Some distance properties of latent root and vector methods used in multivariate analysis

By John C. Gower. 1966

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, background): “Theorems 1 and 2 show that any p.d. matrix B , or equivalently any c.n.d. matrix C , deﬁne a unique set of squared Euclidean distances D between objects (Torgerson 1958; Gower 1966).”
Euclidean Distance Geometry and Applications (2012, methodology): “MDS is complementary to Principal Component Analysis (PCA) [80], in the following sense.”
Associations between child mobile use and digital parenting style in Hungarian families (2019, methodology): “Although PCA is generally suggested for continuous data, it is considered appropriate for binary data as well (Gower, 1966; Jolliffe, 2002; Vyas & Kumaranayake, 2006).”
Generalized discriminant analysis based on distances (2003, methodology): “Previous work on related topics has demonstrated that traditional canonical analysis can be written in terms of Mahalanobis distances between means (Gower, 1966a) or in terms of minimizing a stress function as in multidimensional scaling (Meulman, 1992), while Cuadras & Arenas (1990) have…”
Information Retrieval Perspective to Nonlinear Dimensionality Reduction for Data Visualization (2010, methodology): “PCA is very closely related to linear multidimensional scaling (linear MDS, also called classical scaling; Torgerson, 1952; Gower, 1966), which tries to find lowdimensional coordinates preserving squared distances.”
Localization Algorithms and Strategies for Wireless Sensor Networks: Monitoring and Surveillance Techniques for Target Tracking (2009, background): “In Youssef and Agrawala (2004b), the authors developed an analytical framework for calculating the average distance error and the probability of error in location. They showed that probabilistic decision techniques can provide more accurate localization than deterministic ones, since unlike determin”
Effects of library size variance, sparsity, and compositionality on the analysis of microbiome data (2015, methodology): “Ordination analysis, such as principal 88 coordinates analysis (PCoA) (Gower 1966), is subsequently applied to these normalized data to 89 visualize broad trends of how similar or different bacteria are in certain sample types, such as 90 healthy vs. sick patients).”
Relationships between Staphylococcus aureus Genetic Background, Virulence Factors, agr Groups (Alleles), and Human Disease (2002, methodology): “This finding clearly indicated that agr types are associated with genetic backgrounds of strains. agr group la- beling of each isolate on the AFLP PCO factor map showed a clear relationship between the genetic background, the agr group and the disease type, particularly for toxin-mediated diseases (”
Patterns in the distribution of sponge populations across the central Great Barrier Reef (2004, methodology): “Communities were defined using an agglomerative hierarchical grouping procedure (HGROUP; Veldman 1967) on the first ten eigen vectors derived from a principal coordinate analysis ( Gower 1966 ).”
Animal-sediment relationships re-visited: Characterising species' distributions along an environmental gradient using canonical analysis and quantile regression splines (2008, methodology): “CAP is done using principal coordinates (PCO, Gower, 1966) from the resemblance matrix and a check on overparameterisation (i.e., to avoid including too many axes and finding spurious relationships) is needed.”
Dynamical Hierarchical Tree in Currency Markets (2007, unknown): “As in [24], distances between countries can be constructed using the correlation coefficient.”
Distance‐Based Tests for Homogeneity of Multivariate Dispersions (2006, methodology): “Note also that the Bray-Curtis and binomial deviance measures are semimetric and so, like many other functions used in ecological applications, do not fulfill the triangle inequality (Gower and Legendre, 1986). Legendre and Gallagher (2001) demonstrated how several other ecologically meaningful diss”