Some Algorithms for the Computation of Independent Cluster Solutions

1977 ◽  
Vol 45 (3_suppl) ◽  
pp. 1135-1142
Author(s):  
Richard J. Hofmann
Keyword(s):  
Cluster Solution ◽  
Alternative Algorithm ◽  
Algebraic Framework ◽  
Cluster Solutions

The Harris and Kaiser algorithm for computing independent cluster solutions is discussed and an alternative algorithm is presented. Both algorithms are presented within the context of a general algebraic framework for ideal orthogonal and oblique independent cluster solutions. Finally an example is presented whereby the alternative algorithm defines a better approximation to an ideal independent cluster solution than does Harris and Kaiser's algorithm.

Clustering Women’s Health Behaviors

2002 ◽  
Vol 29 (2) ◽  
pp. 170-182 ◽  
Author(s):  
Lea Hagoel ◽  
Liora Ore ◽  
Efrat Neter ◽  
Zmira Silman ◽  
Gad Rennert
Keyword(s):  
Cluster Analysis ◽  
Health Behaviors ◽  
Mammography Screening ◽  
Behavior Patterns ◽  
Cluster Solution ◽  
Phone Interview ◽  
Health Lifestyles ◽  
Structural Variables ◽  
Health Promoting ◽  
Cluster Solutions

This study attempts to characterize health lifestyles by subgrouping women with similar behavior patterns. Data on background, health behaviors, and perceptions were collected via phone interview from 1,075 Israeli women aged 50 to 74. From a cluster analysis conducted on health behaviors, three clusters emerged: a “health promoting” cluster (44.1%), women adhering to recommended behaviors; an “inactive” cluster (40.3%), women engaging in neither health-promoting nor compromising behaviors; and an “ambivalent” cluster (15.4%), women engaging somewhat in both health-promoting and compromising behaviors. Clustering was cross-tabulated by demographic and perceptual variables, further validating the subgrouping. The cluster solution was also validated by predicting another health behavior (mammography screening) for which there was an external validating source. Findings are discussed in comparison to published cluster solutions, culminating in suggestions for intervention alternatives. The concept of lifestyle was deemed appropriate to summarize the clustering of these behavioral, perceptual, and structural variables.

SELECTION OF THE NUMBER OF CLUSTERS IN K-MEAN ALGORITHM USING CLUSTER SOLUTION ENTROPY

2021 ◽  
Vol 77 ◽  
pp. 81-92
Author(s):  
V. I. Oreshkov ◽  
Keyword(s):  
Data Mining ◽  
Clustering Algorithm ◽  
Cluster Structure ◽  
Cluster Solution ◽  
Number Of Clusters ◽  
Advantages And Disadvantages ◽  
Analytical Review ◽  
The Mean ◽  
Cluster Solutions ◽  
Selection Of

The article discusses the problem of choosing the number of clusters in popular k-means clustering algorithm. It is noted that an unsuccessful choice of this hyper parameter can lead to the creation of a cluster structure the meaningful interpretation of which in the process of data mining leads to false conclusions and making incorrect management decisions based on them. The aim of the work is to develop a method for automatic selection of the number of clusters for k-means algorithm. The article provides an analytical review of the known methods for determining the number of clusters, their advantages and disadvantages being noted. The proposed approach is based on the elbow method, which uses the entropy of cluster solutions instead of the mean squares of clustering error. A practical example shows that the use of cluster solution entropy makes it possible to choose the number of clusters even in the case when the approach based on clustering error turns out to be untenable.

scholarly journals Additive kinematic formulas for flag area measures

2021 ◽  
Author(s):  
Judit Abardia-Evéquoz ◽  
Andreas Bernig
Keyword(s):  
Recent Result ◽  
Flag Manifold ◽  
Unit Vector ◽  
Algebraic Framework

AbstractWe show the existence of additive kinematic formulas for general flag area measures, which generalizes a recent result by Wannerer. Building on previous work by the second named author, we introduce an algebraic framework to compute these formulas explicitly. This is carried out in detail in the case of the incomplete flag manifold consisting of all $$(p+1)$$ ( p + 1 ) -planes containing a unit vector.

scholarly journals Clifford Spinors and Root System Induction: $$H_4$$ and the Grand Antiprism

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Pierre-Philippe Dechant
Keyword(s):  
Root System ◽  
Root Systems ◽  
Invariant Sets ◽  
Simple Construction ◽  
Reflection Groups ◽  
Computational Work ◽  
Algebraic Framework ◽  
Underlying Geometry ◽  
Coxeter Plane ◽  
Insight Into

