix and its inverse. We also derive an explicit bound for the Kullback Leibler divergence.

stat.ML↗

arXiv2011

Identifying codes of lexicographic product of graphs

Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum cardinality of identifying codes of G[H] in terms of some parameters of G and H.

math.CO↗

arXiv2011

Electronic structure of BaNi$_2$As$_2$

BaNi$_2$As$_2$, with a first order phase transition around 131 K, is studied by the angle-resolved photoemission spectroscopy. The measured electronic structure is compared to the local density approximation calculations, revealing similar large electronlike bands around $\bar{M}$ and differences along $\barΓ$-$\bar{X}$. We further show that the electronic structure of BaNi$_2$As$_2$ is distinct from that of the sibling iron pnictides. Particularly, there is no signature of band folding, indicating no collinear SDW related magnetic ordering. Moreover, across the strong first order phase transition, the band shift exhibits a hysteresis, which is directly related to the significant lattice distortion in BaNi$_2$As$_2$.

cond-mat.supr-con↗

arXiv2010

Forest Density Estimation

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univariate marginals, and apply Kruskal's algorithm to estimate the optimal forest on held out data. We prove an oracle inequality on the excess risk of the resulting estimator relative to the risk of the best forest. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. We prove that finding a maximum weight spanning forest with restricted tree size is NP-hard, and develop an approximation algorithm for this problem. Viewing the tree size as a complexity parameter, we then select a forest using data splitting, and prove bounds on excess risk and structure selection consistency of the procedure. Experiments with simulated data and microarray data indicate that the methods are a practical alternative to Gaussian graphical models.

stat.ML↗

arXiv2010

High-resolution angle-resolved photoemission spectroscopy study of the electronic structure of EuFe2As2

We report the high-resolution angle-resolved photoemission spectroscopy studies of electronic structure of EuFe2As2. The paramagnetic state data are found to be consistent with density-functional calculations. In the antiferromagnetic ordering state of Fe, our results show that the band splitting, folding, and hybridization evolve with temperature, which cannot be explained by a simple folding picture. Detailed measurements reveal that a tiny electron Fermi pocket and a tiny hole pocket are formed near (pi,pi) in the (0,0)-(pi,pi) direction, which qualitatively agree with the results of quantum oscillations, considering kz variation of Fermi surface. Furthermore, no noticeable change within the energy resolution is observed across the antiferromagnetic transition of Eu2+ ordering, suggesting weak coupling between Eu sublattice and FeAs sublattice.

cond-mat.str-el↗

arXiv2005

Time-Resolved Ring Structure of Backscattered Circularly Polarized Beams from Forward Scattering Media

The backscattering of circularly polarized light at normal incidence to a half-space of scattering particles is studied using the Electric Field Monte Carlo (EMC) method. The spatial distribution of the backscattered light intensity is examined for both the time-resolved and continuous-wave cases for large particles with anisotropy factor, g, in the range 0.8 to 0.97. For the time-resolved case, the backscattered light with the same helicity as that of the incident beam (co-polarized) is found to form a ring centered on the point of incidence. The ring expands and simultaneously grows weak as time increases. The intensity of backscattered light with helicity opposite to that of the incident beam (cross-polarized) is found to exhibit a ring behavior for g>=0.85, with significant backscattering at the point of incidence. For the continuous-wave case no such ring pattern is observed in backscattered light for either helicity. The present EMC study suggests that the ring behavior can only be observed in the time domain, in contrast to previous studies of light backscattered from forward scattering media based on the scalar time-independent Fokker-Planck approximation to the radiative transfer equation. The time-dependent ring structure of backscattered light may have potential use in subsurface imaging applications.

physics.optics↗