Search results for "Discriminant Analysis"
showing 10 items of 229 documents
STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling
2012
STATIS is an extension of principal component analysis PCA tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, as in a variant called dual-STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps: First it analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called the compromise that best represents the information common to the different data tables; Second, the PCA of this compromise gives an optimal map of the observation…
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the…
Use of linear discriminant analysis applied to vibrational spectroscopy data to characterize commercial varnishes employed for art purposes.
2007
An improvement of methodologies for characterising synthetic resins used in varnishes employed for art purposes has been suggested. Several kinds of standard of the most common polymeric resins (acrylic, vinyl, poly(vinyl alcohol), alkyd, cellulose nitrate, latex, polyester, polyurethane, epoxy, organosilicic, and ketonic) were analyzed by Fourier transform infrared (FTIR) spectroscopy. Synthetic resins characterization is based on the mathematical treatment of their whole spectrum, dividing it in 13 sections, avoiding the one-by-one interpretation of the absorption bands. The mathematical model takes as variables the maximal absorbance of each section, and each synthetic standard resin as …
Time, frequency and information domain analysis of short-term heart rate variability before and after focal and generalized seizures in epileptic chi…
2019
OBJECTIVE In this work we explore the potential of combining standard time and frequency domain indexes with novel information measures, to characterize pre- and post-ictal heart rate variability (HRV) in epileptic children, with the aim of differentiating focal and generalized epilepsy regarding the autonomic control mechanisms. APPROACH We analyze short-term HRV in 37 children suffering from generalized or focal epilepsy, monitored 10 s, 300 s, 600 s and 1800 s both before and after seizure episodes. Nine indexes are computed in time (mean, standard deviation of normal-to-normal intervals, root mean square of the successive differences (RMSSD)), frequency (low-to-high frequency power rati…
Assessing the territorial influence of an Iberian worship site. The chemical characterisation of the terracotta from the Iron Age sanctuary of La Ser…
2017
This paper presents the study of the prestigious terracotta votive figurines from the Iberian Iron Age sanctuary of La Serreta (Alicante province, Spain) composed of 174 items. Portable X-ray fluorescence (PXRF) was used to identify elemental markers that permit us to observe the differences between local and non-local terracotta figurines and furthermore to evaluate the geographical influence of the La Serreta sanctuary using Principal Component Analysis (PCA). The Partial Least Squares Discriminant Analysis (PLSDA) statistical method was also used to classify the figurines of uncertain geographical origin. The resulting groups were related to typological and stylistic groups of figurines …
A rapid method for the differentiation of yeast cells grown under carbon and nitrogen-limited conditions by means of partial least squares discrimina…
2012
This paper shows the ease of application and usefulness of mid-IR measurements for the investigation of orthogonal cell states on the example of the analysis of Pichia pastoris cells. A rapid method for the discrimination of entire yeast cells grown under carbon and nitrogen-limited conditions based on the direct acquisition of mid-IR spectra and partial least squares discriminant analysis (PLS-DA) is described. The obtained PLS-DA model was extensively validated employing two different validation strategies: (i) statistical validation employing a method based on permutation testing and (ii) external validation splitting the available data into two independent sub-sets. The Variable Importa…
Classification of Pecorino cheeses produced in Italy according to their ripening time and manufacturing technique using Fourier transform infrared sp…
2010
Fourier-transform infrared spectroscopy, followed by linear discriminant analysis of the spectral data, was used to classify Italian Pecorino cheeses according to their ripening time and manufacturing technique. The Fourier transform infrared spectra of the cheeses were divided into 18 regions and the normalized absorbance peak areas within these regions were used as predictors. Linear discriminant analysis models were constructed to classify Pecorino cheeses according to different ripening stages (hard and semi-hard) or according to their manufacturing technique (fossa and nonfossa cheeses). An excellent resolution was achieved according to both ripening time and manufacturing technique. A…
Determination of the cultivar and aging of Sicilian olive oils using HPLC-MS and linear discriminant analysis
2010
A large number of certified samples (84) of Sicilian olive oils arising from the eight cultivars most represented in Sicily (Biancolilla, Cerasuola, Moresca, Nocellara del Belice, Nocellara Etnea, Oglialora Messinese, Brandofino and Tonda Iblea) have been collected and analyzed by HPLC/MS using an atmospheric pressure chemical ionization (APCI) source. The sample preparation is very simple; in fact, the oil samples are diluted without any chemical derivatization. A following statistical data treatment by general discriminant analysis (GDA) allows the determination of the olive oil cultivar. Furthermore, changes in the composition of glyceridic components of the olive oils lead to easy discr…
Multi-class pairwise linear dimensionality reduction using heteroscedastic schemes
2010
Accepted version of an article published in the journal: Pattern Recognition. Published version on Sciverse: http://dx.doi.org/10.1016/j.patcog.2010.01.018 Linear dimensionality reduction (LDR) techniques have been increasingly important in pattern recognition (PR) due to the fact that they permit a relatively simple mapping of the problem onto a lower-dimensional subspace, leading to simple and computationally efficient classification strategies. Although the field has been well developed for the two-class problem, the corresponding issues encountered when dealing with multiple classes are far from trivial. In this paper, we argue that, as opposed to the traditional LDR multi-class schemes…