Francesco Palumbo

A PCA for interval-valued data based on midpoints and radii

In this paper, we propose a new approach to Principal Component Analysis, for interval-valued data. On the basis of the interval arithmetic we show that any continuous interval can be expressed in terms of a midpoint (location) and of a radius (variation). Moving from this result, we propose a well suited factorial analysis, which exploits this characteristic of interval data. Both the location and variation information are represented on maps.

Principal Component Analysis for Non-Precise Data

Many real world phenomena are better represented by non-precise data rather than by single-valued data. In fact, non-precise data represent two sources of variability: the natural phenomena variability and the variability or uncertainty induced by measurement errors or determined by specific experimental conditions. The latter variability source is named imprecision. When there are information about the imprecision distribution the fuzzy data coding is used to represent the imprecision. However, in many cases imprecise data are natively defined only by the minimum and maximum values. Technical specifications, stock-market daily prices, survey data are some examples of such kind of data. In these cases, interval data represent a good data coding to take into account the imprecision. This paper aims at describing multiple imprecise data by means of a suitable Principal Component Analysis that is based on specific interval data coding taking into account both sources of variation.

Exploratory data analysis leading towards the most interesting simple association rules

Association rules (AR) represent one of the most powerful and largely used approaches to detect the presence of regularities and paths in large databases. Rules express the relations (in terms of co-occurrence) between pairs of items and are defined in two measures: support and confidence. Most techniques for finding AR scan the whole data set, evaluate all possible rules and retain only rules that have support and confidence greater than thresholds, which should be fixed in order to avoid both that only trivial rules are retained and also that interesting rules are not discarded. A multistep approach aims to the identification of potentially interesting items exploiting well-known techniques of multidimensional data analysis. In particular, interesting pairs of items have a well-defined degree of association: an item pair is well defined if its degree of co-occurrence is very high with respect to one or more subsets of the considered set of transactions.

Fuzzy PLS Path Modeling: A New Tool For Handling Sensory Data

In sensory analysis a panel of assessors gives scores to blocks of sensory attributes for profiling products, thus yielding a three-way table crossing assessors, attributes and products. In this context, it is important to evaluate the panel performance as well as to synthesize the scores into a global assessment to investigate differences between products. Recently, a combined approach of fuzzy regression and PLS path modeling has been proposed. Fuzzy regression considers crisp/fuzzy variables and identifies a set of fuzzy parameters using optimization techniques. In this framework, the present work aims to show the advantages of fuzzy PLS path modeling in the context of sensory analysis.

Clustering and Dimensionality Reduction to Discover Interesting Patterns in Binary Data

The attention towards binary data coding increased consistently in the last decade due to several reasons. The analysis of binary data characterizes several fields of application, such as market basket analysis, DNA microarray data, image mining, text mining and web-clickstream mining. The paper illustrates two different approaches exploiting a profitable combination of clustering and dimensionality reduction for the identification of non-trivial association structures in binary data. An application in the Association Rules framework supports the theory with the empirical evidence.

A Two-Step Iterative Procedure for Clustering of Binary Sequences

Association Rules (AR) are a well known data mining tool aiming to detect patterns of association in data bases. The major drawback to knowledge extraction through AR mining is the huge number of rules produced when dealing with large amounts of data. Several proposals in the literature tackle this problem with different approaches. In this framework, the general aim of the present proposal is to identify patterns of association in large binary data. We propose an iterative procedure combining clustering and dimensionality reduction techniques: each iteration involves a quantification of the starting binary attributes and an agglomerative algorithm on the obtained quantitative variables. The objective is to find a quantification that emphasizes the presence of groups of co-occurring attributes in data.

Huge Multidimensional Data Visualization: Back to the Virtue of Principal Coordinates and Dendrograms in the New Computer Age

Many papers refer to Tukey’s (1977) treatise on exploratory data analysis as the contribution that transformed statistical thinking. In actual fact, new ideas introduced by Tukey prompted many statisticians to give a more prominent role to data visualization and more generally to data. However, J.W. Tukey in 1962 had already begun his daring provocation when at the annual meeting of the Institute of Mathematical Statistics he gave his talk entitled “The Future of Data Analysis” (Tukey, 1962).

Possibilistic PLS Path Modeling: A New Approach to the Multigroup Comparison

Structural equation models are reference techniques for measuring cause-effect relationships in complex systems. In many real cases observations are a priori grouped into homogeneous segments according to a specific characteristic, so that different models can be assessed for each segment. The present paper proposes to adopt an Euclidean metric based on the model parameters: the aim is to determine differences among models. However, estimated models assess the relation structures in different proportions, i.e. the residual component can vary with respect to the different models. In order to overcome this shortcoming, the present work proposes alternative models with fuzzy parameters.

Analyzing Research Potential through Redundancy Analysis: the case of the Italian University System

The paper proposes a multivariate approach to study the dependence of the scientific productivity on the human research potential in the Italian University system. In spite of the heterogeneity of the system, Redundancy Analysis is exploited to analyse the University research system as a whole. The proposed approach is embedded in an exploratory data analysis framework.

On the Use of Archetypes and Interval Coding in Sensory Analysis

Archetypal analysis is a statistical method aiming at synthesizing a set of multivariate observations through few points not necessarily observed. On the other hand, coding data as interval values allows to include variability and variation in the data itself. This work proposes the use of archetypal analysis for interval-coded sensory data to synthesize profiling data taking into account assessor panel variability.