Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.

Measure of Global Specialization and Spatial Clustering for the Identification of "Specialized" Agglomeration

The intensity of regional specialization in specific activities, and conversely, the level of industrial concentration in specific locations, has been used as a complementary evidence for the existence and significance of externalities. Additionally, economists have mainly focused the debate on disentangling the sources of specialization and concentration processes according to three vectors: natural advantages, internal, and external scale economies. The arbitrariness of partitions plays a key role in capturing these effects, while the selection of the partition would have to reflect the actual characteristics of the economy. Thus, the identification of spatial boundaries to measure specialization becomes critical, since most likely the model will be adapted to different scales of distance, and be influenced by different types of externalities or economies of agglomeration, which are based on the mechanisms of interaction with particular requirements of spatial proximity. This work is based on the analysis of the spatial aspect of economic specialization supported by the manufacturing industry case. The main objective is to propose, for discrete and continuous space: i) a measure of global specialization; ii) a local disaggregation of the global measure; and iii) a spatial clustering method for the identification of specialized agglomerations.

Comparing Different Approaches for Clustering Categorical Data

There are different ways to do cluster analysis of categorical data in the literature and the choice among them is strongly related to the aim of the researcher, if we do not take into account time and economical constraints. Main approaches for clustering are usually distinguished into model-based and distance-based methods: the former assume that objects belonging to the same class are similar in the sense that their observed values come from the same probability distribution, whose parameters are unknown and need to be estimated; the latter evaluate distances among objects by a defined dissimilarity measure and, basing on it, allocate units to the closest group. In clustering, one may be interested in the classification of similar objects into groups, and one may be interested in finding observations that come from the same true homogeneous distribution. But do both of these aims lead to the same clustering? And how good are clustering methods designed to fulfil one of these aims in terms of the other? In order to answer, two approaches, namely a latent class model (mixture of multinomial distributions) and a partition around medoids one, are evaluated and compared by Adjusted Rand Index, Average Silhouette Width and Pearson-Gamma indexes in a fairly wide simulation study. Simulation outcomes are plotted in bi-dimensional graphs via Multidimensional Scaling; size of points is proportional to the number of points that overlap and different colours are used according to the cluster membership.

A copy of the general map the most part compiled from the actual survey by order of the commisioners appointed to settle the partition line between the provinces of New York and New Jersey : manuscript map, 1769

Map showing the whole of New Jersey and its borders with as well as part of Pennsylvania and New York. Map is drawn in black ink with green, pink, and yellow watercolors used to show features such as waterways, borders, and places of interest. Notes on map concern border disputes between New Jersey and New York.

Copy of the return of the writ of partition relating to the lands of Peter Weare & others of Casco Bay : manuscript, [1730]

Document concerns how certain lands around Casco Bay, York Co., Maine, were partitioned in accordance with an order of a writ.

Photoelastic Analysis Of Fixed Partial Prosthesis Crown Height And Implant Length On Distribution Of Stress In Two Dental Implant Systems.

The aim of this study was to evaluate by photoelastic analysis stress distribution on short and long implants of two dental implant systems with 2-unit implant-supported fixed partial prostheses of 8 mm and 13 mm heights. Sixteen photoelastic models were divided into 4 groups: I: long implant (5 × 11 mm) (Neodent), II: long implant (5 × 11 mm) (Bicon), III: short implant (5 × 6 mm) (Neodent), and IV: short implants (5 × 6 mm) (Bicon). The models were positioned in a circular polariscope associated with a cell load and static axial (0.5 Kgf) and nonaxial load (15°, 0.5 Kgf) were applied to each group for both prosthetic crown heights. Three-way ANOVA was used to compare the factors implant length, crown height, and implant system (α = 0.05). The results showed that implant length was a statistically significant factor for both axial and nonaxial loading. The 13 mm prosthetic crown did not result in statistically significant differences in stress distribution between the implant systems and implant lengths studied, regardless of load type (P > 0.05). It can be concluded that short implants showed higher stress levels than long implants. Implant system and length was not relevant factors when prosthetic crown height were increased.

Waist-to-height Ratio Percentiles And Cutoffs For Obesity: A Cross-sectional Study In Brazilian Adolescents.

