Clustering Vertices in Weighted Graphs

Rapid Evaluation-Based Feature Diminution algorithm involves finding a reduced set with the essential Feature which produces as the original set of Feature. The Feature diminution is performed by removing the irrelevant and redundant Features. The Rapid Evaluation-Based Feature Diminution algorithm (REFD) removes the irrelevancy by identifying relevant Feature to the target, and removing the rest and finally formed as weight graph. The weighted graph is converted to MST by Boruvka's algorithm. In the resultant set the representative features are selected by reducing MST into forest using Symmetric Uncertainty measures. The efficiency of REFD is improved by using efficient Minimum Spanning Tree (MST) clustering algorithm. The image, microarray and text dataset are taken as input to the REFD algorithm and reduced set given as the input to classifiers called the Naive Bayes and the decision tree and compared with original set of Features. The REFD produces smaller subsets of Features yet increases the performances.

Wireless capsule endoscopy (WCE), a widely used tool for gastrointestinal tract lesion detection, produces a large number of images. However, it is difficult and inefficient to manually search for and find bleeding lesions among these images. In this study, a new method for the automatic identification of bleeding frames in WCE has been proposed. The minimum spanning tree (MST) clustering algorithm was applied to reduce the background noise. Then, the images' features are extracted from the clustering result and classified by support vector machine (SVM). The experimental results, suggest that this method can correctly identify and mark the bleeding areas in WCE images. The final sensitivity, specificity and accuracy of our proposed method are 91.69%, 94.59%, and 94.10%, respectively.

ABSTRACTAnalysis of ‘omics’ data is a central issue of system biology. As one of the most widely used ‘omics ’ data, gene expression profiles from microarray experiments are applied to many frontier studies. The first and important step to analyze microarray data is to identify differentially expressed genes (DEGs) under two experimental conditions. Thereby, several DEG-identifying algorithms have been proposed. However, both traditional algorithms, such as Fold-Change, T-test and Significance Analysis of Microarrays (SAM), and modern ones, such as Rank Product, Outlier Robust t-statistic and Outlier Sums, are statistics-based approaches with the same core idea, which considers DEGs as the differences between two series of numbers. We present a novel view based on the hypothesis that DEGs are the differences between two input modes rather than the differences between two digital series, and then propose a novel non-statistical algorithm based on this idea, named Spring (SPG), which uses a Self-Organization Map (SOM) neural network to detect the input modals of DEGs under two sets of conditions. Firstly, the input matrix for SOM is constructed by reconstruction of the gene expression matrix, amplification of the difference of DEG and use of pairs of units divided from reconstructed gene expression matrix; and then, the strategy to improve the accuracy and stability is proposed by the Mass Spring Model, Minimum Spanning Tree Clustering and fuzzy clustering matrix. Compared with T-test and SAM, our algorithm obtains more DEGs in higher accuracy from both simulation and Homo sapiens datasets. Especially, we describe the details to transform SPG to a meta-analysis algorithm at the end.

An adaptive evolutionary multi-objective clustering based on the data properties of the base partitions

In view of today's unprecedented diverse and discrete mass text data processing, this paper presents a distributed MST (minimum spanning tree) algorithm based on MapReduce programming model. And with this MST algorithm, a distributed MST text clustering algorithm is designed and implemented. In this paper, this clustering algorithm is analyzed in three aspects: text feature vector extraction, graph construction and MST construction. And some data was used to experimentally compare this algorithm with ordinary MST clustering algorithm and MapReduce-based K-means clustering algorithm.

The minimum spanning tree (MST), a graph constructed from a distribution of points, draws lines between pairs of points so that all points are linked in a single skeletal structure that contains no loops and has minimal total edge length. The MST has been used in a broad range of scientific fields such as particle physics (to distinguish classes of events in collider collisions), in astronomy (to detect mass segregation in star clusters) and cosmology (to search for filaments in the cosmic web). Its success in these fields has been driven by its sensitivity to the spatial distribution of points and the patterns within. MiSTree, a public Python package, allows a user to construct the MST in a variety of coordinates systems, including Celestial coordinates used in astronomy. The package enables the MST to be constructed quickly by initially using a k-nearest neighbour graph (kNN, rather than a matrix of pairwise distances) which is then fed to Kruskal's algorithm to construct the MST. MiSTree enables a user to measure the statistics of the MST and provides classes for binning the MST statistics (into histograms) and plotting the distributions. Applying the MST will enable the inclusion of high-order statistics information from the cosmic web which can provide additional information to improve cosmological parameter constraints. This information has not been fully exploited due to the computational cost of calculating N-point statistics. MiSTree was designed to be used in cosmology but could be used in any field which requires extracting non-Gaussian information from point distributions. The source code for MiSTree is available on GitHub at https://github.com/knaidoo29/mistree

