arXiv subjects

Min Xu

Publications and source records attributed to Min Xu.

At least 253 records · Page 14Linked to original sources

arXiv2017

Fault-free Hamiltonian cycles in balanced hypercube with conditional edge faults

The balanced hypercube, $BH_n$, is a variant of hypercube $Q_n$. Zhou et al. [Inform. Sci. 300 (2015) 20-27] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in $BH_n$ with each vertex incident to at least two fault-free edges. In this paper, we consider this problem and show that each fault-free edge lies on a fault-free Hamiltonian cycle in $BH_n$ after no more than $4n-5$ faulty edges occur if each vertex is incident with at least two fault-free edges for all $n\ge 2$. Our result is optimal with respect to the maximum number of tolerated edge faults.

math.CO↗

arXiv2017

The g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes

In the work of Peng et al. in 2012, a new measure was proposed for fault diagnosis of systems: namely, g-good-neighbor conditional diagnosability, which requires that any fault-free vertex has at least g fault-free neighbors in the system. In this paper, we establish the g-good-neighbor conditional diagnosability of locally twisted cubes under the PMC model and the MM^* model.

cs.DM↗

arXiv2016

Shift equivalence in the generalized factor order

We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.

math.CO↗

arXiv2016

Modelling Temporal Information Using Discrete Fourier Transform for Recognizing Emotions in User-generated Videos

With the widespread of user-generated Internet videos, emotion recognition in those videos attracts increasing research efforts. However, most existing works are based on framelevel visual features and/or audio features, which might fail to model the temporal information, e.g. characteristics accumulated along time. In order to capture video temporal information, in this paper, we propose to analyse features in frequency domain transformed by discrete Fourier transform (DFT features). Frame-level features are firstly extract by a pre-trained deep convolutional neural network (CNN). Then, time domain features are transferred and interpolated into DFT features. CNN and DFT features are further encoded and fused for emotion classification. By this way, static image features extracted from a pre-trained deep CNN and temporal information represented by DFT features are jointly considered for video emotion recognition. Experimental results demonstrate that combining DFT features can effectively capture temporal information and therefore improve emotion recognition performance. Our approach has achieved a state-of-the-art performance on the largest video emotion dataset (VideoEmotion-8 dataset), improving accuracy from 51.1% to 62.6%.

cs.CV↗

arXiv2016

The super spanning connectivity of arrangement graph

A $k$-container $C(u, v)$ of a graph $G$ is a set of $k$ internally disjoint paths between $u$ and $v$. A $k$-container $C(u, v)$ of $G$ is a $k^*$-container if it is a spanning subgraph of $G$. A graph $G$ is $k^*$-connected if there exists a $k^*$-container between any two different vertices of G. A $k$-regular graph $G$ is super spanning connected if $G$ is $i^*$-container for all $1\le i\le k$. In this paper, we prove that the arrangement graph $A_{n, k}$ is super spanning connected if $n\ge 4$ and $n-k\ge 2$.

math.CO↗

arXiv2016

De novo visual proteomics in single cells through pattern mining

Cryo-electron tomography enables 3D visualization of cells in a near native state at molecular resolution. The produced cellular tomograms contain detailed information about all macromolecular complexes, their structures, their abundances and their specific spatial locations in the cell. However, extracting this information is very challenging and current methods usually rely on templates of known structure. Here, we formulate a template-free visual proteomics analysis as a de novo pattern mining problem and propose a new framework called "Multi Pattern Pursuit" for supporting proteome-scale de novo discovery of macromolecular complexes in cellular tomograms without using templates of known structures. Our tests on simulated and experimental tomograms show that our method is a promising tool for template-free visual proteomics analysis.

q-bio.QM↗

arXiv2015

Integrative analysis of gene expression and phenotype data

The linking genotype to phenotype is the fundamental aim of modern genetics. We focus on study of links between gene expression data and phenotype data through integrative analysis. We propose three approaches. 1) The inherent complexity of phenotypes makes high-throughput phenotype profiling a very difficult and laborious process. We propose a method of automated multi-dimensional profiling which uses gene expression similarity. Large-scale analysis show that our method can provide robust profiling that reveals different phenotypic aspects of samples. This profiling technique is also capable of interpolation and extrapolation beyond the phenotype information given in training data. It can be used in many applications, including facilitating experimental design and detecting confounding factors. 2) Phenotype association analysis problems are complicated by small sample size and high dimensionality. Consequently, phenotype-associated gene subsets obtained from training data are very sensitive to selection of training samples, and the constructed sample phenotype classifiers tend to have poor generalization properties. To eliminate these obstacles, we propose a novel approach that generates sequences of increasingly discriminative gene cluster combinations. Our experiments on both simulated and real datasets show robust and accurate classification performance. 3) Many complex phenotypes, such as cancer, are the product of not only gene expression, but also gene interaction. We propose an integrative approach to find gene network modules that activate under different phenotype conditions. Using our method, we discovered cancer subtype-specific network modules, as well as the ways in which these modules coordinate. In particular, we detected a breast-cancer specific tumor suppressor network module with a hub gene, PDGFRL, which may play an important role in this module.

q-bio.QM↗

arXiv2015

Automatic tracking of protein vesicles

With the advance of fluorescence imaging technologies, recently cell biologists are able to record the movement of protein vesicles within a living cell. Automatic tracking of the movements of these vesicles become key for qualitative analysis of dynamics of theses vesicles. In this thesis, we formulate such tracking problem as video object tracking problem, and design a dynamic programming method for tracking single object. Our experiments on simulation data show that the method can identify a track with high accuracy which is robust to the choose of tracking parameters and presence of high level noise. We then extend this method to the tracking multiple objects using the track elimination strategy. In multiple object tracking, the above approach often fails to correctly identify a track when two tracks cross. We solve this problem by incorporating the Kalman filter into the dynamic programming framework. Our experiments on simulated data show that the tracking accuracy is significantly improved.

