“DATA SCIENCE” Workshop
November 12-13, 2015
Paris-Dauphine University
Place du Maréchal de Lattre de Tassigny, 75016 Paris
“DATA SCIENCE” Workshop will be held
at Paris-Dauphine university, on November 12th and 13th, 2015
« DATA SCIENCE » Workshop (cf. www.univ-orleans.fr/mapmo/colloques/sda2015/DS.php)
is a satellite workshop of SDA2015 (cf. www.univ-orleans.fr/mapmo/colloques/sda2015 )
Organizers: Edwin Diday, Patrice Bertrand (CEREMADE Paris-Dauphine University)
Tristan Cazenave, Suzanne Pinson (LAMSADE Paris-Dauphine University)
Registration is free but mandatory due to a limited number of participants.
To register, please send an email to E. Diday (diday@ceremade.dauphine.fr)
Interested students may have their travel expenses reimbursed; Please send your request
with a CV .when your inscription is confirmed.
CONTEXT AND AIM OF THIS « DATA SCIENCE » SATELLITE WORKSHOP.
A “Data Scientist” is someone who is able to extract knew knowledge from Standard, Big and Complex
Data: unstructured data, unpaired samples, multi sources data (as mixture of numerical, textual, image,
social networks data). The fusion of such data can be done into classes of row statistical units which are
considered as new statistical units. The description of these classes can be vectors of intervals, probability
distributions, weighted sequences, functions, and the like, in order to express the within-class variability.
One of the advantage of this approach is that unstructured data and unpaired samples at the level of row
units, become structured and paired at the level of classes. The study of such new type of data, built in
order to describe classes in an explanatory way, has led to a new domain called Symbolic Data Analysis
(SDA). Recently, four international journals have published special issues on SDA, including ADAC
which is now known as a leading international journal of classification.
In this satellite meeting of the next SDA’2015 workshop (Orléans, November 17-19,
http://www.univ-orleans.fr/mapmo/colloques/sda2015/), the talks will concern the state of the
art and recent advances in SDA, or more generally visualization in Data Science.
SCHEDULE
Nov.12 th.
Welcome speech: 14:00 to 14:15
Lynne Billard: 14:15 to 15:15
“Data Science and Statistics” followed by
Maximum Likelihood Estimation for Interval-valued Data
Chun-houh Chen: 15:15 to 15:45
Matrix Visualization: New Generation of Exploratory Data Analysis
Coffee Break: 15:45 to 16:15
Oldemar Rodrıguez: 16:15 to 16:45
Shrinkage linear regression for symbolic interval-valued variables
Edwin Diday, Richard Emilion: 16:45 to 17:30
Symbolic Bayesian Networks
Nov. 13 th
Welcome Breakfast: 8h30
Edwin Diday: 9:15 to 10:00
Thinking by classes in Data Sciences: the Symbolic Data Analysis paradigm for Big
and Complex Data
Oldemar Rodrıguez:: 10:00 to 10:45
Probabilistic/statistical setting of SDA
Coffee Break: 10:45 to 11:00
Richard Emilion 11:00 to 11:45
Latest developments of the RSDA: An R package for Symbolic Data Analysis
Lunch: 12:00 to 14:00
Manabu Ichino: 14:00 to 14:45
The Lookup Table Regression Model for Symbolic Data
Paula Brito: 14:45 to 15:30
Multivariate Parametric Analysis of Interval Data
Coffee Break: 15:30 to 16:00
Chun-houh Chen: 16:00 to 16:45
Some Extensions of Matrix Visualization: the GAP Approach for Standard and
Symbolic Data Analysis.
Cheng Wang: 16:45 to 17:30
Multiple Correspondence Analysis for Mixed Symbolic Data
ABSTRACTS
Nov. 12th
 Lynne Billard (University of Georgia, USA)
Title: Maximum Likelihood Estimation for Interval-valued Data
Abstract: Bertrand and Goupil (2000) obtained empirical formulas for the mean and variance of
interval-valued observations. These are in effect moment estimators. We show how, under
certain probability assumptions, these are the same as the maximum likelihood estimators for the
corresponding population parameters.
