Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing. Re-deriving "contrast-loss" using the law of large numbers, we show it results in a distribution's instances concentrating on a thin "hyper-shell". The hollow center means apparently chaotically overlapping distributions are actually intrinsically separable. We use this to develop distribution-clustering, an elegant algorithm for grouping of data points by their (unknown) underlying distribution. Distribution-clustering, creates notably clean clusters from raw unlabeled data, estimates the number of clusters for itself and is inherently robust to "outliers" which form their own clusters. This enables trawling for patterns in unorganized data and may be the key to enabling machine intelligence.
To date, there are a wide variety of clustering algorithms @cite_44 @cite_23 @cite_35 @cite_45 @cite_0 @cite_33 customized to various tasks. A comprehensive survey is provided in @cite_29 @cite_31 . Despite the variety, we believe distribution-clustering is the first to utilize the peculiarities of high dimensional space. The result in a fundamentally different clustering algorithm.
@cite_35 @cite_33 @cite_29 @cite_44 @cite_0 @cite_45 @cite_23 @cite_31
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Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, we present the new clustering algorithm DBSCAN relying on a density-based notion of clusters which is designed to discover clusters of arbitrary shape. DBSCAN requires only one input parameter and supports the user in determining an appropriate value for it. We performed an experimental evaluation of the effectiveness and efficiency of DBSCAN using synthetic data and real data of the SEQUOIA 2000 benchmark. The results of our experiments demonstrate that (1) DBSCAN is significantly more effective in discovering clusters of arbitrary shape than the well-known algorithm CLARANS, and that (2) DBSCAN outperforms CLARANS by a factor of more than 100 in terms of efficiency. We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging. Clustering is the division of data into groups of similar objects. In clustering, some details are disregarded in exchange for data simplification. Clustering can be viewed as a data modeling technique that provides for concise summaries of the data. Clustering is therefore related to many disciplines and plays an important role in a broad range of applications. The applications of clustering usually deal with large datasets and data with many attributes. Exploration of such data is a subject of data mining. This survey concentrates on clustering algorithms from a data mining perspective. Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems. We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least.87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of 1 2 for MAX CUT and 3 4 or MAX 2SAT. Slight extensions of our analysis lead to a.79607-approximation algorithm for the maximum directed cut problem (MAX DICUT) and a.758-approximation algorithm for MAX SAT, where the best previously known approximation algorithms had performance guarantees of 1 4 and 3 4, respectively. Our algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms. In k-means clustering, we are given a set of n data points in d-dimensional space R sup d and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation. Data analysis is used as a common method in modern science research, which is across communication science, computer science and biology science. Clustering, as the basic composition of data analysis, plays a significant role. On one hand, many tools for cluster analysis have been created, along with the information increase and subject intersection. On the other hand, each clustering algorithm has its own strengths and weaknesses, due to the complexity of information. In this review paper, we begin at the definition of clustering, take the basic elements involved in the clustering process, such as the distance or similarity measurement and evaluation indicators, into consideration, and analyze the clustering algorithms from two perspectives, the traditional ones and the modern ones. All the discussed clustering algorithms will be compared in detail and comprehensively shown in Appendix Table 22.