q-bio.QM↗

arXiv2015

Gene selection for cancer classification using a hybrid of univariate and multivariate feature selection methods

Various approaches to gene selection for cancer classification based on microarray data can be found in the literature and they may be grouped into two categories: univariate methods and multivariate methods. Univariate methods look at each gene in the data in isolation from others. They measure the contribution of a particular gene to the classification without considering the presence of the other genes. In contrast, multivariate methods measure the relative contribution of a gene to the classification by taking the other genes in the data into consideration. Multivariate methods select fewer genes in general. However, the selection process of multivariate methods may be sensitive to the presence of irrelevant genes, noises in the expression and outliers in the training data. At the same time, the computational cost of multivariate methods is high. To overcome the disadvantages of the two types of approaches, we propose a hybrid method to obtain gene sets that are small and highly discriminative. We devise our hybrid method from the univariate Maximum Likelihood method (LIK) and the multivariate Recursive Feature Elimination method (RFE). We analyze the properties of these methods and systematically test the effectiveness of our proposed method on two cancer microarray datasets. Our experiments on a leukemia dataset and a small, round blue cell tumors dataset demonstrate the effectiveness of our hybrid method. It is able to discover sets consisting of fewer genes than those reported in the literature and at the same time achieve the same or better prediction accuracy.

q-bio.QM↗

arXiv2015

Global Gene Expression Analysis Using Machine Learning Methods

Microarray is a technology to quantitatively monitor the expression of large number of genes in parallel. It has become one of the main tools for global gene expression analysis in molecular biology research in recent years. The large amount of expression data generated by this technology makes the study of certain complex biological problems possible and machine learning methods are playing a crucial role in the analysis process. At present, many machine learning methods have been or have the potential to be applied to major areas of gene expression analysis. These areas include clustering, classification, dynamic modeling and reverse engineering. In this thesis, we focus our work on using machine learning methods to solve the classification problems arising from microarray data. We first identify the major types of the classification problems; then apply several machine learning methods to solve the problems and perform systematic tests on real and artificial datasets. We propose improvement to existing methods. Specifically, we develop a multivariate and a hybrid feature selection method to obtain high classification performance for high dimension classification problems. Using the hybrid feature selection method, we are able to identify small sets of features that give predictive accuracy that is as good as that from other methods which require many more features.

q-bio.QM↗

arXiv2014

Faithful Variable Screening for High-Dimensional Convex Regression

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that estimates a sum of one-dimensional convex functions, followed by one-dimensional concave regression fits on the residuals. In contrast to previous methods for sparse additive models, the optimization is finite dimensional and requires no tuning parameters for smoothness. Under appropriate assumptions, we prove that the procedure is faithful in the population setting, yielding no false negatives. We give a finite sample statistical analysis, and introduce algorithms for efficiently carrying out the required quadratic programs. The approach leads to computational and statistical advantages over fitting a full model, and provides an effective, practical approach to variable screening in convex regression.

math.ST↗

arXiv2014

Connectivity-preserving Geometry Images

We propose connectivity-preserving geometry images (CGIMs), which map a three-dimensional mesh onto a rectangular regular array of an image, such that the reconstructed mesh produces no sampling errors, but merely round-off errors. We obtain a V-matrix with respect to the original mesh, whose elements are vertices of the mesh, which intrinsically preserves the vertex-set and the connectivity of the original mesh in the sense of allowing round-off errors. We generate a CGIM array by using the Cartesian coordinates of corresponding vertices of the V-matrix. To reconstruct a mesh, we obtain a vertex-set and an edge-set by collecting all the elements with different pixels, and all different pairwise adjacent elements from the CGIM array respectively. Compared with traditional geometry images, CGIMs achieve minimum reconstruction errors with an efficient parametrization-free algorithm via elementary permutation techniques. We apply CGIMs to lossy compression of meshes, and the experimental results show that CGIMs perform well in reconstruction precision and detail preservation.

cs.GR↗

arXiv2014

Efficient Hybrid Inline and Out-of-line Deduplication for Backup Storage

Backup storage systems often remove redundancy across backups via inline deduplication, which works by referring duplicate chunks of the latest backup to those of existing backups. However, inline deduplication degrades restore performance of the latest backup due to fragmentation, and complicates deletion of ex- pired backups due to the sharing of data chunks. While out-of-line deduplication addresses the problems by forward-pointing existing duplicate chunks to those of the latest backup, it introduces additional I/Os of writing and removing duplicate chunks. We design and implement RevDedup, an efficient hybrid inline and out-of-line deduplication system for backup storage. It applies coarse-grained inline deduplication to remove duplicates of the latest backup, and then fine-grained out-of-line reverse deduplication to remove duplicates from older backups. Our reverse deduplication design limits the I/O overhead and prepares for efficient deletion of expired backups. Through extensive testbed experiments using synthetic and real-world datasets, we show that RevDedup can bring high performance to the backup, restore, and deletion operations, while maintaining high storage efficiency comparable to conventional inline deduplication.

cs.DC↗

arXiv2012

Conditional Sparse Coding and Grouped Multivariate Regression

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated to form a model within each group. We refer to the method as conditional sparse coding since it is a coding procedure for the response vectors Y conditioned on the covariate vectors X. This approach captures the shared information across the groups while adapting to the structure within each group. It exploits the same intuition behind sparse coding that has been successfully developed in computer vision and computational neuroscience. We propose an algorithm for conditional sparse coding, analyze its theoretical properties in terms of predictive accuracy, and present the results of simulation and brain imaging experiments that compare the new technique to reduced rank regression.

cs.LG↗

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↗