Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

Use Multilevel Graph Partitioning Scheme to solve traveling salesman problem

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

Parallel dynamic graph-partitioning for unstructured meshes

A parallel method for the dynamic partitioning of unstructured meshes is described. The method introduces a new iterative optimisation technique known as relative gain optimisation which both balances the workload and attempts to minimise the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.

A Scalable General Purpose System for Large-Scale Graph Processing

Graph analytics is an important and computationally demanding class of data analytics. It is essential to balance scalability, ease-of-use and high performance in large scale graph analytics. As such, it is necessary to hide the complexity of parallelism, data distribution and memory locality behind an abstract interface. The aim of this work is to build a scalable graph analytics framework that does not demand significant parallel programming experience based on NUMA-awareness.
The realization of such a system faces two key problems:
(i)~how to develop a scale-free parallel programming framework that scales efficiently across NUMA domains; (ii)~how to efficiently apply graph partitioning in order to create separate and largely independent work items that can be distributed among threads.

Parallel partitioning of unstructured meshes

A method is outlined for optimising graph partitions which arise in mapping un- structured mesh calculations to parallel computers. The method employs a combination of iterative techniques to both evenly balance the workload and minimise the number and volume of interprocessor communications. They are designed to work efficiently in parallel as well as sequentially and when combined with a fast direct partitioning technique (such as the Greedy algorithm) to give an initial partition, the resulting two-stage process proves itself to be both a powerful and flexible solution to the static graph-partitioning problem. The algorithms can also be used for dynamic load-balancing and a clustering technique can additionally be employed to speed up the whole process. Experiments indicate that the resulting parallel code can provide high quality partitions, independent of the initial partition, within a few seconds.

Mesh partitioning and load balancing for distributed memory parallel systems

A method is outlined for optimising graph partitions which arise in mapping unstructured mesh calculations to parallel computers. The method employs a relative gain iterative technique to both evenly balance the workload and minimise the number and volume of interprocessor communications. A parallel graph reduction technique is also briefly described and can be used to give a global perspective to the optimisation. The algorithms work efficiently in parallel as well as sequentially and when combined with a fast direct partitioning technique (such as the Greedy algorithm) to give an initial partition, the resulting two-stage process proves itself to be both a powerful and flexible solution to the static graph-partitioning problem. Experiments indicate that the resulting parallel code can provide high quality partitions, independent of the initial partition, within a few seconds. The algorithms can also be used for dynamic load-balancing, reusing existing partitions and in this case the procedures are much faster than static techniques, provide partitions of similar or higher quality and, in comparison, involve the migration of a fraction of the data.

Comitês de grupamento aplicados a dados de expressão gênica

The main goal of this work is to investigate the suitability of applying cluster ensemble techniques (ensembles or committees) to gene expression data. More specifically, we will develop experiments with three diferent cluster ensembles methods, which have been used in many works in literature: coassociation matrix, relabeling and voting, and ensembles based on graph partitioning. The inputs for these methods will be the partitions generated by three clustering algorithms, representing diferent paradigms: kmeans, ExpectationMaximization (EM), and hierarchical method with average linkage. These algorithms have been widely applied to gene expression data. In general, the results obtained with our experiments indicate that the cluster ensemble methods present a better performance when compared to the individual techniques. This happens mainly for the heterogeneous ensembles, that is, ensembles built with base partitions generated with diferent clustering algorithms

Image segmentation through combined methods: watershed transform, unsupervised distance learning and normalized cut

Research on image processing has shown that combining segmentation methods may lead to a solid approach to extract semantic information from different sort of images. Within this context, the Normalized Cut (NCut) is usually used as a final partitioning tool for graphs modeled in some chosen method. This work explores the Watershed Transform as a modeling tool, using different criteria of the hierarchical Watershed to convert an image into an adjacency graph. The Watershed is combined with an unsupervised distance learning step that redistributes the graph weights and redefines the Similarity matrix, before the final segmentation step using NCut. Adopting the Berkeley Segmentation Data Set and Benchmark as a background, our goal is to compare the results obtained for this method with previous work to validate its performance.

Scalable unstructured mesh decomposition

As the efficiency of parallel software increases it is becoming common to measure near linear speedup for many applications. For a problem size N on P processors then with software running at O(N=P ) the performance restrictions due to file i/o systems and mesh decomposition running at O(N) become increasingly apparent especially for large P . For distributed memory parallel systems an additional limit to scalability results from the finite memory size available for i/o scatter/gather operations. Simple strategies developed to address the scalability of scatter/gather operations for unstructured mesh based applications have been extended to provide scalable mesh decomposition through the development of a parallel graph partitioning code, JOSTLE [8]. The focus of this work is directed towards the development of generic strategies that can be incorporated into the Computer Aided Parallelisation Tools (CAPTools) project.

Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method. Journal of the Operational Research Society (2012) 63, 183-200. doi: 10.1057/jors.2011.6 Published online 17 August 2011

Applied Graph Theory in Computer Vision and Pattern Recognition

This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

Mesh partitioning: A multilevel balancing and refinement algorithm

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan-Lin partition optimisation algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of the-art partitioner and shown to provide improved results.

Multilevel mesh partitioning for optimising domain shape

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Multilevel mesh partitioning for optimising subdomain aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Multilevel mesh partitioning for aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight, however it has been shown that for certain classes of solution algorithm, the convergence of the solver is strongly influenced by the subdomain aspect ratio. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.