Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

Given a set of time series, it is of interest to discover subsets that share similar properties. For instance, this may be useful for identifying and estimating a single model that may fit conveniently several time series, instead of performing the usual identification and estimation steps for each one. On the other hand time series in the same cluster are related with respect to the measures assumed for cluster analysis and are suitable for building multivariate time series models. Though many approaches to clustering time series exist, in this view the most effective method seems to have to rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coe±cients, spectral measures or the eigenvectors of the covariance matrix. Some new indexes based on goodnessof-fit criteria will be proposed in this paper for fuzzy clustering of multivariate time series. A general purpose fuzzy clustering algorithm may be used to estimate the proper cluster structure according to some internal criteria of cluster validity. Such indexes are known to measure actually definite often conflicting cluster properties, compactness or connectedness, for instance, or distribution, orientation, size and shape. It is argued that the multiobjective optimization supported by genetic algorithms is a most effective choice in such a di±cult context. In this paper we use the Xie-Beni index and the C-means functional as objective functions to evaluate the cluster validity in a multiobjective optimization framework. The concept of Pareto optimality in multiobjective genetic algorithms is used to evolve a set of potential solutions towards a set of optimal non-dominated solutions. Genetic algorithms are well suited for implementing di±cult optimization problems where objective functions do not usually have good mathematical properties such as continuity, differentiability or convexity. In addition the genetic algorithms, as population based methods, may yield a complete Pareto front at each step of the iterative evolutionary procedure. The method is illustrated by means of a set of real data and an artificial multivariate time series data set.Fuzzy clustering, Internal criteria of cluster validity, Genetic algorithms, Multiobjective optimization, Time series, Pareto optimality

Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

COMISEF Working Papers Series WPS-028 08/02/2010 URL: http://comisef.eu/files/wps028.pd

An Approach to Beneficiation of Apatite Ore of Purulia

West Bengal Mineral Development and Trading Corporation operates the apatite mine in Purulia District of West Bengal. The produce three grades of samples, i.e. (i) High grade above 30% P2O5 (ii) Average grade of about 20% P2O5 and (iii)Low grade of 12% P2O5. The average is directly marketed as fertiliser for application in tea garden etc. The medium or average grade sample is mined from areas around the main ore body and contains substantial amount of ferruginous material besides other gangue minerals. The low grade ore is dumped separately and occasionally blended with high grade of ore to prepare the average grade for direct marketing. Thus every bit of apatite from the mines is used except for the top soil. But with reduc-ed demand, the manufacturer is faced with a selling problem and reduced production. Value addition by way of making high grade product is one option to pursue with. The typical problem is of iron removal as presence of high iron hinders value addition in terms of phosphate during down stream operation. Studies on the average grade sample indicated that using suitable processing steps the phos-phate content could be increased to +38% P205 with very low content of iron & silica. The present paper deals approach adopted in beneficiating the average grade apatite ore of Purulia. Key Words: apatite, Purulia, iron, magnetic separation, flotation

A Novel Biclustering Approach to Association Rule Mining for Predicting HIV-1–Human Protein Interactions

Identification of potential viral-host protein interactions is a vital and useful approach towards development of new drugs targeting those interactions. In recent days, computational tools are being utilized for predicting viral-host interactions. Recently a database containing records of experimentally validated interactions between a set of HIV-1 proteins and a set of human proteins has been published. The problem of predicting new interactions based on this database is usually posed as a classification problem. However, posing the problem as a classification one suffers from the lack of biologically validated negative interactions. Therefore it will be beneficial to use the existing database for predicting new viral-host interactions without the need of negative samples. Motivated by this, in this article, the HIV-1–human protein interaction database has been analyzed using association rule mining. The main objective is to identify a set of association rules both among the HIV-1 proteins and among the human proteins, and use these rules for predicting new interactions. In this regard, a novel association rule mining technique based on biclustering has been proposed for discovering frequent closed itemsets followed by the association rules from the adjacency matrix of the HIV-1–human interaction network. Novel HIV-1–human interactions have been predicted based on the discovered association rules and tested for biological significance. For validation of the predicted new interactions, gene ontology-based and pathway-based studies have been performed. These studies show that the human proteins which are predicted to interact with a particular viral protein share many common biological activities. Moreover, literature survey has been used for validation purpose to identify some predicted interactions that are already validated experimentally but not present in the database. Comparison with other prediction methods is also discussed

Comparison of bioinspired algorithms applied to the timetabling problem

The problem of timetabling events is present in various organizations such as schools, hospitals, transportation centers. The purpose of timetabling activities at a university is to ensure that all students attend their required subjects in accordance with the available resources. The set of constraints that must be considered in the design of timetables involves students, teachers and infrastructure. This study shows that acceptable solutions are generated through the application of genetic, memetic and immune system algorithms for the problem of timetabling. The algorithms are applied to real instances of the University of Mumbai in India and their results are comparable with those of a human expert

