A graph model for mutual information based clustering

As society has progressed through periods of evolution and revolution, technology has played a key role as an enabler. In the same manner, mechanical machines of the 1800s drove the industrial revolution, now digitalized machines are driving another industrial revolution. Manufacturers are increasing the digital footprint on the factory floor. It is challenging to harness the vast amounts of data generated, stored, analyzed, archived, and returned. Data centralization has several well-known challenges, such as collection bottlenecks, secure retrieval, single point of failure, and data scheme fragility as data heterogeneity increases. This paper proposes a method of information distribution based on the principle of data at its source . It proposes that contextual data be used at runtime through the creation of dynamic queries that build compositions of different systems. Such system of systems (SoS) compositions handle the flow of data across its life cycle and present it as information to the initiating system. The proposal starts by creating a graph model of the Arrowhead framework. Then, building on the graph model, the query-based approach for specifying, validating, and forming the SoS is proposed. The proposed graph model allows for unambiguous description of systems and their interrelations, including security relations. The proposed composer operates on the edge computing hardware and gives the production floor the ability to extract information without impacting the overall operation of the factory.

The quantitative analysis on the mobility behaviors of subcellular structures is essential for understanding eukaryotic cells establishment and maintenance. Tagged by the fluorescent marker proteins, the subcellular structures are visualized under the modern microscope. In this paper, we propose a graph model to formulate the tracking problem on fluorescent marker protein. By minimizing the energy of the proposed graph model, we present an algorithm for multiple objects tracking to classify the mobility behavior of the fluorescent marker protein. We have carried out extensive experiments on the tracking of fluorescent marker protein and the proposed method achieves satisfactory tracking accuracy.

The field of Metaheuristics has produced a large number of algorithms for continuous, black-box optimization. In contrast, there are few standard benchmark problem sets, limiting our ability to gain insight into the empirical performance of these algorithms. Clustering problems have been used many times in the literature to evaluate optimization algorithms. However, much of this work has occurred independently on different problem instances and the various experimental methodologies used have produced results which are frequently incomparable and provide little knowledge regarding the difficulty of the problems used, or any platform for comparing and evaluating the performance of algorithms. This paper discusses sum of squares clustering problems from the optimization viewpoint. Properties of the fitness landscape are analysed and it is proposed that these problems are highly suitable for algorithm benchmarking. A set of 27 problem instances (from 4-D to 40-D), based on three well-known datasets, is specified. Baseline experimental results are presented for the Covariance Matrix Adaptation-Evolution Strategy and several other standard algorithms. A web-repository has also been created for this problem set to facilitate future use for algorithm evaluation and comparison.

