Probabilistic consensus clustering using evidence accumulation

Clustering ensemble methods produce a consensus partition of a set of data points by combining the results of a collection of base clustering algorithms. In the evidence accumulation clustering (EAC) paradigm, the clustering ensemble is transformed into a pairwise co-association matrix, thus avoiding the label correspondence problem, which is intrinsic to other clustering ensemble schemes. In this paper, we propose a consensus clustering approach based on the EAC paradigm, which is not limited to crisp partitions and fully exploits the nature of the co-association matrix. Our solution determines probabilistic assignments of data points to clusters by minimizing a Bregman divergence between the observed co-association frequencies and the corresponding co-occurrence probabilities expressed as functions of the unknown assignments. We additionally propose an optimization algorithm to find a solution under any double-convex Bregman divergence. Experiments on both synthetic and real benchmark data show the effectiveness of the proposed approach.

Additive adaptive thinking in 1st and 2nd grades pupils

This paper is part of the Project “Adaptive thinking and flexible computation: Critical issues”. It discusses what is meant by adaptive thinking and presents the results of individual interviews with four pupils. The main goal of the study is to understand pupils’ reasoning when solving numerical tasks involving additive situations, and identify features associated with adaptive thinking. The results show that, in the case of first grade pupils, the semantic aspects of the problem are involved in its resolution and the pupils’ performance appears to be related to the development of number sense. The 2nd grade pupils seem to see the quantitative difference as an invariant numerical relationship.

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

A MAP approach to evidence accumulation clustering

The Evidence Accumulation Clustering (EAC) paradigm is a clustering ensemble method which derives a consensus partition from a collection of base clusterings obtained using different algorithms. It collects from the partitions in the ensemble a set of pairwise observations about the co-occurrence of objects in a same cluster and it uses these co-occurrence statistics to derive a similarity matrix, referred to as co-association matrix. The Probabilistic Evidence Accumulation for Clustering Ensembles (PEACE) algorithm is a principled approach for the extraction of a consensus clustering from the observations encoded in the co-association matrix based on a probabilistic model for the co-association matrix parameterized by the unknown assignments of objects to clusters. In this paper we extend the PEACE algorithm by deriving a consensus solution according to a MAP approach with Dirichlet priors defined for the unknown probabilistic cluster assignments. In particular, we study the positive regularization effect of Dirichlet priors on the final consensus solution with both synthetic and real benchmark data.

Mn-II and Cu-II complexes with arylhydrazones of active methylene compounds as effective heterogeneous catalysts for solvent- and additive-free microwave-assisted peroxidative oxidation of alcohols

A one-pot template reaction of sodium 2-(2-(dicyanomethylene) hydrazinyl) benzenesulfonate (NaHL1) with water and manganese(II) acetate tetrahydrate led to the mononuclear complex [Mn(H2O)(6)](HL1a)(2)center dot 4H(2)O (1), where (HL1a) -= 2-(SO3-)C6H4(NH)=N=C(C N) (CONH2) is the carboxamide species derived from nucleophilic attack of water on a cyano group of (HL1) . The copper tetramer [Cu-4(H2O)(10)(-) (1 kappa N: kappa O-2: kappa O, 2 kappa N: k(O)-L-2)(2)]center dot 2H(2)O (2) was obtained from reaction of Cu(NO3)(2)center dot 2.5H(2)O with sodium 5-(2( 4,4-dimethyl-2,6-dioxocyclohexylidene) hydrazinyl)-4-hydroxybenzene-1,3-disulfonate (Na2H2L2). Both complexes were characterized by elemental analysis, IR spectroscopy, ESI-MS and single crystal X-ray diffraction. They exhibit a high catalytic activity for the solvent-and additive-free microwave (MW) assisted oxidation of primary and secondary alcohols with tert-butylhydroperoxide, leading to yields of the oxidized products up to 85.5% and TOFs up to 1.90 x 103 h(-1) after 1 h under low power (5-10 W) MW irradiation. Moreover, the heterogeneous catalysts are easily recovered and reused, at least for three consecutive cycles, maintaining 89% of the initial activity and a high selectivity.

Comparing clustering solutions: the use of adjusted paired indices

In the present paper we compare clustering solutions using indices of paired agreement. We propose a new method - IADJUST - to correct indices of paired agreement, excluding agreement by chance. This new method overcomes previous limitations known in the literature as it permits the correction of any index. We illustrate its use in external clustering validation, to measure the accordance between clusters and an a priori known structure. The adjusted indices are intended to provide a realistic measure of clustering performance that excludes agreement by chance with ground truth. We use simulated data sets, under a range of scenarios - considering diverse numbers of clusters, clusters overlaps and balances - to discuss the pertinence and the precision of our proposal. Precision is established based on comparisons with the analytical approach for correction specific indices that can be corrected in this way are used for this purpose. The pertinence of the proposed correction is discussed when making a detailed comparison between the performance of two classical clustering approaches, namely Expectation-Maximization (EM) and K-Means (KM) algorithms. Eight indices of paired agreement are studied and new corrected indices are obtained.

Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations Research

DC Fuzzy Multicriteria Approach to Increase the Probability of Delivering Power in Distribution Networks

This paper proposes a methodology to increase the probability of delivering power to any load point through the identification of new investments. The methodology uses a fuzzy set approach to model the uncertainty of outage parameters, load and generation. A DC fuzzy multicriteria optimization model considering the Pareto front and based on mixed integer non-linear optimization programming is developed in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power to all customers in the distribution network at the minimum possible cost for the system operator, while minimizing the non supplied energy cost. To illustrate the application of the proposed methodology, the paper includes a case study which considers an 33 bus distribution network.

Algorithms for time series clustering applied to biomedical signals

Thesis submitted in the fulfillment of the requirements for the Degree of Master in Biomedical Engineering

Intake of milk, but not total dairy, yogurt, or cheese, is negatively associated with the clustering of cardiometabolic risk factors in adolescents

Epidemiologic studies have reported an inverse association between dairy product consumption and cardiometabolic risk factors in adults, but this relation is relatively unexplored in adolescents. We hypothesized that a higher dairy product intake is associated with lower cardiometabolic risk factor clustering in adolescents. To test this hypothesis, a cross-sectional study was conducted with 494 adolescents aged 15 to 18 years from the Azorean Archipelago, Portugal. We measured fasting glucose, insulin, total cholesterol, high-density lipoprotein cholesterol, triglycerides, systolic blood pressure, body fat, and cardiorespiratory fitness. We also calculated homeostatic model assessment and total cholesterol/high-density lipoprotein cholesterol ratio. For each one of these variables, a z score was computed using age and sex. A cardiometabolic risk score (CMRS) was constructed by summing up the z scores of all individual risk factors. High risk was considered to exist when an individual had at least 1 SD from this score. Diet was evaluated using a food frequency questionnaire, and the intake of total dairy (included milk, yogurt, and cheese), milk, yogurt, and cheese was categorized as low (equal to or below the median of the total sample) or “appropriate” (above the median of the total sample).The association between dairy product intake and CMRS was evaluated using separate logistic regression, and the results were adjusted for confounders. Adolescents with high milk intake had lower CMRS, compared with those with low intake (10.6% vs 18.1%, P = .018). Adolescents with appropriate milk intake were less likely to have high CMRS than those with low milk intake (odds ratio, 0.531; 95% confidence interval, 0.302-0.931). No association was found between CMRS and total dairy, yogurt, and cheese intake. Only milk intake seems to be inversely related to CMRS in adolescents.

An intelligent clustering scheme for distributed intrusion detection in vehicular cloud computing

In recent years, vehicular cloud computing (VCC) has emerged as a new technology which is being used in wide range of applications in the area of multimedia-based healthcare applications. In VCC, vehicles act as the intelligent machines which can be used to collect and transfer the healthcare data to the local, or global sites for storage, and computation purposes, as vehicles are having comparatively limited storage and computation power for handling the multimedia files. However, due to the dynamic changes in topology, and lack of centralized monitoring points, this information can be altered, or misused. These security breaches can result in disastrous consequences such as-loss of life or financial frauds. Therefore, to address these issues, a learning automata-assisted distributive intrusion detection system is designed based on clustering. Although there exist a number of applications where the proposed scheme can be applied but, we have taken multimedia-based healthcare application for illustration of the proposed scheme. In the proposed scheme, learning automata (LA) are assumed to be stationed on the vehicles which take clustering decisions intelligently and select one of the members of the group as a cluster-head. The cluster-heads then assist in efficient storage and dissemination of information through a cloud-based infrastructure. To secure the proposed scheme from malicious activities, standard cryptographic technique is used in which the auotmaton learns from the environment and takes adaptive decisions for identification of any malicious activity in the network. A reward and penalty is given by the stochastic environment where an automaton performs its actions so that it updates its action probability vector after getting the reinforcement signal from the environment. The proposed scheme was evaluated using extensive simulations on ns-2 with SUMO. The results obtained indicate that the proposed scheme yields an improvement of 10 % in detection rate of malicious nodes when compared with the existing schemes.

Analysis of UV spectral bands using multidimensional scaling

This study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200–400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a Shimadzu UV–VIS 2550, which is in the world the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.