Categorical data clustering using a minimum message length criterion

Research on cluster analysis for categorical data continues to develop, new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. We propose a new approach in which clustering and the estimation of the number of clusters is done simultaneously for categorical data. We assume that the data originate from a finite mixture of multinomial distributions and use a minimum message length criterion (MML) to select the number of clusters (Wallace and Bolton, 1986). For this purpose, we implement an EM-type algorithm (Silvestre et al., 2008) based on the (Figueiredo and Jain, 2002) approach. The novelty of the approach rests on the integration of the model estimation and selection of the number of clusters in a single algorithm, rather than selecting this number based on a set of pre-estimated candidate models. The performance of our approach is compared with the use of Bayesian Information Criterion (BIC) (Schwarz, 1978) and Integrated Completed Likelihood (ICL) (Biernacki et al., 2000) using synthetic data. The obtained results illustrate the capacity of the proposed algorithm to attain the true number of cluster while outperforming BIC and ICL since it is faster, which is especially relevant when dealing with large data sets.

Determining the number of clusters in categorical data

Cluster analysis for categorical data has been an active area of research. A well-known problem in this area is the determination of the number of clusters, which is unknown and must be inferred from the data. In order to estimate the number of clusters, one often resorts to information criteria, such as BIC (Bayesian information criterion), MML (minimum message length, proposed by Wallace and Boulton, 1968), and ICL (integrated classification likelihood). In this work, we adopt the approach developed by Figueiredo and Jain (2002) for clustering continuous data. They use an MML criterion to select the number of clusters and a variant of the EM algorithm to estimate the model parameters. This EM variant seamlessly integrates model estimation and selection in a single algorithm. For clustering categorical data, we assume a finite mixture of multinomial distributions and implement a new EM algorithm, following a previous version (Silvestre et al., 2008). Results obtained with synthetic datasets are encouraging. The main advantage of the proposed approach, when compared to the above referred criteria, is the speed of execution, which is especially relevant when dealing with large data sets.

Flexibility in a Stackelberg leadership with differentiated goods

We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.

Previsão de curto prazo do consumo de energia elétrica

Dissertação para a obtenção do grau de Mestre em Engenharia Electrotécnica - Ramo de Energia

Metaheuristic approach to the Holt-Winters optimal short term load forecast

Electricity short-term load forecast is very important for the operation of power systems. In this work a classical exponential smoothing model, the Holt-Winters with double seasonality was used to test for accurate predictions applied to the Portuguese demand time series. Some metaheuristic algorithms for the optimal selection of the smoothing parameters of the Holt-Winters forecast function were used and the results after testing in the time series showed little differences among methods, so the use of the simple local search algorithms is recommended as they are easier to implement.

Metaheuristhic approach to the Holt-Winters optimal short term load forecast

Electricity short-term load forecast is very important for the operation of power systems. In this work a classical exponential smoothing model, the Holt-Winters with double seasonality was used to test for accurate predictions applied to the Portuguese demand time series. Some metaheuristic algorithms for the optimal selection of the smoothing parameters of the Holt-Winters forecast function were used and the results after testing in the time series showed little differences among methods, so the use of the simple local search algorithms is recommended as they are easier to implement.

Fatty liver automatic diagnosis from ultrasound images

In this paper an automatic classification algorithm is proposed for the diagnosis of the liver steatosis, also known as, fatty liver, from ultrasound images. The features, automatically extracted from the ultrasound images used by the classifier, are basically the ones used by the physicians in the diagnosis of the disease based on visual inspection of the ultrasound images. The main novelty of the method is the utilization of the speckle noise that corrupts the ultrasound images to compute textural features of the liver parenchyma relevant for the diagnosis. The algorithm uses the Bayesian framework to compute a noiseless image, containing anatomic and echogenic information of the liver and a second image containing only the speckle noise used to compute the textural features. The classification results, with the Bayes classifier using manually classified data as ground truth show that the automatic classifier reaches an accuracy of 95% and a 100% of sensitivity.

Spatial patterns of leprosy in a hyperendemic state in Northern Brazil, 2001-2012

ABSTRACT OBJECTIVE To describe the spatial patterns of leprosy in the Brazilian state of Tocantins. METHODS This study was based on morbidity data obtained from the Sistema de Informações de Agravos de Notificação (SINAN – Brazilian Notifiable Diseases Information System), of the Ministry of Health. All new leprosy cases in individuals residing in the state of Tocantins, between 2001 and 2012, were included. In addition to the description of general disease indicators, a descriptive spatial analysis, empirical Bayesian analysis and spatial dependence analysis were performed by means of global and local Moran’s indexes. RESULTS A total of 14,542 new cases were recorded during the period under study. Based on the annual case detection rate, 77.0% of the municipalities were classified as hyperendemic (> 40 cases/100,000 inhabitants). Regarding the annual case detection rate in < 15 years-olds, 65.4% of the municipalities were hyperendemic (10.0 to 19.9 cases/100,000 inhabitants); 26.6% had a detection rate of grade 2 disability cases between 5.0 and 9.9 cases/100,000 inhabitants. There was a geographical overlap of clusters of municipalities with high detection rates in hyperendemic areas. Clusters with high disease risk (global Moran’s index: 0.51; p < 0.001), ongoing transmission (0.47; p < 0.001) and late diagnosis (0.44; p < 0.001) were identified mainly in the central-north and southwestern regions of Tocantins. CONCLUSIONS We identified high-risk clusters for transmission and late diagnosis of leprosy in the Brazilian state of Tocantins. Surveillance and control measures should be prioritized in these high-risk municipalities.