The series of IEC 61850 standards is currently the most widely used source for description of a digital substation’s equipment and processes; therefore, advanced technologies in the field of designing relay protection and automatic controls (PAC) shall inevitably be developed in compliance with the requirements of these standards. However, the scope of this standard series was originally limited to describing SCADA-controlled facilities and processes, which poses certain restrictions on the standard series capabilities. PAC systems should be designed subject to the IEC 61850 requirements, but at the same time, the IEC 61850 standard does not provide any tools and has no intent for thoroughly describing the structure and operational principle of PAC devices, and only describes the external interface for monitoring the necessary data, which is sufficient from the SCADA system perspective. Such restrictions of the standard series can be clearly seen when it comes to designing centralized PAC systems, PACs with migrating functions and digital substation computer-aided designing and monitoring systems, which pose more stringent (compared to a SCADA) requirements for describing the information model structure and for data exchange between its parts. The fact that the actual algorithmic support of the PAC functions differs from their information models has an impact on designing the functional requirements for logic units (LU). The functional requirements for LUs cannot be developed unless there is understanding of the logical device (LD) structure that will reflect a certain function; however, IEC 61850 does not specify any logical device structure. As a result, both the structure of logical devices and the functions implemented within one LU may differ essentially from manufacturer to manufacturer, which has a negative impact on the compatibility of the solutions offered in the market. The development of logical devices and units within the research framework revealed a number of problems connected with the specific features of implementing IEC 61850, which result in lack of unambiguity of LU and LD implementations. Thus, the standard does not specify the sources of signals supporting the LU operation, nor does it consider a functional for processing and producing measurements for relay protection as part of the information model. The standard does not describe the functions typical for the domestically adopted PAC designing practice. It should also be noted that the UES Federal Grid Company’s corporate profile specifies them only partially since it inherits the description structure from IEC 61850. The article suggests a change in the approach to the use of logical units. Currently, the function information model represents only an external interface. This interface makes it possible to obtain, from the midst of algorithmic support, the values of necessary signals with the required semantics, which is functionally useful only for the SCADA. Thus, it turns out that the functional requirements for an LU should define the requirements for the external interface instead of the algorithmic support implementing the PAC function, which to a certain degree makes a nonsense. The article proposes to set up, for each LU, an independent separate algorithmic support, so that the algorithmic support structure would be consistent with that of the information model. In view of this feature, logical devices and units are developed that reflect the PAC functions for facilities of medium and high voltage classes. In addition, data objects are classified into input, output signals and setting parameters, and the extensions of LU information models, should a need to do so arises, are suggested. The study has revealed multiple applications of similar LUs in different PAC functions, which pose specific requirements for the LU operation. In this connection, it is decided to standardize the entire specific functional within a single LU type with the possibility to choose the necessary operation mode by changing the setting parameters. The development of the algorithmic support has revealed repeating types of LU algorithmic support structure, which were combined into three categories: measuring, starting-functional, and functional. For each of the LU types, there is a certain set of LU functional blocks. The designing of PAC functions on the basis of the new approach to the use of LUs has the following advantages: the protection scheme modular structure makes it possible to select the set of protection functions in a wide range at the designing stage; strict definition of interconnections and data exchange between LUs simplifies the understanding of protection operation, and opens the possibility to evaluate the influence of the LU operation mode on the performance of the protection function as a whole; the protection scheme modular structure with a predictable behavior of LUs makes it possible not only to monitor the correct operation of protection using special automatic tools, but also to automatically develop protection schemes. The disadvantage of this approach is the need to develop the PAC algorithmic support from scratch, because the previously developed algorithms do not imply the information model structure. The process of developing a logical device is shown within the article framework on the example of the medium voltage class overhead power line overcurrent protection with a detailed description of the logic device structure and the purpose of the presented LUs. A configurator software was developed during the study, which makes it possible to configure logical devices based on the library of developed LUs with subsequently making binary files to be uploaded on a hardware platform. The unambiguous description of information exchange between LUs generated the need to extend the SCL syntax, as a result of which a new format of CLD files was produced. The mechanism of applying reference data objects like InRef and BlkRef, that are part of the standard SCL syntax is not applicable because they lack semantic meaning. The article describes a successful process of testing and validation of the developed algorithms/logic units and logic devices on a hardware platform, as well as the problems revealed during the testing, which are connected with the lack of regulatory requirements for functional testing of logic units and methods for taking into account the impact of various quality labels of data objects.

The Shot Boundary Detection (SBD) is an early step for most of the video applications involving understanding, indexing, characterization, or categorization of video. The SBD is temporal video segmentation and it has been an active topic of research in the area of content based video analysis. The research efforts have resulted in a variety of algorithms. The major methods that have been used for shot boundary detection include pixel intensity based, histogram-based, edge-based, and motion vectors based, technique. Recently researchers have attempted use of graph theory based methods for shot boundary detection. The proposed algorithm is one such graph based model and employs graph partition mechanism for detection of shot boundaries. Graph partition model is one of the graph theoretic segmentation algorithms, which offers data clustering by using a graph model. Pair-wise similarities between all data objects are used to construct a weighted graph represented as an adjacency matrix (weighted similarity matrix) that contains all necessary information for clustering. Representing the data set in the form of an edge-weighted graph converts the data clustering problem into a graph partitioning problem. The algorithm is experimented on sports and movie videos and the results indicate the promising performance.

An important application of graph partitioning is data clustering using a graph model - the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. In this paper, we propose a new algorithm for graph partitioning with an objective function that follows the min-max clustering principle. The relaxed version of the optimization of the min-max cut objective function leads to the Fiedler vector in spectral graph partitioning. Theoretical analyses of min-max cut indicate that it leads to balanced partitions, and lower bounds are derived. The min-max cut algorithm is tested on newsgroup data sets and is found to out-perform other current popular partitioning/clustering methods. The linkage-based refinements to the algorithm further improve the quality of clustering substantially. We also demonstrate that a linearized search order based on linkage differential is better than that based on the Fiedler vector, providing another effective partitioning method.

