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[en] A method for clustering large amounts of data is presented which is a sequenced composition of two algorithms: the former builds a partition of input space into Voronoi regions and the latter clusters them. First, a model of clusters as high-density regions in input space is presented, then it is shown how a Voronoi partition and its topological map a) can be built and b) used as a low complexity approximation of the input space. During the b) step, the usage of 'watershed' algorithm is presented which has been previously used for image segmentation, but it is its application to a data space partition that is proposed by the authors.
[ru]В данной статье представлен метод кластеризации данных большого объема в виде последовательной композиции двух алгоритмов: первый строит разбиение входного пространства на области Вороного, а второй кластеризует их. Во-первых, представлена модель кластеризации данных как областей большой плотности во входном пространстве, затем показано, как разбиение Вороного и его топология могут быть а) построены и б) использованы как упрощенное приближение входного пространства. В течение шага б) показано действие алгоритма 'Водораздел', который часто используется для сегментации изображений, но это его первое применение в разбиении пространства входных данных, известное авторам.
[en] This systematic review aimed to synthesise multimorbidity profiling literature to identify replicable and clinically meaningful groupings of multimorbidity. We searched six electronic databases (Medline, EMBASE, PsycINFO, CINAHL, Scopus, and Web of Science) for articles reporting multimorbidity profiles. The identified profiles were synthesised with multidimensional scaling, stratified by type of statistical analysis used in the derivation of profiles. The 51 studies that met inclusion criteria reported results of 98 separate analyses of multimorbidity profiling, with a total of 407 multimorbidity profiles identified. The statistical techniques used to identify multimorbidity profiles were exploratory factor analysis, cluster analysis of diseases, cluster analysis of people, and latent class analysis. Reporting of methodological details of statistical methods was often incomplete. The discernible groupings of multimorbidity took the form of both discrete categories and continuous dimensions. Mental health conditions and cardio-metabolic conditions grouped along identifiable continua in the synthesised results of all four methods. Discrete groupings of chronic obstructive pulmonary disease with asthma, falls and fractures with sensory deficits and of Parkinson’s disease and cognitive decline where partially replicable (identifiable in the results of more than one method), while clustering of musculoskeletal conditions and clustering of reproductive systems were each observed only in one statistical approach. The two most replicable multimorbidity profiles were mental health conditions and cardio-metabolic conditions. Further studies are needed to understand aetiology and evolution of these multimorbidity groupings. Guidelines for strengthening the reporting of multimorbidity profiling studies are proposed.
[en] Based on daily precipitation records at 52 meteorological stations in Jiangsu Province, southeast China, the space and time changes of characteristics in rainfall erosivity (RE) during 1961–2012 were analyzed. The meteorological and topographical diagnosis methods including Mann–Kendall trend test, Ensemble Empirical Mode Decomposition (EEMD), and K-means cluster analysis (KCA) were used. The result showed that the average annual RE in Jiangsu was 8621.8 (MJ mm ha−1 h−1 a−1), and more than 50% of the annual RE was concentrated in summer. In contrast, the intra-annual distribution of RE in north Jiangsu presented higher concentration. There was an obvious seasonal difference in temporal trends of RE at the scale of station, and most of stations were characterized by increasing RE in winter and summer. Especially all the stations were dominated by significantly increasing RE in winter. By using KCA, Jiangsu could be divided into three sub-regions with different temporal variations in annual RE such as northern, central and southern area, and the southern area was dominated by a significant increasing tendency. Furthermore, EEMD for regional series of annual RE indicated that a 2.5–2.6 year periodical feature was noticeable in each sub-region.
[en] Intuitionistic fuzzy relations are used to construct hierarchical structures for the evaluation of vague complicated humanistic systems. A novel algorithm to develop partition trees at different levels according to different intuitionistic fuzzy triangular norm composition is presented. Examples are given to demonstrate the usefulness of the proposed algorithm.