 Chun-houh Chen (Institute of Stat. Science, Academia Sinica, Taiwan)
Title: Matrix Visualization: New Generation of Exploratory Data Analysis
Abstract: “It is important to understand what you CAN DO before you learn to measure how
WELL you seem to have DONE it” (Exploratory Data Analysis: John Tukey, 1977). Data analysts
and statistics practitioners nowadays are facing difficulties in understanding higher and higher
dimensional data with more and more complex nature while conventional graphics/visualization
tools do not answer the needs. It is statisticians’ responsibility for coming up with
graphics/visualization environment that can help users really understand what one CAN DO for
complex data generated from modern techniques and sophisticated experiments. Matrix
visualization (MV) for continuous, binary, ordinal, and nominal data with various types of
extensions provide users more comprehensive information embedded in complex high
dimensional data than conventional EDA tools such as boxplot, scatterplot, with dimension
reduction techniques such as principal component analysis and multiple correspondence
analysis. In this talk I’ll summarize our works on creating MV environment for conducting
statistical analyses and introducing statistical concepts into MV environment for visualizing
more versatile and complex data structure. Many real world examples will be demonstrated in
this talk for illustrating the strength of MV for visualizing all types of datasets collected from
scientific experiments and social surveys.
 Oldemar Rodrıguez (University of Costa Rica, San José, Costa Rica)
Title: Shrinkage linear regression for symbolic interval-valued variables
Abstract: This paper proposes a new approach to fit a linear regression for symbolic internalvalued variables, which improves both the Center Method suggested by Billard and Diday (2006)
and the Center and Range Method suggested by Lima-Neto, E.A. and De Carvalho, F.A.T.
(2008). Just in the Centers Method and the Center and Range Method, the new methods proposed
fit the linear regression model on the midpoints and in the half of the length of the intervals as
an additional variable (ranges) assumed by the predictor variables in the training data set, but to
make these fitments in the regression models, the methods Ridge Regression, Lasso, and Elastic
Net proposed by Tibshirani, R. Hastie, T., and Zou H are used. The prediction of the lower and
upper of the interval response (dependent) variable is carried out from their midpoints and
ranges, which are estimated from the linear regression models with shrinkage generated in the
midpoints and the ranges of the interval-valued predictors. Methods presented in this document
are applied to three real data sets “cardiologic interval data set”, “Prostate interval data set” and
“US Murder interval data set” to then compare their performance and facility of interpretation
regarding the Center Method and the Center and Range Method. For this evaluation, the rootmean-squared error and the correlation coefficient are used. Besides, the reader may use all the
methods presented herein and verify the results using the RSDA package written in R language,
that can be downloaded and installed directly from CRAN.
 Edwin Diday (Ceremade, University Paris-Dauphine, France), Richard Emilion (University
of Orléans, France)
Title: Symbolic Bayesian Networks
Abstract:
We first consider a n x p table of probability vectors. Each vector in column j is the probability
distribution of a random variable taking values in a finite set Vj that only depends on j, with |Vj|
= dj. Column j is considered as a sample of size n of a random distribution Pj on Vj. We are
considering the problem of building a Bayesian network from these samples in order to express
the joint distribution of (P1, …, Pj ,..., Pp).
This problem is very popular for estimating the joint distribution of p real-valued random
variables, we extend it to the case it of random distributions.
A first solution to the finite sets case consists in discretizing the probability vectors. A second
solution consists in using partial distance correlations (Székély-Rizzo, Ann. Stat. 2014) that
evaluate the influence of Pj on Pj'. The general case will be discussed.
Nov. 13th
 Edwin Diday (Ceremade, Paris-Dauphine University, France)
Title: Thinking by classes in Data Sciences: the Symbolic Data Analysis paradigm for Big and
Complex Data
Abstract: Data science is, in general terms, the extraction of knowledge from data, considered as
a science by itself. The Symbolic Data Analysis (SDA) gives a new way of thinking in Data
Sciences by extending standard data to “symbolic data” in order to extract knowledge from
aggregated classes of individual entities. The SDA is born from the classification domain by
considering classes of a given population to be units of a higher level population to be studied.
Such classes allow a summary of the population and often represent the real units of interest. In
order to take care of the variability between the members of each class, these classes are
described by intervals, distributions, set of categories or numbers sometimes weighted and the
like. In that way, we obtain new kinds of data expressing variability, called "symbolic" as they
cannot be reduced to numbers without losing much information. The aim of SDA is to study and
extract new knowledge from these new kinds of data by at least an extension of Computer
Statistics and Data Mining to symbolic data. We show that SDA is a new paradigm which opens
up a vast domain of research and applications to standard, complex and big data.
