4 citations · 11 across the 15 of their papers we have counts for
15 papers
Geometric Interpretation of the Robustness of Taxicab Singular Value Decomposition of High-Dimensional Sparse Data
Vartan Choulakian
This paper examines the fundamental properties of projections in L2-normed (Euclidean) and L1-normed (Taxicab) spaces through two complementary frameworks : projection operators an…
Binary Trees and Taxicab Correspondence Analysis of Extremely Sparse Binary Textual Data: A Case Study
Vartan Choulakian, Jacques Allard, Ron Kenett
This is a case study, where Taxicab Correspondence Analysis reveals that the underlying structure of an extremely sparse binary textual data set can be represented by a binary tree…
Distortion in Correspondence Analysis and in Taxicab Correspondence Analysis: A Comparison
Vartan Choulakian
Distortion is a fundamental well-studied topic in dimension reduction papers, and intimately related with the underlying intrinsic dimension of a mapping of a high dimensional data…
Scale Invariant Correspondence Analysis
Vartan Choulakian
Correspondence analysis is a dimension reduction method for visualization of nonnegative data sets, in particular contingency tables ; but it depends on the marginals of the data s…
Visualization of Extremely Sparse Contingency Table by Taxicab Correspondence Analysis: A Case Study of Textual Data
V. Choulakian, J. Allard
We present an overview of taxicab correspondence analysis, a robust variant of correspondence analysis, for visualization of extremely sparse ontingency tables. In particular we vi…
On the choice of weights in aggregate compositional data analysis
Vartan Choulakian, Jules De Tibeiro, Pasquale Sarnacchiaro
In this paper, we distinguish between two kinds of compositional data sets: elementary and aggregate. This fact will help us to decide the choice of the weights to use in log inter…
Notes on Correspondence Analysis of Power Transformed Data Sets
Vartan Choulakian
We prospect for a clear simple picture on CA of power transformed or the Box-Cox transformed data initiated since 2009 by Grenacre. We distinguish two types of data sets : strictly…
Some notes on Goodman's marginal-free correspondence analysis
Vartan Choulakian
In his seminal paper Goodman (1996) introduced marginal-free correspondence analysis; where his principal aim was to reconcile Pearson correlation measure with Yule's association m…
Quantification of intrinsic quality of a principal dimension in correspondence analysis and taxicab correspondence analysis
Vartan Choulakian
Collins(2002, 2011) raised a number of issues with regards to correspondence analysis (CA), such as: qualitative information in a CA map versus quantitative information in the rele…
Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling
Vartan Choulakian, Jacques Allard
Let n respondents rank order d items, and suppose that d << n. Our main task is to uncover and display the structure of the observed rank data by an exploratory riffle shuffling pr…
Comments on "correspondence analysis makes you blind"
Vartan Choulakian
Collins' (2002) statement "correspondence analysis makes you blind" followed after his seriation like description of a brand attribute count data set analyzed by Whitlark and Smith…
Globally Homogenous Mixture Components and Local Heterogeneity of Rank Data
V Choulakian
The traditional methods of finding mixture components of rank data are mostly based on distance and latent class models; these models may exhibit the phenomenon of masking of group…
Matrix Factorizations Based on Induced Norms
Vartan Choulakian
We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by considering Y as a mapping from a finite dimensional Banach space into another finite dimensional Bana…
Taxicab Correspondence Analysis of Sparse Contingency Tables
Vartan Choulakian
Visualization and interpretation of contingency tables by correspondence analysis (CA), as developed by Benzecri, has a rich structure based on Euclidean geometry. However, it is a…
Some Numerical Results on the Rank of Generic Three-Way Arrays over R
Vartan Choulakian
The aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array. We show that the rank of a three-way array over R is intim…