Direct Integration of the Topological String

We present a new method to solve the holomorphic anomaly equations governing the free energies of type B topological strings. The method is based on direct integration with respect to the non-holomorphic dependence of the amplitudes, and relies on the interplay between non-holomorphicity and modularity properties of the topological string amplitudes. We develop a formalism valid for any Calabi-Yau manifold and we study in detail two examples, providing closed expressions for the amplitudes at low genus, as well as a discussion of the boundary conditions that fix the holomorphic ambiguity. The first example is the non-compact Calabi-Yau underlying Seiberg-Witten theory and its gravitational corrections. The second example is the Enriques Calabi-Yau, which we solve in full generality up to genus six. We discuss various aspects of this model: we obtain a new method to generate holomorphic automorphic forms on the Enriques moduli space, we write down a new product formula for the fiber amplitudes at all genus, and we analyze in detail the field theory limit. This allows us to uncover the modularity properties of SU(2), N=2 super Yang-Mills theory with four massless hypermultiplets.Comment: 75 pages, 3 figure

Multi-Class Clustering of Cancer Subtypes through SVM Based Ensemble of Pareto-Optimal Solutions for Gene Marker Identification

With the advancement of microarray technology, it is now possible to study the expression profiles of thousands of genes across different experimental conditions or tissue samples simultaneously. Microarray cancer datasets, organized as samples versus genes fashion, are being used for classification of tissue samples into benign and malignant or their subtypes. They are also useful for identifying potential gene markers for each cancer subtype, which helps in successful diagnosis of particular cancer types. In this article, we have presented an unsupervised cancer classification technique based on multiobjective genetic clustering of the tissue samples. In this regard, a real-coded encoding of the cluster centers is used and cluster compactness and separation are simultaneously optimized. The resultant set of near-Pareto-optimal solutions contains a number of non-dominated solutions. A novel approach to combine the clustering information possessed by the non-dominated solutions through Support Vector Machine (SVM) classifier has been proposed. Final clustering is obtained by consensus among the clusterings yielded by different kernel functions. The performance of the proposed multiobjective clustering method has been compared with that of several other microarray clustering algorithms for three publicly available benchmark cancer datasets. Moreover, statistical significance tests have been conducted to establish the statistical superiority of the proposed clustering method. Furthermore, relevant gene markers have been identified using the clustering result produced by the proposed clustering method and demonstrated visually. Biological relationships among the gene markers are also studied based on gene ontology. The results obtained are found to be promising and can possibly have important impact in the area of unsupervised cancer classification as well as gene marker identification for multiple cancer subtypes

Minerological aspects of lead sintering

A brief overview on lead sinter microstructure is presented. Characteristic micro-structural features of a good and bad sinter are highlighted and these are used in a case study involving use of a low grade and complex concentrate of lead (-40% Pb) in the sintering operation. The plant sinter produced exhibited low strength and its nticrostructural examination revealed non-uniform distribution of porosity along with unsintered galena and low melting lead silicate phase. Part replacement of limestone by lime helped in producing sinter with good physical properties and desirable microstructure. The sinter with modified feed chemistry had more uniform distribution of porosity and presence of primarily a Pb-Fe silicate phase characterised by a (Pb+Fe):Si mole ratio of 3:1. Ca-Pb-Zn-Fe-Al-silicate phase identified as hardysonite and a spine! phase of the type (Fe,Zn)O.(Fe,Al),OJ. Lead nietal/oxide/sulphide occurred in the sinter only rarely. The likely implications of lime addition to the sinter charge mix are discussed Key Words: Lead. Complex and low grade concentrate. Sintering. Process Mineralog

Instanton counting, Macdonald function and the moduli space of D-branes

We argue the connection of Nekrasov's partition function in the \Omega background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters \epsilon_1, \epsilon_2 of toric action on C^2 factorizes correctly as the character of SU(2)_L \times SU(2)_R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F_0. We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T^2 action allows us to obtain the generating functions of equivariant \chi_y and elliptic genera of the Hilbert scheme of n points on C^2 by the method of topological vertex.Comment: 33 pages, 2 figures, (v2) minor changes, references added, (v3) Comments and more references adde

Prediction of protein interactions on HIV-1-human PPI data using a novel closure-based integrated approach

Discovering Protein-Protein Interactions (PPI) is a new interesting challenge in computational biology. Identifying interactions among proteins was shown to be useful for finding new drugs and preventing several kinds of diseases. The identification of interactions between HIV-1 proteins and Human proteins is a particular PPI problem whose study might lead to the discovery of drugs and important interactions responsible for AIDS. We present the FIST algorithm for extracting hierarchical bi-clusters and minimal covers of association rules in one process. This algorithm is based on the frequent closed itemsets framework to efficiently generate a hierarchy of conceptual clusters and non-redundant sets of association rules with supporting object lists. Experiments conducted on a HIV-1 and Human proteins interaction dataset show that the approach efficiently identifies interactions previously predicted in the literature and can be used to predict new interactions based on previous biological knowledge