AbstractRecent work has shown that every 3D root system allows the construction of a corresponding 4D root system via an ‘induction theorem’. In this paper, we look at the icosahedral case of $$H_3\rightarrow H_4$$ H 3 → H 4 in detail and perform the calculations explicitly. Clifford algebra is used to perform group theoretic calculations based on the versor theorem and the Cartan–Dieudonné theorem, giving a simple construction of the $${\mathrm {Pin}}$$ Pin and $${\mathrm {Spin}}$$ Spin covers. Using this connection with $$H_3$$ H 3 via the induction theorem sheds light on geometric aspects of the $$H_4$$ H 4 root system (the 600-cell) as well as other related polytopes and their symmetries, such as the famous Grand Antiprism and the snub 24-cell. The uniform construction of root systems from 3D and the uniform procedure of splitting root systems with respect to subrootsystems into separate invariant sets allows further systematic insight into the underlying geometry. All calculations are performed in the even subalgebra of $${\mathrm {Cl}}(3)$$ Cl ( 3 ) , including the construction of the Coxeter plane, which is used for visualising the complementary pairs of invariant polytopes, and are shared as supplementary computational work sheets. This approach therefore constitutes a more systematic and general way of performing calculations concerning groups, in particular reflection groups and root systems, in a Clifford algebraic framework.

scholarly journals Heart and Mind: Essential Components in Sound Decision-Making

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 364-364
Author(s):  
Michaela Clark ◽  
Julie Hicks Patrick ◽  
Michaela Reardon
Keyword(s):  
Decision Making ◽  
Decision Quality ◽  
Cluster Solution ◽  
Cognitive Resources ◽  
Cluster Membership ◽  
Essential Components ◽  
Decision Making Processes ◽  
Affective Components ◽  
Heart And Mind

Abstract Consumer tasks permit an ecologically-valid context in which to examine the contributions of affective and cognitive resources to decision-making processes and outcomes. Although previous work shows that cognitive factors are important when individuals make decisions (Patrick et al., 2013; Queen et al.), the role of affective components is less clear. We examine these issues in two studies. Study 1 used data from 1000+ adults to inform a cluster analysis examining affective aspects (importance, meaningfulness) of making different types of decisions. A 4-cluster solution resulted. In Study 2, we used affective cluster membership and cognitive performance as predictors of experimental decision-making outcomes among a subset of participants (N = 60). Results of the regression (F(2, 40) = 6.51, p < .01, R2 = .25.) revealed that both the affective clusters (b = .37, p = .01) and cognitive ability (b = -.30, p = .04) uniquely contributed to the variance explained in decision quality. Age did not uniquely contribute. Results are discussed in the context of developing measures that enable us to move the field forward.

An alternative ISBN checking algorithm

1981 ◽  
Vol 3 (5) ◽  
pp. 235-237 ◽  
Author(s):  
George McMurdo
Keyword(s):  
International Standard ◽  
Validity Check ◽  
Alternative Algorithm

The International Standard Book Number (ISBN) has an inbuilt validity check. An alternative checking algorithm to that defined by the Standard Book Numbering Agency is presented. The alternative algorithm is demonstrated to pro duce identical results and is marginally more efficient.

scholarly journals Evaluation of a High-Resolution SPI for Monitoring Local Drought Severity

2016 ◽  
Vol 55 (10) ◽  
pp. 2247-2262 ◽  
Author(s):  
Rebecca V. Cumbie-Ward ◽  
Ryan P. Boyles
Keyword(s):  
United States ◽  
High Resolution ◽  
Standardized Precipitation Index ◽  
Stage Iv ◽  
Drought Severity ◽  
Cluster Solution ◽  
Historical Distribution ◽  
Drought Conditions ◽  
Hydrologic Prediction ◽  
Strong Agreement

AbstractA standardized precipitation index (SPI) that uses high-resolution, daily estimates of precipitation from the National Weather Service over the contiguous United States has been developed and is referred to as HRD SPI. There are two different historical distributions computed in the HRD SPI dataset, each with a different combination of normals period (1971–2000 or 1981–2010) and clustering solution of gauge stations. For each historical distribution, the SPI is computed using the NCEP Stage IV and Advanced Hydrologic Prediction Service (AHPS) gridded precipitation datasets for a total of four different HRD SPI products. HRD SPIs are found to correlate strongly with independently produced SPIs over the 10-yr period from 2005 to 2015. The drought-monitoring utility of the HRD SPIs is assessed with case studies of drought in the central and southern United States during 2012 and over the Carolinas during 2007–08. A monthly comparison between HRD SPIs and independently produced SPIs reveals generally strong agreement during both events but weak agreement in areas where radar coverage is poor. For both study regions, HRD SPI is compared with the U.S. Drought Monitor (USDM) to assess the best combination of precipitation input, normals period, and station clustering solution. SPI generated with AHPS precipitation and the 1981–2010 PRISM normals and associated cluster solution is found to best capture the spatial extent and severity of drought conditions indicated by the USDM. This SPI is also able to resolve local variations in drought conditions that are not shown by either the USDM or comparison SPI datasets.

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