On the Generalization of the Mahalanobis Distance

Martos, Gabriel; Muñoz, Alberto; González, Javier

doi:10.1007/978-3-642-41822-8_16

Cited by 12 publications

(6 citation statements)

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“…Outliers were defined to facilitate the development of models that would (statistically) reliably describe the direction and dynamics of LUC within each set. It was achieved with an outlier criterion based on the Mahalanobis distance, which is a measure of dissimilarity of multi-attribute objects and a metric commonly used in cluster analysis [70,71]. The literature offers many modifications of the Mahalanobis distance [72] that can be used to identify outliers [73].…”

Section: Methodsmentioning

confidence: 99%

National Level Land-Use Changes in Functional Urban Areas in Poland, Slovakia, and Czechia

Wnęk

Kudas

Štych

2021

Land

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Land-use and cover change (LUCC) impacts global environmental changes. Therefore, it is crucial to obtain cross-national level LUCC data that represents past and actual LUCC. As urban areas exhibit the most significant dynamics of the changes, accompanied by such processes as urban sprawl, it seems desirable to take into account LUCC information from such areas to acquire national level information. The paper analyses land-use changes (LUCs) in urban areas in Czechia, Poland, and Slovakia. The analysis is based on functional urban area (FUA) data from the European Urban Atlas project for 2006 and 2012. The area of urbanised land grew at the expense of agricultural areas, semi-natural areas, and wetlands over the investigated period in all three countries. The authors determined LUC direction models in urban areas based on the identified land-use change. The proposed LUC direction models for the investigated period and area should offer national level LUC data for such purposes as modelling of future changes or can be the point of reference for planning analyses. The paper proposes the following models: mean model, median model, weighted mean model where the weight is the urbanised to vegetated area ratio, and weighted mean model where the weight is the share of urbanised areas. According to the proposed LUC models, areas considered as urbanised grow in FUAs on average in six years by 5.5900‰ in Czechia, 7.5936‰ in Poland, and 4.0769‰ in Slovakia. Additionally, the change models facilitated determination of a LUC dynamics ratio in each country. It reached the highest values in Poland and the lowest in Slovakia.

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Section: Methodsmentioning

confidence: 99%

National Level Land-Use Changes in Functional Urban Areas in Poland, Slovakia, and Czechia

Wnęk

Kudas

Štych

2021

Land

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“…The phonetic distance between the Korean/Austrian VOTs to the American English target VOT spaces was assessed by calculating the Mahalanobis distance (Kartushina, Hervais-Adelman, Frauenfelder, & Golestani, 2015), which computes the distance of a test point from the distribution mean by considering the covariance matrix (Martos, Muñoz, & González, 2013). The Mahalanobis distance takes into account natural variability in speech production by calculating the number of standard deviations from a learner's VOT to the mean of the target spaces (computed per plosive type) derived from the American English speakers, along each principal component axis of the target spaces (Kartushina et al, 2015).…”

Section: Variables Vot Distancementioning

confidence: 99%

Phonotactic Probabilities and Sub-syllabic Segmentation in Language Learning

Luef

Resnik

2023

TAPSLA

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High phonotactic probabilities are known to exert a facilitative effect on word learning in children and adults in their first language. The present study was designed to investigate the role of phonotactic probabilities when learning a foreign language. Focusing on Austrian and Korean learners of English, we investigated two hypotheses related to phonotactic frequency effects: (1) High-frequency segments have more deeply entrenched phonetic representations, with more automatized pronunciation patterns, rendering phonetic learning of homophonous segments more difficult; (2) High-frequency segments are associated with higher phonetic variability in the first language, which can facilitate phonetic learning in a foreign language. Additionally, the locus of phoneme/ bigram frequency effects was analyzed in relation to left-branching and right-branching syllable structure in German and Korean. We found that proximity to English voice-onset time is correlated with phoneme and bigram frequencies in the first language, but results varied by learner group. Sub-syllabic segmentation of the first language was also shown to be an influential factor. Our study is grounded in research on frequency effects and combines its central premise with phonetic learning in a foreign language. The results show a tight relationship between first language statistical probabilities and phonetic learning in a foreign language.

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“…In this paper we generalize the work in [9] by introducing a family of kernels based on the underlying density function of the sample at hand that gives rise to new distances that generalize the MD. The distances proposed in this article preserve the essential property of the Mahalanobis distance: "all the points that belong to the same probability curve, that is L c (f P ) = {x|f P (x) = c} where f P is the density function of the r.v.…”

Section: S21mentioning

confidence: 99%

Generalizing the Mahalanobis distance via density kernels

Martos

Muòoz

González

2014

IDA

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The Mahalanobis distance (MD) is a distance widely used in Statistics, Machine Learning and Pattern Recognition. When the data come from a Gaussian distribution, the MD uses the covariance matrix to evaluate the distance between a data point and the distribution mean. In this paper, we generalize the MD for general unimodal distributions, introducing a particular class of Mercer kernel, the density kernel, based on the underlying data density. Density kernels induce distances that generalize the MD and that are useful when data do not fit to the Gaussian distribution. We study the theoretical properties of the proposed distance and show its performance on a variety of artificial and real data analysis problems.

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On the Generalization of the Mahalanobis Distance

Cited by 12 publications

References 10 publications

National Level Land-Use Changes in Functional Urban Areas in Poland, Slovakia, and Czechia

National Level Land-Use Changes in Functional Urban Areas in Poland, Slovakia, and Czechia

Phonotactic Probabilities and Sub-syllabic Segmentation in Language Learning

Generalizing the Mahalanobis distance via density kernels

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