This study aimed to describe the distribution of waist-to-height ratio (WHtR) percentiles and cutoffs for obesity in Brazilian adolescents. A cross-sectional study including adolescents aged 10 to 15 years was conducted in the city of São Paulo, Brazil; anthropometric measurements (weight, height, and waist-circumference) were taken, and WHtRs were calculated and then divided into percentiles derived by using Least Median of Squares (LMS) regression. The receiver operating characteristic (ROC) curve was used in determining cutoffs for obesity (BMI ≥ 97th percentile) and Mann-Whitney and Kruskal-Wallis tests were used for comparing variables. The study included 8,019 adolescents from 43 schools, of whom 54.5% were female, and 74.8% attended public schools. Boys had higher mean WHtR than girls (0.45 ± 0.06 vs 0.44 ± 0.05; p=0.002) and higher WHtR at the 95th percentile (0.56 vs 0.54; p<0.05). The WHtR cutoffs according to the WHO criteria ranged from 0.467 to 0.506 and 0.463 to 0.496 among girls and boys respectively, with high sensitivity (82.8-95%) and specificity (84-95.5%). The WHtR was significantly associated with body adiposity measured by BMI. Its age-specific percentiles and cutoffs may be used as additional surrogate markers of central obesity and its co-morbidities.

Clustering Of Water Bodies In Unpolluted And Polluted Environments Based On Escherichia Coli Phylogroup Abundance Using A Simple Interaction Database.

Different types of water bodies, including lakes, streams, and coastal marine waters, are often susceptible to fecal contamination from a range of point and nonpoint sources, and have been evaluated using fecal indicator microorganisms. The most commonly used fecal indicator is Escherichia coli, but traditional cultivation methods do not allow discrimination of the source of pollution. The use of triplex PCR offers an approach that is fast and inexpensive, and here enabled the identification of phylogroups. The phylogenetic distribution of E. coli subgroups isolated from water samples revealed higher frequencies of subgroups A1 and B23 in rivers impacted by human pollution sources, while subgroups D1 and D2 were associated with pristine sites, and subgroup B1 with domesticated animal sources, suggesting their use as a first screening for pollution source identification. A simple classification is also proposed based on phylogenetic subgroup distribution using the w-clique metric, enabling differentiation of polluted and unpolluted sites.

Validity and reliability of self-reported weight and height measures for the diagnoses of adolescent's nutritional status

OBJETIVO: Avaliar a validade do peso, estatura e Índice de Massa Corporal (IMC) referidos e sua confiabilidade para o diagnóstico do estado nutricional de adolescentes de Piracicaba. MÉTODOS: Participaram do estudo 360 adolescentes de ambos os sexos, de escolas públicas de Piracicaba, com idade entre 10 e 15 anos. Os adolescentes auto-relataram seu peso e estatura, sendo esses valores obtidos por medidas diretas, logo em seguida, pelos entrevistadores. A validade do IMC referido foi calculada segundo índices de sensibilidade, especificidade e valor preditivo positivo (VPP). Avaliou-se a concordância entre as categorias de IMC obtido por meio das medidas referidas e aferidas a partir do coeficiente kappa ponderado, coeficiente de correlação de Lin. e gráficos de Bland e Altman e Lin. RESULTADOS: Verificou-se que tanto os meninos quanto as meninas subestimaram o peso (-1,0 meninas e meninos) e a estatura (meninas -1,2 e meninos -0,8) (p < 0,001). Os valores de IMC aferidos e referidos apresentaram uma concordância moderada. A sensibilidade do IMC referido para classificar os indivíduos obesos foi maior para os meninos (87,5%), enquanto a especificidade foi maior para as meninas (92,7%). O VPP foi elevado somente para a classificação da eutrofia. CONCLUSÕES: As medidas referidas de peso e estatura de adolescentes não representam medidas válidas e, portanto, não devem ser usadas em substituição aos valores mensurados. Além disso, verificou-se que 10% dos meninos obesos e 40% das meninas obesas poderiam permanecer não identificados utilizando-se as medidas auto-referidas, confirmando a baixa validade das medidas auto-referidas.