 Richard Emilion (University of Orléans, France)
Title: Probabilistic/statistical setting of SDA
Abstract: Given some raw units described by some variables and a specific class variable,
Symbolic Data Analysis (SDA) deals with objects described by probability distributions
describing classes of raw units. Our SDA formalism hinges on the notion of random distribution.
In the case of paired samples, we show that this formalism depends on a regular conditional
probability existence theorem. We also show the interest of SDA in the case of unpaired samples.
We then discuss on the extension of some classical methods such as PCA and probabilistic
classification.
 Oldemar Rodrıguez (University of Costa Rica, San José, Costa Rica)
Title: Latest developments of the RSDA: An R package for Symbolic Data Analysis
Abstract: This package aims to execute some models on Symbolic Data Analysis. Symbolic Data
Analysis was propose by the professor E. DIDAY in 1987 in his paper “Introduction à l’approche
symbolique en Analyse des Données”. Premières Journées Symbolique-Numérique. Université
Paris IX Dauphine. Décembre 1987. A very good reference to symbolic data analysis can be
found in “From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis”
of L. Billard and E. Diday that is the journal American Statistical Association Journal of the
American Statistical Association June 2003, Vol. 98. The main purpose of Symbolic Data
Analysis is to substitute a set of rows (cases) in a data table for an concept (second order
statistical unit). For example, all of the transactions performed by one person (or any object) for
a single “transaction” that summarizes all the original ones (Symbolic-Object) so that millions
of transactions could be summarized in only one that keeps the customary behavior of the person.
This is achieved thanks to the fact that the new transaction will have in its fields, not only
numbers (like current transactions), but can also have objects such as intervals, histograms, or
rules. This representation of an object as a conjunction of properties fits within a data analytic
framework concerning symbolic data and symbolic objects, which has proven useful in dealing
with big databases. In RSDA version 1.2, methods like centers interval principal components
analysis, histogram principal components analysis, multi-valued correspondence analysis,
interval multidemensional scaling (INTERSCAL), symbolic hierarchical clustering, CM, CRM,
Lasso, Ridge and Elastic Net Linear regression model to interval variables have been
implemented. This new version also includes new features to manipulate symbolic data through
a new data structure that implements Symbolic Data Frames and methods for converting SODAS
and XML SODAS files to RSDA files.
 Manabu Ichino (Tokyo Denki University, Japan)
Title: The Lookup Table Regression Model for Symbolic Data
Abstract: This paper presents a preliminary research on the lookup table regression model for
symbolic data. We apply the quantile method to the given symbolic data table of the size (N
objects)×(d feature variables), and we represent each object by (m+1) d-dimensional numerical
vectors, called the quantile vectors, for a preselected integer m. The integer m controls the
granularity of the descriptions for symbolic objects. In the new data table of the size
{N×(m+1)}×d, we interchange N×(m+1) rows according to the values of the selected objective
variable from the smallest to the largest. For each of remained d-1 features, i.e., columns, we
execute the segmentation of feature values into blocks so that the generated blocks satisfy the
monotone property. We discard columns that have only a single block. Then, we execute the
segmentation of the objective variable according to the blocks of the remained explanatory
feature variables. Finally, we obtain the lookup table of the size N’×d’, where N’ ≤ N×(m+1) and
d’ ≤ d. Each element of the table is an interval value corresponding to the segmented block. We
realize the interval-value estimation rule for the objective variable by the search of the “nearest
element” in the lookup table. We present examples to illustrate the lookup table regression
model.
 Paula Brito (Porto University, Portugal)
Title: Multivariate Parametric Analysis of Interval Data
Abstract: In this work we focus on the study of interval data, i.e., when the variables' values are
intervals of |R.
Parametric probabilistic models for interval-valued variables have been proposed and studied in
(Brito & Duarte Silva, 2012). These models are based on the representation of each observed
interval by its MidPoint and LogRange, and Multivariate Normal and Skew-Normal distributions
are assumed for the whole set of 2p MidPoints and LogRanges of the original p interval-valued
variables. The intrinsic nature of the interval-valued variables leads to different structures of the
variance-covariance matrix, represented by different possible configurations. For all cases,
maximum likelihood estimators of the corresponding parameters have been derived. This
framework may be applied to different statistical multivariate methodologies, thereby allowing
for inference approaches for symbolic data.