[en] The profile management of nanomaterials requires a complicated synergy between component function and shape, material, process, and costs. This study attempts to uncover these relationships by grouping nanomaterial profile components with matching characteristics using cluster analysis. The analysis resulted in the identification of 11 distinct clusters, out of which the physicochemical properties appear to have the higher complexity. We found that this is an efficient method for inspecting the heterogeneity of the nanomaterial profile building blocks and for quantifying nanomaterial characteristics. Using the Cynefin framework, we identified the parameters, which allowed us to comprehend the complexity of the issues, design relative strategies, and overcome difficulties stemming from the application of reductionist approaches on complicated circumstances. It introduces the emergence and implications of “complex” approaches within nanomaterial profile. Cost lies in the disorder domain and the urgency to address the critical issue of asymmetric information calls to understand complex relations. The crux of the issue is the lack of a connected profiling chain that links the nanomaterial development process steps, cost, risk, and toxicity studies, which could reduce opposition from “nano-skeptics” providing sufficient safeguards given the predictive growth of nanomaterials. .
[en] The warming trend in the Arctic is almost twice as large as the global average in recent decades. This is known as Arctic amplification. In this paper, we perform a cluster analysis of temperature time series for eight latitude bands. Our empirical findings confirm the Arctic amplification and further shed light on this phenomenon. In particular, our investigation allows us to go beyond the simple descriptive analysis of the data. The adopted distance measures the differences between the data generating processes behind the series. Differences in the dynamic structures of the considered series are then taken into consideration allowing for a more comprehensive understanding of the phenomenon.
[en] Using two volume-limited Main galaxy samples of the Sloan Digital Sky Survey Data Release 10 (SDSS DR10), we investigate the dependence of the clustering properties of galaxies on stellar velocity dispersion by cluster analysis. It is found that in the luminous volume-limited Main galaxy sample, except at r=1.2, richer and larger systems can be more easily formed in the large stellar velocity dispersion subsample, while in the faint volume-limited Main galaxy sample, at r≥0.9, an opposite trend is observed. According to statistical analyses of the multiplicity functions, we conclude in two volume-limited Main galaxy samples: small stellar velocity dispersion galaxies preferentially form isolated galaxies, close pairs and small group, while large stellar velocity dispersion galaxies preferentially inhabit the dense groups and clusters. However, we note the difference between two volume-limited Main galaxy samples: in the faint volume-limited Main galaxy sample, at r≥0.9, the small stellar velocity dispersion subsample has a higher proportion of galaxies in superclusters (n≥200) than the large stellar velocity dispersion subsample.
[en] Highlights: • First use of topological data analysis in spectroscopic imaging. • Detection of minor compounds in a multiphase chemical system. • TDA: a new paradigm for cluster analysis in the framework of imaging. - Abstract: Analytical chemistry is rapidly changing. Indeed we acquire always more data in order to go ever further in the exploration of complex samples. Hyperspectral imaging has not escaped this trend. It quickly became a tool of choice for molecular characterisation of complex samples in many scientific domains. The main reason is that it simultaneously provides spectral and spatial information. As a result, chemometrics has provided many exploration tools (PCA, clustering, MCR-ALS …) well-suited for such data structure at early stage. However we are today facing a new challenge considering the always increasing number of pixels in the data cubes we have to manage. The idea is therefore to introduce a new paradigm of Topological Data Analysis in order explore hyperspectral imaging data sets highlighting its nice properties and specific features. With this paper, we shall also point out the fact that conventional chemometric methods are often based on variance analysis or simply impose a data model which implicitly defines the geometry of the data set. Thus we will show that it is not always appropriate in the framework of hyperspectral imaging data sets exploration.
[en] Fullerenes tend to form clusters in different solutions. In this work, a brief survey and some results in the field of investigations of the structure and kinetics of clusters growing in C60 solutions are presented. The general character of this phenomenon for fullerenes is emphasized, and the considerations of mechanisms responsible for the formation and growth of clusters are discussed. We distinguish different types of fullerene solvents by the aggregation mechanism. The kinetics of cluster growth measured via the dynamic light scattering is presented. The complicated structure of clusters in different solutions is briefly discussed. (author)
[en] Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was proved that when the degrees obey a power law with exponent , the sequence of clusters ordered in decreasing size and multiplied through by converges as to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237–269, 2001) for the Erdős–Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.