Multiple taxicab correspondence analysis

A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE

One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimede...

New Upper Bounds for Taxicab and Cabtaxi Numbers

Hardy was surprised by Ramanujan’s remark about a London taxi numbered 1729: “it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways”. In memory of this story, this number is now called Taxicab(2) = 1729 = 9 + 10 = 1 + 12, Taxicab(n) being the smallest number expressible in n ways as a sum of two cubes. We can generalize the problem by...

Equality Constraints in Multiple Correspondence Analysis

Multiple Correspondence Analysis

Multiple correspondence analysis (MCA) is an extension of correspondence analysis (CA) which allows one to analyze the pattern of relationships of several categorical dependent variables. As such, it can also be seen as a generalization of principal component analysis when the variables to be analyzed are categorical instead of quantitative. Because MCA has been (re)discovered many times, equiv...

On the use of Multiple Correspondence Analysis to visually explore affiliation networks

In this paper we discuss the use of Multiple Correspondence Analysis to analyze and graphically represent two-mode networks, and we propose to apply it in a Greenacre’s doubling perspective. We discuss how orrespondence Analysis oubling ctor and event covariates Multiple Correspondence Analysis: (i) properly takes into account the nature of relational data and the intrinsic asymmetry of actors/...