Data Mining is concerned with the discovery of interesting patterns and knowledge in data repositories. Cluster Analysis which belongs to the core methods of data mining is the process of discovering homogeneous groups called clusters. Given a data-set and some measure of similarity between data objects, the goal in most clustering algorithms is maximizing both the homogeneity within each cluster and the heterogeneity between different clusters. In this work, two multilevel algorithms for the clustering problem are introduced. The multilevel paradigm suggests looking at the clustering problem as a hierarchical optimization process going through different levels evolving from a coarse grain to fine grain strategy. The clustering problem is solved by first reducing the problem level by level to a coarser problem where an initial clustering is computed. The clustering of the coarser problem is mapped back level-bylevel to obtain a better clustering of the original problem by refining the intermediate different clustering obtained at various levels. A benchmark using a number of data sets collected from a variety of domains is used to compare the effectiveness of the hierarchical approach against its single-level counterpart.

Mining users'= topics of interest is one of the most important tasks for social media services. Given known topic associations for some fraction of the users in an online microblogging platform, our goal is to infer the topics of interest for the remaining users in the same site. Specifically, we proposed a novel bi-relational graph model to capture the interactions among users and their shared topics of interests. The proposed graph model contains two sub-graphs: one corresponds to users and the other corresponds to topics. Such a representation allows for effective exploitation of both user homophily relation and topic correlation simultaneously. This is in contrast with previous work where these two factors are considered in isolation. Subsequently, the user interest discovery problem is formulated as a multi-label learning problem on the bi-relational graph, with the goal to estimate the optimized associations between user nodes and topic nodes across the two sub-graphs. Our experiment is carried out with a complete month-long data collected from Twitter and Tumblr via GNIP Decahose1 and Firehose2 respectively. The large-scale studies shed light on the effectiveness of inferring user interests based on the underlying social connections.

Social networks are often analyzed through a graph model of the network. The dot product model assumes that two individuals are connected in the social network if their attributes or opinions are similar. In the model, a d-dimensional vector av represents the extent to which individual v has each of a set of d attributes or opinions. Then two individuals u and v are assumed to be friends, that is, they are connected in the graph model, if and only if au · av ≥ t, for some fixed, positive threshold t. The resulting graph is called a d-dot product graph..We consider two measures for diversity and clustering in social networks by using a d-dot product graph model for the network. Diversity is measured through the size of the largest independent set of the graph, and clustering is measured through the size of the largest clique. We obtain a tight result for the diversity problem, namely that it is polynomial-time solvable for d = 2, but NP-complete for d ≥ 3. We show that the clustering problem is polynomial-time solvable for d = 2. To our knowledge, these results are also the first on the computational complexity of combinatorial optimization problems on dot product graphs.We also consider the situation when two individuals are connected if their preferences are not opposite. This leads to a variant of the standard dot product graph model by taking the threshold t to be zero. We prove in this case that the diversity problem is polynomial-time solvable for any fixed d.KeywordsSocial NetworkMaximum CliqueStructural ResultProduct GraphInterval GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The problem of detecting spatially-coherent groups of data that exhibit anomalous behavior has started to attract attention due to applications across areas such as epidemic analysis and weather forecasting. Earlier efforts from the data mining community have largely focused on finding outliers, individual data objects that display deviant behavior. Such point-based methods are not easy to extend to find groups of data that exhibit anomalous behavior. Scan statistics are methods from the statistics community that have considered the problem of identifying regions where data objects exhibit a behavior that is atypical of the general dataset. The spatial scan statistic and methods that build upon it mostly adopt the framework of defining a character for regions (e.g., circular or elliptical) of objects and repeatedly sampling regions of such character followed by applying a statistical test for anomaly detection. In the past decade, there have been efforts from the statistics community to enhance efficiency of scan statistics as well as to enable discovery of arbitrarily shaped anomalous regions. On the other hand, the data mining community has started to look at determining anomalous regions that have behavior divergent from their neighborhood. In this chapter, we survey the space of techniques for detecting anomalous regions on spatial data from across the data mining and statistics communities while outlining connections to well-studied problems in clustering and image segmentation. We analyze the techniques systematically by categorizing them appropriately to provide a structured birds-eye view of the work on anomalous region detection; we hope that this would encourage better cross-pollination of ideas across communities to help advance the frontier in anomaly detection.

Approximation schemes for Min-Sum [formula omitted]-Clustering

Clustering problem is an unsupervised learning problem. It is a procedure that partition data objects into matching clusters. The data objects in the same cluster are quite similar to each other and dissimilar in the other clusters. The traditional algorithms do not meet the latest multiple requirements simultaneously for objects. Density-based clustering algorithms find clusters based on density of data points in a region. DBSCAN algorithm is one of the density-based clustering algorithms. It can discover clusters with arbitrary shapes and only requires two input parameters.In this paper, we propose a new algorithm based on DBSCAN. We design a new method for automatic parameters generation that create clusters with different densities and generates arbitrary shaped clusters. The kd-tree is used for increasing the memory efficiency. The performance of proposed algorithm is compared with DBSCAN. Experimental results indicate the superiority of proposed algorithm.