The proposed modelling has first been applied to (M)ANOVA of interval data, using a
likelihood-ratio approach. Linear and quadratic models for discriminant analysis of data
described by interval-valued variables have been obtained, and their performance compared with
alternative distance-based approaches. We have also addressed the problem of mixture
distributions, developing model-based clustering using the proposed models.
For the Gaussian model, the problem of outlier identification is addressed, using Mahalanobis
distances based on robust estimations of the joint mean values and the covariance matrices.
The referred modelling, for the Gaussian case, has been implemented in the R-package
MAINT.DATA, available on CRAN. MAINT.DATA introduces a data class for representing
interval data and includes functions for modeling and analysing these data. In particular,
maximum likelihood estimation and statistical tests for the different considered configurations
are addressed. Methods for (M)ANOVA and Linear and Quadratic Discriminant Analysis of this
data class are also currently provided.
 Chun-houh Chen (Institute of Stat. Science, Academia Sinica, Taiwan)
Title: Some Extensions of Matrix Visualization: the GAP Approach
Abstract: Exploratory data analysis (EDA, Tukey, 1977) has been extensively used for nearly 40
years yet boxplot and scatterplot are still the major EDA tools for visualizing continuous data in
the 21st century. Many extended modules of matrix visualization via the Generalized Association
Plots (GAP) approach have been developed or under developing. Some details of the following
MV modules will be provided in this talk:
1. Matrix visualization for high-dimensional categorical data structure. For categorical data,
MCA (multiple correspondence analysis) is most popular for visualizing reduced joint space for
samples and variables of categorical nature. But similar to it’s continuous counter part: PCA
(principal component analysis), MCA loses its efficiency when data dimensionality gets really
high. In this study we extend the framework of matrix visualization from continuous data to
categorical data. Categorical matrix visualization can effectively present complex information
patterns for thousands of subjects on thousands of categorical variables in a single matrix
visualization display.
2. Matrix Visualization for High-Dimensional Data with a Cartography Link. When a cartography
link is attached to each subject of a high-dimensional categorical data, it is necessary to use a
geographical map to illustrate the pattern of subject (region)-clusters with variable-groups
embedded in the high-dimensional space. This study presents an interactive cartography system
with systematic color-coding by integrating the homogeneity analysis into matrix visualization.
3. Matrix visualization for symbolic data analysis. Symbolic data analysis (SDA) has gained
popularity over the past few years because of its potential for handling data having a dependent
and hierarchical nature. Here we introduce matrix visualization (MV) for visualizing and
clustering SDA data using interval-valued symbolic data as an example; it is by far the most
popular SDA data type in the literature and the most commonly encountered one in practice.
Many MV techniques for visualizing and clustering conventional data are converted to SDA
data, and several techniques are newly developed for SDA data. Various examples of data with
simple to complex structures are brought in to illustrate the proposed methods.
4. Covariate-adjusted matrix visualization via correlation decomposition. In this study, we extend
the framework of matrix visualization (MV) by incorporating a covariate adjustment process
through the estimation of conditional correlations. MV can explore the grouping and/or
clustering structure of high-dimensional large-scale data sets effectively without dimension
reduction. The benefit is in the exploration of conditional association structures among the
subjects or variables that cannot be done with conventional MV.
Several biomedical examples will be employed for illustrating the versatility of the GAP
approach matrix visualization. (cf. http://gap.stat.sinica.edu.tw/Software/)
 Cheng Wang (Beihang University), Edwin Diday, Richard Emilion, Huiwen Wang
Title: Multiple Correspondence Analysis for Mixed Symbolic Data
Abstract: Under the circumstance of cross-platform data collection technology develops rapidly
and the big data era is coming, there are always a mixture of single-valued data, histogram data,
composition data and functional data in one table, which can be called mixed feature-data.
Different types of data may be belong to different space, which leads to that it is a pretty
complicated problem to conduct crosstab analysis among several data types. In this paper, we
propose a Multiple Correspondence Analysis (MCA) for mixed data to detect and represent
underlying structures involved. Before MCA, we first transfer different types of data to vector
data, which is further converted to nominal data. Two ways are considered to convert the vector
data to nominal data, respectively is hierarchal clustering and discretization. An empirical
analysis is conducted to compare the performance of MCA for mixed data based on these two
different ways.