Recently, sequence anomaly detection has been widely used in many fields. Sequence data in these fields are usually multi-dimensional over the data stream. It is a challenge to design an anomaly detection method for a multi-dimensional sequence over the data stream to satisfy the requirements of accuracy and high speed. It is because: (1) Redundant dimensions in sequence data and large state space lead to a poor ability for sequence modeling; (2) Anomaly detection cannot adapt to the high-speed nature of the data stream, especially when concept drift occurs, and it will reduce the detection rate. On one hand, most existing methods of sequence anomaly detection focus on the single-dimension sequence. On the other hand, some studies concerning multi-dimensional sequence concentrate mainly on the static database rather than the data stream. To improve the performance of anomaly detection for a multi-dimensional sequence over the data stream, we propose a novel unsupervised fast and accurate anomaly detection (FAAD) method which includes three algorithms. First, a method called “information calculation and minimum spanning tree cluster” is adopted to reduce redundant dimensions. Second, to speed up model construction and ensure the detection rate for the sequence over the data stream, we propose a method called “random sampling and subsequence partitioning based on the index probabilistic suffix tree.” Last, the method called “anomaly buffer based on model dynamic adjustment” dramatically reduces the effects of concept drift in the data stream. FAAD is implemented on the streaming platform Storm to detect multi-dimensional log audit data. Compared with the existing anomaly detection methods, FAAD has a good performance in detection rate and speed without being affected by concept drift.

A fast sparse graph based clustering technique using dispersion of data points

A minimum spanning tree problem (MST) is a tree that identifies a subset of edges which connects all the vertices of a connected, undirected, and edge-weighted graph with the least total weight. In general, the edge weight can be distance, cost, time, etc. However, in case of any ambiguity of information, the edge weight may not be a deterministic value. A neutrosophic set is a powerful tool for complexity, dealing with imprecise, ambiguous, and inconsistent information in the actual wide world. In neutrosophic MST, the edge weight is represented by a neutrosophic number set. When compared to the fuzzy MST, neutrosophic MST graphs give more accuracy and compatibility in a neutrosophic environment. To solve the neutrosophic MST, least edge weight algorithm is proposed and executed in MATLAB.

Clustering with a minimum spanning tree of scale-free-like structure

In a complete graphwith independent uniform(or exponential) edge weights, letbe the minimum‐weight spanning tree (MST), andthe MST after deleting the edges of all previous trees. We show that each tree's weightconverges in probability to a constant, with, and we conjecture that. The problem is distinct from Frieze and Johansson's minimum combined weightofkedge‐disjoint spanning trees; indeed,. With an edge of weightw“arriving” at time, Kruskal's algorithm defines forests, initially empty and eventually equal to, each edge added to the first possible. Using tools of inhomogeneous random graphs we obtain structural results including that the fraction of vertices in the largest component ofconverges to some. We conjecture that the functionstend to time translations of a single function.

This paper considers the problem of minimum spanning trees in uncertain networks in which the edge weights are random variables. We propose the concept of expected minimum spanning tree and formulate the model according to expected value. In order to solve the model, a hybrid intelligent algorithm combined genetic algorithm and stochastic simulation is given, and the Prufer encoding schemes represented spanning trees are adopted. The algorithm has been proved to be useful for solving practical problems by a numerical example.

Two distributed algorithms are presented for a network using a common communication channel (e.g. radio) in which all nodes are within signal range and in line of sight of each other: (a) an algorithm to compute all\(\left( {\begin{array}{*{20}c} N \\ 2 \\ \end{array} } \right)\) internode distances (in terms of propagation delays) in the network. the algorithm requires only 2 messages per node, and provides each node with the distances to all other nodes. (b) An algorithm for constructing a minimum-weight spanning tree (MST) in such a network. This algorithm starts out with the information provided by (a) and ends with each node possessing the explicit knowledge of the full MST. The algorithm requires at most log2N messages per node. The internal processing in each node needsO(N logN) time andO(N) space. All messages required by (a) and (b) contain at most one edge weight plus 2 log2N bits. Some possible applications of the algorithms are: position-location, tuning acknowledgement time-out mechanisms, tuning the scheduling functions of access protocols that are sensitive to individual internode propagation delays, and selecting performance effective transmission sequences for round robin access protocols.

Gene expression data clustering provides a powerful tool for studying functional relationships of genes in a biological process. Identifying correlated expression patterns of genes represents the basic challenge in this clustering problem. This paper describes a new framework for representing a set of multi-dimensional gene expression data as a Minimum Spanning Tree (MST), a concept from the graph theory. A key property of this representation is that each cluster of the expression data corresponds to one subtree of the MST, which rigorously converts a multi-dimensional clustering problem to a tree partitioning problem. We have demonstrated that though the inter-data relationship is greatly simplified in the MST representation, no essential information is lost for the purpose of clustering. Two key advantages in representing a set of multi-dimensional data as an MST are: (1) the simple structure of a tree facilitates efficient implementations of rigorous clustering algorithms, which otherwise are highly computationally challenging; and (2) as an MST-based clustering does not depend on detailed geometric shape of a cluster, it can overcome many of the problems faced by classical clustering algorithms. Based on the MST representation, we have developed a number of rigorous and efficient clustering algorithms, including two with guaranteed global optimality. We have implemented these algorithms as a computer software EXpression data Clustering Analysis and VisualizATiOn Resource (EXCAVATOR). To demonstrate its effectiveness, we have tested it on three data sets, i.e. expression data from yeast Saccharomyces cerevisiae, expression data in response of human fibroblasts to serum, and Arabidopsis expression data in response to chitin elicitation. The test results are highly encouraging. EXCAVATOR is available on request from the authors.

We consider the problem of maintaining a minimum spanning tree of a dynamically changing graph, subject to changes on edge weights. We propose an on-line fully-dynamic algorithm that runs in time O(|E|) when the easy-to-implement DRD-trees data structure for dynamic trees is used. Numerical experiments illustrate the efficiency of the approach.