clustering

The performance of judiciary branches is evaluated based on specific indicators determined by the Statistics and Information Technology Center of Judiciary‎. ‎These indicators‎, ‎which are usually documents recorded in court cases‎, ‎have a specific administrative or judicial score for the branch‎, ‎and by calculating the total scores‎, ‎the performance of the branches is evaluated‎. ‎However‎, ‎with the expansion of these indicators‎, ‎ranking and evaluating branch performance has become more complex‎. ‎In this article‎, ‎clustering is used as one of the most important data mining tools to evaluate branch performance‎. ‎By identifying similar branches‎, ‎examining branches‎, ‎and facing upcoming challenges more effectively‎, ‎more effective decisions can be made in the judiciary system‎. ‎Here‎, ‎to organize 19 law branches based on 49 different administrative and judicial indicators‎, ‎the K-means clustering algorithm is applied based on two criteria of Euclidean dissimilarity distance and random forests‎. ‎In addition‎, ‎the Dunn index is used to evaluate clustering‎. ‎The value of this index is calculated as 0.82 by applying the dissimilarity of random forests‎, ‎indicating the successful performance of the algorithm used in determining similar branches.

The two main goals in model selection are firstly introducing an approach to test homogeneity of several rival models and secondly selecting a set of reasonable models or estimating the best rival model to the true one. In this paper we extend Vuong's method for several models to cluster them. Based on the working paper of Katayama $(2008)$, we propose an approach to test whether rival models have expected relations. The multivariate extension of Vuong's test gives the opportunity to examine some hypotheses about the rival models and their relations with respect to the unknown true model. On the other hand, the standard method of model selection provides an implementation of Occam's razor, in which parsimony or simplicity is balanced against goodness of fit. Therefore, we are interested in clustering the rival models based on their divergence from the true model to select a suitable set of rival models. In this paper we have introduced two approaches to select suitable sets of rival models based on the multivariate extension of Vuong's test and quasi clustering approach.

Today, data is produced in large volumes, and from multiple sources, so this has caused problems in service. These problems can also affect the speed and accuracy of emergency services. Therefore, access to various resources and databases, information extraction to evaluate and analyze data and provide appropriate solutions for citizens is inevitable. In this paper evaluation of clusters is used for Getis-ord Gi* statistics and Anselin Local Moranchr('39')s I statistics to identify the behavioral pattern of data. The data used in this article is a large free dataset of Spatio-temporal emergency call events from the United States. Accidental call events in five years are evaluated from this dataset. Moran statistics are used to identify and detect the events which have the pattern of spatial distribution. A high/low distribution pattern of accidental events was obtained through Hotspot maps, an annual comparison and evaluation are made by survey the distribution map of events. Clustering Hotspots Map with Gi* statistics represents the spatial correlation between positive and negative events. In these distribution patterns, clusters with high value are called Hot-spots, and low-value clusters are called Cold-spots. Similarly, clustering maps of accidental events get evaluated every five years; then the Gi indicator evaluates each cluster for every two years. A positive z-score and G-index indicate that the data have a positive spatial correlation; its results show that the distribution pattern is similar in each year with an average of 93 percent. Then, hot/cold spot clustering maps of 5-year accidental events are also created with the general Moran indicator. Moreover, a confidence level is created after calculating the p-value and z-score. In all 5-year data calculations, the Moran coefficient of accidental events is greater than the expected coefficient. Evaluation of biennial clustering maps with Moran index showed that there is more than 96percent behavioral similarity of dispersion pattern in both years. Raster clustering maps are also created to evaluate the clustering of Moran and Gi indicates. The similarity of raster clusters is more than 95percent per year. The results show that the pattern of accident distribution is the same in 5 years. Although the number of accidents has decreased during this period, the hotspots of accidents have not changed significantly in the city. Furthermore, hotspots indicate a high density of accidental events with 95percent confidence in the study area, and most accidents occur on the South Claiborne and New Orleans highways and at intersections with major streets.

The use of mixture models for clustering and classification has burgeoned into an important subfield of multivariate analysis. These approaches have been around for a half-century or so, with significant activity in the area over the past decade. The primary focus of this paper is to review work in model-based clustering, classification, and discriminant analysis, with particular attention being paid to two techniques that can be implemented using respective R packages. Parameter estimation and model selection are also discussed. The paper concludes with a summary, discussion, and some thoughts on future work.