Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial intervalvalued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster. In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values

Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial interval-valued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster. In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values

Categorical and Fuzzy Ensemble-Based Algorithms for Cluster Analysis

This dissertation focuses on improving multivariate methods of cluster analysis. In Chapter 3 we discuss methods relevant to the categorical clustering of tertiary data while Chapter 4 considers the clustering of quantitative data using ensemble algorithms. Lastly, in Chapter 5, future research plans are discussed to investigate the clustering of spatial binary data. Cluster analysis is an unsupervised methodology whose results may be influenced by the types of variables recorded on observations. When dealing with the clustering of categorical data, solutions produced may not accurately reflect the structure of the process that generated them. Increased variability within the latent structure of the data and the presence of noisy observations are two issues that may be obscured within the categories. It is also the presence of these issues that may cause clustering solutions produced in categorical cases to be less accurate. To remedy this, in Chapter 3, a method is proposed that utilizes concepts from statistics to improve the accuracy of clustering solutions produced in tertiary data objects. By pre-smoothing the dissimilarities used in traditional clustering algorithms, we show it is possible to produce clustering solutions more reflective of the latent process from which observations arose. To do this the Fienberg-Holland estimator, a shrinkage-based statistical smoother, is used along with 3 choices of smoothing. We show the method results in more accurate clusters via simulation and an application to diabetes. Solutions produced from clustering algorithms may vary regardless of the type of variables observed. Such variations may be due to the clustering algorithm used, the initial starting point of an algorithm, or by the type of algorithm used to produce such solutions. Furthermore, it may sometimes be of interest to produce clustering solutions that allow observations to share similarities with more than one cluster. One method proposed to combat these problems and add flexibility to clustering solutions is fuzzy ensemble-based clustering. In Chapter 4 three fuzzy ensemble based clustering algorithms are introduced for the clustering of quantitative data objects and compared to the performance of the traditional Fuzzy C-Means algorithm. The ensembles proposed in this case, however, differ from traditional ensemble-based methods of clustering in that the clustering solutions produced within the generation process have resulted from supervised classifiers and not from clustering algorithms. A simulation study and two data applications suggest that in certain settings, the proposed fuzzy ensemble-based algorithms of clustering produce more accurate clusters than the Fuzzy C-Means algorithm. In both of the aforementioned cases, only the types of variables recorded on each object were of importance in the clustering process. In Chapter 5 the types of variables recorded and their spatial nature are both of importance. An idea is presented that combines applications to geodesics with categorical cluster analysis to deal with the spatial and categorical nature of observations. The focus in this chapter is on producing an accurate method of clustering the binary and spatial data objects found in the Global Terrorism Database

Segmentation of articular cartilage and early osteoarthritis based on the fuzzy soft thresholding approach driven by modified evolutionary ABC optimization and local statistical aggregation

Articular cartilage assessment, with the aim of the cartilage loss identification, is a crucial task for the clinical practice of orthopedics. Conventional software (SW) instruments allow for just a visualization of the knee structure, without post processing, offering objective cartilage modeling. In this paper, we propose the multiregional segmentation method, having ambitions to bring a mathematical model reflecting the physiological cartilage morphological structure and spots, corresponding with the early cartilage loss, which is poorly recognizable by the naked eye from magnetic resonance imaging (MRI). The proposed segmentation model is composed from two pixel's classification parts. Firstly, the image histogram is decomposed by using a sequence of the triangular fuzzy membership functions, when their localization is driven by the modified artificial bee colony (ABC) optimization algorithm, utilizing a random sequence of considered solutions based on the real cartilage features. In the second part of the segmentation model, the original pixel's membership in a respective segmentation class may be modified by using the local statistical aggregation, taking into account the spatial relationships regarding adjacent pixels. By this way, the image noise and artefacts, which are commonly presented in the MR images, may be identified and eliminated. This fact makes the model robust and sensitive with regards to distorting signals. We analyzed the proposed model on the 2D spatial MR image records. We show different MR clinical cases for the articular cartilage segmentation, with identification of the cartilage loss. In the final part of the analysis, we compared our model performance against the selected conventional methods in application on the MR image records being corrupted by additive image noise.Web of Science117art. no. 86