Ratio of weight to height gain: a useful tool for identifying children at risk of becoming overweight or obese at preschool age

PURPOSE: To analyze the usefulness of the weight gain/height gain ratio from birth to two and three years of age as a predictive risk indicator of excess weight at preschool age. METHODS: The weight and height/length of 409 preschool children at daycare centers were measured according to internationally recommended rules. The weight values and body mass indices of the children were transformed into a z-score per the standard method described by the World Health Organization. The Pearson correlation coefficients (rP) and the linear regressions between the anthropometric parameters and the body mass index z-scores of preschool children were statistically analyzed (alpha = 0.05). RESULTS: The mean age of the study population was 3.2 years (± 0.3 years). The prevalence of excess weight was 28.8%, and the prevalence of overweight and obesity was 8.8%. The correlation coefficients between the body mass index z-scores of the preschool children and the birth weights or body mass indices at birth were low (0.09 and 0.10, respectively). There was a high correlation coefficient (rP = 0.79) between the mean monthly gain of weight and the body mass index z-score of preschool children. A higher coefficient (rP = 0.93) was observed between the ratio of the mean weight gain per height gain (g/cm) and the preschool children body mass index z-score. The coefficients and their differences were statistically significant. CONCLUSION: Regardless of weight or length at birth, the mean ratio between the weight gain per g/cm of height growth from birth presented a strong correlation with the body mass index of preschool children. These results suggest that this ratio may be a good indicator of the risk of excess weight and obesity in preschool-aged children.

Spatial clustering analysis of the foot-and-mouth disease outbreaks in Mato Grosso do Sul state, Brazil - 2005

In the southern region of Mato Grosso do Sul state, Brazil, a foot-and-mouth disease (FMD) epidemic started in September 2005. A total of 33 outbreaks were detected and 33,741 FMD-susceptible animals were slaughtered and destroyed. There were no reports of FMD cases in other species than bovines. Based on the data of this epidemic, it was carried out an analysis using the K-function and it was observed spatial clustering of outbreaks within a range of 25km. This observation may be related to the dynamics of foot-and-mouth disease spread and to the measures undertaken to control the disease dissemination. The control measures were effective once the disease did not spread to farms more than 47 km apart from the initial outbreaks.

The full Bayesian significance test for mixture models: results in gene expression clustering

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method's sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results.

Load Ratio Estimation Through Striation Height and Spacing Analysis of an Aerospace Al Alloy 7475-T7351

It is well known that striation spacing may be related to the crack growth rate, da/dN, through Paris equation, as well as the maximum and minimum loads under service loading conditions. These loads define the load ratio, R, and are considered impossible to be evaluated from the inter-spacing striations analysis. In this way, this study discusses the methodology proposed by Furukawa to evaluate the maximum and minimum loads based on the experimental fact that the relative height of a striation, H, and the striation spacing, s, are strongly influenced by the load ratio, R. Fatigue tests in C(T) specimens were conducted on SAE 7475-T7351 Al alloy plates at room temperature and the results showed a straightforward correlation between the parameters H, s, and R. Measurements of striation height, H, were performed using scanning electron microscopy and field emission gun (FEG) after sectioning the specimen at a large inclined angle to amplify the height of the striations. The results showed that for increasing R the values of H/s tend to increase. Striation height, striation spacing, and load ratio correlations were obtained, which allows one to estimate service loadings from fatigue fracture surface survey.

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

Visual Display Height

We examined the influence of backrest inclination and vergence demand on the posture and gaze angle that-workers adopt to view visual targets placed in different vertical locations. In the study 12 participants viewed a small video monitor placed in 7 locations around a 0.65-m radius arc (from 650 below to 300 above horizontal eye height). Trunk posture was manipulated by changing the backrest inclination of an adjustable chair. Vergence demand was manipulated by using ophthalmic lenses and prisms to mimic the visual consequences of varying target distance. Changes in vertical target location caused large changes in atlantooccipital posture and gaze angle. Cervical posture was altered to a lesser extent by changes in vertical target location. Participants compensated for changes in backrest inclination by changing cervical posture, though they did not significantly alter atlanto-occipital posture and gaze angle. The posture adopted to view any target represents a compromise between visual and musculoskeletal demands. These results provide support for the argument that the optimal location of visual targets is at least 15 below horizontal eye level. Actual or potential applications of this work include the layout of computer workstations and the viewing of displays from a seated posture.