Minimisation of discrete energies defined over factors is an important problem in computer vision, and a vast number of MAP inference algorithms have been proposed. Different inference algorithms perform better on factor graph models (GMs) from different underlying problem classes, and in general it is difficult to know which algorithm will yield the lowest energy for a given GM. To mitigate this difficulty, survey papers [1, 2, 3] advise the practitioner on what algorithms perform well on what classes of models. We take the next step forward, and present a technique to automatically select the best inference algorithm for an input GM. We validate our method experimentally on an extended version of the OpenGM2 benchmark [3], containing a diverse set of vision problems. On average, our method selects an inference algorithm yielding labellings with 96 % of variables the same as the best available algorithm.

<p>Clustering is an unsupervised machine learning technique, which involves discovering different clusters (groups) of similar objects in unlabeled data and is generally considered to be a NP hard problem. Clustering methods are widely used in a verity of disciplines for analyzing different types of data, and a small improvement in clustering method can cause a ripple effect in advancing research of multiple fields. Clustering any type of data is challenging and there are many open research questions. The clustering problem is exacerbated in the case of text data because of the additional challenges such as issues in capturing semantics of a document, handling rich features of text data and dealing with the well known problem of the curse of dimensionality. In this thesis, we investigate the limitations of existing text clustering methods and address these limitations by providing five new text clustering methods--Query Sense Clustering (QSC), Dirichlet Weighted K-means (DWKM), Multi-View Multi-Objective Evolutionary Algorithm (MMOEA), Multi-objective Document Clustering (MDC) and Multi-Objective Multi-View Ensemble Clustering (MOMVEC). These five new clustering methods showed that the use of rich features in text clustering methods could outperform the existing state-of-the-art text clustering methods. The first new text clustering method QSC exploits user queries (one of the rich features in text data) to generate better quality clusters and cluster labels. The second text clustering method DWKM uses probability based weighting scheme to formulate a semantically weighted distance measure to improve the clustering results. The third text clustering method MMOEA is based on a multi-objective evolutionary algorithm. MMOEA exploits rich features to generate a diverse set of candidate clustering solutions, and forms a better clustering solution using a cluster-oriented approach. The fourth and the fifth text clustering method MDC and MOMVEC address the limitations of MMOEA. MDC and MOMVEC differ in terms of the implementation of their multi-objective evolutionary approaches. All five methods are compared with existing state-of-the-art methods. The results of the comparisons show that the newly developed text clustering methods out-perform existing methods by achieving up to 16\% improvement for some comparisons. In general, almost all newly developed clustering algorithms showed statistically significant improvements over other existing methods. The key ideas of the thesis highlight that exploiting user queries improves Search Result Clustering(SRC); utilizing rich features in weighting schemes and distance measures improves soft subspace clustering; utilizing multiple views and a multi-objective cluster oriented method improves clustering ensemble methods; and better evolutionary operators and objective functions improve multi-objective evolutionary clustering ensemble methods. The new text clustering methods introduced in this thesis can be widely applied in various domains that involve analysis of text data. The contributions of this thesis which include five new text clustering methods, will not only help researchers in the data mining field but also to help a wide range of researchers in other fields.</p>

This paper analyses the data clustering problem from the continuous black-box optimization point of view and proposes methodological guidelines for a standard benchmark of clustering problem instances. Clustering problems have been used many times in the literature to evaluate evolutionary, metaheuristic and other global optimization algorithms. However much of this work has occurred independently and the various experimental methodologies used have produced results which tend to be incomparable and provide little collective wisdom as to the difficulty of the problems used, or an objective measure for comparing and evaluating the performance of algorithms. This paper surveys some of the clustering literature and results to identify issues relevant for benchmarking. A set of 27 problem instances ranging from 4-D to 40-D and based on three well-known datasets is identified. To establish some pilot results on this benchmark set, experiments are presented for the Covariance Matrix Adaptation-Evolution Strategy and several other standard algorithms. A web-repository has also been created for this problem set to facilitate better experimental evaluations of algorithms.KeywordsAlgorithm BenchmarkingContinuous Black-box OptimizationClustering