Determinants of the use of health care services: multilevel analysis in the Metropolitan Region of Sao Paulo

OBJECTIVE To evaluate the individual and contextual determinants of the use of health care services in the metropolitan region of Sao Paulo.METHODS Data from the Sao Paulo Megacity study – the Brazilian version of the World Mental Health Survey multicenter study – were used. A total of 3,588 adults living in 69 neighborhoods in the metropolitan region of Sao Paulo, SP, Southeastern Brazil, including 38 municipalities and 31 neighboring districts, were selected using multistratified sampling of the non-institutionalized population. Multilevel Bayesian logistic models were adjusted to identify the individual and contextual determinants of the use of health care services in the past 12 months and presence of a regular physician for routine care.RESULTS The contextual characteristics of the place of residence (income inequality, violence, and median income) showed no significant correlation (p > 0.05) with the use of health care services or with the presence of a regular physician for routine care. The only exception was the negative correlation between living in areas with high income inequality and presence of a regular physician (OR: 0.77; 95%CI 0.60;0.99) after controlling for individual characteristics. The study revealed a strong and consistent correlation between individual characteristics (mainly education and possession of health insurance), use of health care services, and presence of a regular physician. Presence of chronic and mental illnesses was strongly correlated with the use of health care services in the past year (regardless of the individual characteristics) but not with the presence of a regular physician.CONCLUSIONS Individual characteristics including higher education and possession of health insurance were important determinants of the use of health care services in the metropolitan area of Sao Paulo. A better understanding of these determinants is essential for the development of public policies that promote equitable use of health care services.

Spatial analysis of avoidable hospitalizations due to tuberculosis in Ribeirao Preto, SP, Brazil (2006-2012)

ABSTRACT OBJECTIVE To describe the spatial distribution of avoidable hospitalizations due to tuberculosis in the municipality of Ribeirao Preto, SP, Brazil, and to identify spatial and space-time clusters for the risk of occurrence of these events. METHODS This is a descriptive, ecological study that considered the hospitalizations records of the Hospital Information System of residents of Ribeirao Preto, SP, Southeastern Brazil, from 2006 to 2012. Only the cases with recorded addresses were considered for the spatial analyses, and they were also geocoded. We resorted to Kernel density estimation to identify the densest areas, local empirical Bayes rate as the method for smoothing the incidence rates of hospital admissions, and scan statistic for identifying clusters of risk. Softwares ArcGis 10.2, TerraView 4.2.2, and SaTScanTM were used in the analysis. RESULTS We identified 169 hospitalizations due to tuberculosis. Most were of men (n = 134; 79.2%), averagely aged 48 years (SD = 16.2). The predominant clinical form was the pulmonary one, which was confirmed through a microscopic examination of expectorated sputum (n = 66; 39.0%). We geocoded 159 cases (94.0%). We observed a non-random spatial distribution of avoidable hospitalizations due to tuberculosis concentrated in the northern and western regions of the municipality. Through the scan statistic, three spatial clusters for risk of hospitalizations due to tuberculosis were identified, one of them in the northern region of the municipality (relative risk [RR] = 3.4; 95%CI 2.7–4,4); the second in the central region, where there is a prison unit (RR = 28.6; 95%CI 22.4–36.6); and the last one in the southern region, and area of protection for hospitalizations (RR = 0.2; 95%CI 0.2–0.3). We did not identify any space-time clusters. CONCLUSIONS The investigation showed priority areas for the control and surveillance of tuberculosis, as well as the profile of the affected population, which shows important aspects to be considered in terms of management and organization of health care services targeting effectiveness in primary health care.

Probabilistic models for mechanical properties of prestressing strands

This study focus on the probabilistic modelling of mechanical properties of prestressing strands based on data collected from tensile tests carried out in Laboratório Nacional de Engenharia Civil (LNEC), Portugal, for certification purposes, and covers a period of about 9 years of production. The strands studied were produced by six manufacturers from four countries, namely Portugal, Spain, Italy and Thailand. Variability of the most important mechanical properties is examined and the results are compared with the recommendations of the Probabilistic Model Code, as well as the Eurocodes and earlier studies. The obtained results show a very low variability which, of course, benefits structural safety. Based on those results, probabilistic models for the most important mechanical properties of prestressing strands are proposed.

Bertrand model under incomplete information

We consider a Bertrand duopoly model with unknown costs. The firms' aim is to choose the price of its product according to the well-known concept of Bayesian Nash equilibrium. The chooses are made simultaneously by both firms. In this paper, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We analyse the advantages, for firms and for consumers, of using the technology with highest production cost versus the one with cheapest production cost. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.

Bertrand oligopoly when rivals' costs are unknown

We study a Bertrand oligopoly model with incomplete information about rivals' costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian-Nash equilibrium of this game, the ex-ante expected profit and the ex-post profit of each firm. We see that, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.

Cournot competition between a non-profit firm and a for-profit firm with uncertainty

In this paper, we consider a Cournot competition between a nonprofit firm and a for-profit firm in a homogeneous goods market, with uncertain demand. Given an asymmetric tax schedule, we compute explicitly the Bayesian-Nash equilibrium. Furthermore, we analyze the effects of the tax rate and the degree of altruistic preference on market equilibrium outcomes.

Bertrand and Cournot oligopolies when rivals' costs are unknown

We study Bertrand and Cournot oligopoly models with incomplete information about rivals’ costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian- Nash equilibrium of both games, the ex-ante expected profits and the ex-post profits of each firm. We see that, in the price competition, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.