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

Palumbo, Francesco; Lauro, C. di

doi:10.1007/978-4-431-66996-8_74

Cited by 53 publications

(25 citation statements)

References 2 publications

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“…An axiomatic definition of interval numbers is given in Dong and Shah (1987). The most popular technique in the context of PCA of interval data is the Vertices Method (Cazes et al 1997;Chouakria 1998;Chouakria et al 1999), but other interesting proposals are present in the literature (Godwa et al 1995;Lauro and Palumbo 2000;Palumbo and Lauro 2003;D'Urso and Giordani 2004;Gioia and Lauro 2006).…”

Section: Pca With Interval Datamentioning

confidence: 98%

Principal component analysis with interval imputed missing values

Zuccolotto

2011

AStA Adv Stat Anal

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In this paper some statistical properties of Interval Imputation are derived in the context of Principal Component Analysis. Interval Imputation is a recent proposal for the treatment of missing values, consisting of replacing blanks with intervals and then analyzing the resulting data matrix using Symbolic Data Analysis techniques. The most noticeable virtue of this method is that it does not require a single-valued imputation, so it allows us to take into account that incomplete observations are affected by a degree of uncertainty. Illustrative examples and simulation studies are carried out in order to illustrate the functioning of the technique.

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Section: Pca With Interval Datamentioning

confidence: 98%

Principal component analysis with interval imputed missing values

Zuccolotto

2011

AStA Adv Stat Anal

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“…Thus, this proposal admits single representations of ranges and midpoints in addition to the global representation. See, for more details, Palumbo and Lauro (2003). Notice that a different standardization procedure is introduced in MM-PCA.…”

Section: Simulation Studymentioning

confidence: 98%

“…Specifically, the methods simply consider the domain on which the fuzzy data are defined (the interval whose bounds are m − l and m + r, where m is the center and l and r the left and right spreads, respectively) without considering the codomain (the membership function and, thus, the weights associated to the values in the interval). The most common data reduction methods for interval valued data are the Centers-Principal Component Analysis (hereinafter C-PCA) and the Vertices-Principal Component Analysis (hereinafter V-PCA) proposed by Cazes, Chouakria, Diday, and Schektman (1997) (see also Bock & Diday, 2000;Lauro & Palumbo, 2000;Cazes, 2002) and the Midpoint-Midrange Principal Component Analysis (hereinafter MM-PCA) proposed by Palumbo and Lauro (2003). We will consider such methods in more detail in Section 6.…”

Section: Principal Component Analysis Of Fuzzy Data (Pcaf)mentioning

confidence: 99%

Component Models for Fuzzy Data

2006

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“…Douzal- Chouakria et al (2011) also proposed another possible way to accommodate intervals of differing lengths by replacing each interval variable via two surrogate variables, viz., the mid point and range variables. See also, Lauro and Palumbo (2000), and Palumbo and Lauro (2003). We consider the correlation within vertex data and reduce its redundancy in a different manner.…”

Section: Introductionmentioning

confidence: 99%