Cluster Analysis using RCmdr

Start Date: 11/01/2020

Course Type: Common Course

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Cluster analysis Some of the measures of quality of a cluster algorithm using external criterion include:
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 or another) to each other than to those in other groups (clusters). It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, bioinformatics, data compression, and computer graphics.
Cluster analysis Cluster analysis was originated in anthropology by Driver and Kroeber in 1932 and introduced to psychology by Zubin in 1938 and Robert Tryon in 1939 and famously used by Cattell beginning in 1943 for trait theory classification in personality psychology.
Cluster analysis 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 notion of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances among the cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The appropriate clustering algorithm and parameter settings (including values such as the distance function to use, a density threshold or the number of expected clusters) depend on the individual data set and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery or interactive multi-objective optimization that involves trial and failure. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.
Cluster analysis When a clustering result is evaluated based on the data that was clustered itself, this is called internal evaluation. These methods usually assign the best score to the algorithm that produces clusters with high similarity within a cluster and low similarity between clusters. One drawback of using internal criteria in cluster evaluation is that high scores on an internal measure do not necessarily result in effective information retrieval applications. Additionally, this evaluation is biased towards algorithms that use the same cluster model. For example, k-Means clustering naturally optimizes object distances, and a distance-based internal criterion will likely overrate the resulting clustering.
Cluster analysis The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms. There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different algorithms can be given. The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include:
Moving-cluster method Using the moving-cluster method, the distance to a given star cluster can be determined using the following equation:
Cluster analysis Evaluation of clustering results sometimes is referred to as cluster validation.
Cluster analysis In centroid-based clustering, clusters are represented by a central vector, which may not necessarily be a member of the data set. When the number of clusters is fixed to k, "k"-means clustering gives a formal definition as an optimization problem: find the formula_4 cluster centers and assign the objects to the nearest cluster center, such that the squared distances from the cluster are minimized.
Modal analysis using FEM The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of the
Cluster analysis The key drawback of DBSCAN and OPTICS is that they expect some kind of density drop to detect cluster borders. Moreover, they cannot detect intrinsic cluster structures which are prevalent in the majority of real life data. A variation of DBSCAN, EnDBSCAN, efficiently detects such kinds of structures. On data sets with, for example, overlapping Gaussian distributions - a common use case in artificial data - the cluster borders produced by these algorithms will often look arbitrary, because the cluster density decreases continuously. On a data set consisting of mixtures of Gaussians, these algorithms are nearly always outperformed by methods such as EM clustering that are able to precisely model this kind of data.
Beowulf cluster A cluster can be set up by using Knoppix bootable CDs in combination with OpenMosix. The computers will automatically link together, without need for complex configurations, to form a Beowulf cluster using all CPUs and RAM in the cluster. A Beowulf cluster is scalable to a nearly unlimited number of computers, limited only by the overhead of the network.
Cluster analysis A number of measures are adapted from variants used to evaluate classification tasks. In place of counting the number of times a class was correctly assigned to a single data point (known as true positives), such "pair counting" metrics assess whether each pair of data points that is truly in the same cluster is predicted to be in the same cluster.
Cluster labeling Differential cluster labeling labels a cluster by comparing term distributions across clusters, using techniques also used for feature selection in document classification, such as mutual information and chi-squared feature selection. Terms having very low frequency are not the best in representing the whole cluster and can be omitted in labeling a cluster. By omitting those rare terms and using a differential test, one can achieve the best results with differential cluster labeling.
Coupled cluster The Schrödinger equation can be written, using the coupled-cluster wave function, as
Cluster state Cluster states have been realized experimentally. They have been obtained in photonic experiments using
Cluster analysis Connectivity based clustering, also known as "hierarchical clustering", is based on the core idea of objects being more related to nearby objects than to objects farther away. These algorithms connect "objects" to form "clusters" based on their distance. A cluster can be described largely by the maximum distance needed to connect parts of the cluster. At different distances, different clusters will form, which can be represented using a dendrogram, which explains where the common name "hierarchical clustering" comes from: these algorithms do not provide a single partitioning of the data set, but instead provide an extensive hierarchy of clusters that merge with each other at certain distances. In a dendrogram, the y-axis marks the distance at which the clusters merge, while the objects are placed along the x-axis such that the clusters don't mix.
Geographical cluster Identifying geographical clusters can be an important stage in a geographical analysis. Mapping the locations of unusual concentrations may help identify causes of these. Some techniques include the Geographical Analysis Machine and Besag and Newell's cluster detection method.
Cluster analysis Most k-means-type algorithms require the number of clusters - formula_4 - to be specified in advance, which is considered to be one of the biggest drawbacks of these algorithms. Furthermore, the algorithms prefer clusters of approximately similar size, as they will always assign an object to the nearest centroid. This often leads to incorrectly cut borders in between of clusters (which is not surprising, as the algorithm optimized cluster centers, not cluster borders).
Phoenix Cluster The Phoenix Cluster was initially detected using the Sunyaev–Zel'dovich effect by the South Pole Telescope collaboration.