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SUBCLU
SUBCLU is an algorithm for clustering high-dimensional data by Karin Kailing, Hans-Peter Kriegel and Peer Kröger.Karin Kailing, Hans-Peter Kriegel and Peer Kröger. Density-Connected Subspace Clustering for High-Dimensional Data'. In: ''Proc. SIAM Int. Conf. on Data Mining (SDM'04)'', pp. 246-257, 2004. It is a subspace clustering algorithm that builds on the density-based clustering algorithm DBSCAN. SUBCLU can find clusters in axis-parallel subspaces, and uses a bottom-up, greedy strategy to remain efficient. Approach SUBCLU uses a monotonicity criteria: if a cluster is found in a subspace S, then each subspace T \subseteq S also contains a cluster. However, a cluster C \subseteq DB in subspace S is not necessarily a cluster in T \subseteq S, since clusters are required to be maximal, and more objects might be contained in the cluster in T that contains C. However, a density-connected set in a subspace S is also a density-connected set in T \subseteq S. This ''downward-clos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clustering High-dimensional Data
Clustering high-dimensional data is the cluster analysis of data with anywhere from a few dozen to many thousands of dimensions. Such high-dimensional spaces of data are often encountered in areas such as medicine, where DNA microarray technology can produce many measurements at once, and the clustering of text documents, where, if a word-frequency vector is used, the number of dimensions equals the size of the vocabulary. Problems Four problems need to be overcome for clustering in high-dimensional data: * Multiple dimensions are hard to think in, impossible to visualize, and, due to the exponential growth of the number of possible values with each dimension, complete enumeration of all subspaces becomes intractable with increasing dimensionality. This problem is known as the curse of dimensionality. * The concept of distance becomes less precise as the number of dimensions grows, since the distance between any two points in a given dataset converges. The discrimination of the n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans-Peter Kriegel
Hans-Peter Kriegel (1 October 1948, Germany) is a German computer scientist and professor at the Ludwig Maximilian University of Munich and leading the Database Systems Group in the Department of Computer Science. He was previously professor at the University of Würzburg and the University of Bremen after habilitation at the Technical University of Dortmund and doctorate from Karlsruhe Institute of Technology. Research His most important contributions are the database index structures R*-tree, X-tree and IQ-Tree, the cluster analysis algorithms DBSCAN, OPTICS and SUBCLU and the anomaly detection method Local Outlier Factor (LOF). His research is focused around correlation clustering, high-dimensional data indexing and analysis, spatial data mining and spatial data management as well as multimedia databases. His research group developed a software framework titled ELKI that is designed for the parallel research of index structures, data mining algorithms and their i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subspace Clustering
Clustering high-dimensional data is the cluster analysis of data with anywhere from a few dozen to many thousands of dimensions. Such high-dimensional spaces of data are often encountered in areas such as medicine, where DNA microarray technology can produce many measurements at once, and the clustering of text documents, where, if a word-frequency vector is used, the number of dimensions equals the size of the vocabulary. Problems Four problems need to be overcome for clustering in high-dimensional data: * Multiple dimensions are hard to think in, impossible to visualize, and, due to the exponential growth of the number of possible values with each dimension, complete enumeration of all subspaces becomes intractable with increasing dimensionality. This problem is known as the curse of dimensionality. * The concept of distance becomes less precise as the number of dimensions grows, since the distance between any two points in a given dataset converges. The discrimination of the nea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DBSCAN
Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm proposed by Martin Ester, Hans-Peter Kriegel, Jörg Sander and Xiaowei Xu in 1996. It is a density-based clustering non-parametric algorithm: given a set of points in some space, it groups together points that are closely packed together (points with many nearby neighbors), marking as outliers points that lie alone in low-density regions (whose nearest neighbors are too far away). DBSCAN is one of the most common clustering algorithms and also most cited in scientific literature. In 2014, the algorithm was awarded the test of time award (an award given to algorithms which have received substantial attention in theory and practice) at the leading data mining conference, ACM SIGKDD. , the follow-up paper "DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN" appears in the list of the 8 most downloaded articles of the prestigious ACM Transactions on Database Sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluster Analysis
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Environment For DeveLoping KDD-Applications Supported By Index-Structures
ELKI (for ''Environment for DeveLoping KDD-Applications Supported by Index-Structures'') is a data mining (KDD, knowledge discovery in databases) software framework developed for use in research and teaching. It was originally at the database systems research unit of Professor Hans-Peter Kriegel at the Ludwig Maximilian University of Munich, Germany, and now continued at the Technical University of Dortmund, Germany. It aims at allowing the development and evaluation of advanced data mining algorithms and their interaction with index (database), database index structures. Description The ELKI framework is written in Java (programming language), Java and built around a modular architecture. Most currently included algorithms belong to cluster analysis, clustering, outlier, outlier detection and index (database), database indexes. The Object-oriented programming, object-oriented architecture allows the combination of arbitrary algorithms, data types, distance functions, indexes, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axis-parallel
In geometry, an axis-aligned object (axis-parallel, axis-oriented) is an object in ''n''-dimensional space whose shape is aligned with the coordinate axes of the space. Examples are axis-aligned rectangles (or hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding boxes are often implicitly assumed to be axis-aligned. A more general case is rectilinear polygon A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is ...s, the ones with all sides parallel to coordinate axes or rectilinear polyhedra. Many problems in computational geometry allow for faster algorithms when restricted to (collections of) axis-oriented objects, such as axis-aligned rectangles or axis-aligned line segments. A different kind of example are axis-aligned ellipsoids, i.e., the elli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Top-down And Bottom-up Design
Top-down and bottom-up are both strategies of information processing and knowledge ordering, used in a variety of fields including software, humanistic and scientific theories (see systemics), and management and organization. In practice, they can be seen as a style of thinking, teaching, or leadership. A top-down approach (also known as ''stepwise design'' and stepwise refinement and in some cases used as a synonym of ''decomposition'') is essentially the breaking down of a system to gain insight into its compositional sub-systems in a reverse engineering fashion. In a top-down approach an overview of the system is formulated, specifying, but not detailing, any first-level subsystems. Each subsystem is then refined in yet greater detail, sometimes in many additional subsystem levels, until the entire specification is reduced to base elements. A top-down model is often specified with the assistance of "black boxes", which makes it easier to manipulate. However, black boxes may f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure. Specifics Greedy algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apriori Algorithm
AprioriRakesh Agrawal and Ramakrishnan SrikanFast algorithms for mining association rules Proceedings of the 20th International Conference on Very Large Data Bases, VLDB, pages 487-499, Santiago, Chile, September 1994. is an algorithm for frequent item set mining and association rule learning over relational databases. It proceeds by identifying the frequent individual items in the database and extending them to larger and larger item sets as long as those item sets appear sufficiently often in the database. The frequent item sets determined by Apriori can be used to determine association rules which highlight general trends in the database: this has applications in domains such as market basket analysis. Overview The Apriori algorithm was proposed by Agrawal and Srikant in 1994. Apriori is designed to operate on databases containing transactions (for example, collections of items bought by customers, or details of a website frequentation or IP addresses). Other algorithms are de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
