On p-adic classification

p-Adic mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of p-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.

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“…p-Adic methods were applied to classification problems in [49] and to computer vision problems in [50,51].…”

Section: Data Miningmentioning

confidence: 99%

p-Adic mathematical physics: the first 30 years

Драгович

Khrennikov

Козырев

et al. 2017

P-Adic Num Ultrametr Anal Appl

127

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“…In particular, they would allow the merging of classification results from different types of data sources. In the context of p-adic learning, this means first constructing p-adic classifiers as defined in Bradley (2009b). These incorporate new data into existing hierarchical classifications.…”

Section: Future Workmentioning

confidence: 99%

“…A further p -adic hierarchic classification algorithm is developed in Bradley (2009a) with a view on applications to texts and time series analysis. Bradley (2009b) introduces a first p -adic modification of the well-known algorithm by Linde et al . (1980) for finding optimal clusterings.…”

Section: Introductionmentioning

confidence: 99%

An ultrametric interpretation of building related event data

Bradley

2010

Construction Management and Economics

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The long-term behaviour of the built environment is relevant to practising architects and engineers as well as to investors and policy makers. In contrast to this, the size, structure and dynamics of that important capital of society are not well established. As a first step towards assessing the dynamics of new constructions, refurbishments, demolitions and other building related event variables in urban building stocks in Southwest Germany, a first random sample of event data is examined using the more efficient ultrametric hierarchical classification in order to compare their dynamics. To this end, different ways of binary encodings of the multivariate data are carried out, and their ultrametric classification results compared. It turns out that municipalities of comparable sizes show similar behaviour in contrast to those of differing sizes, which corresponds to previous findings. Consequently, ultrametric methods can be applied to the study of building stock dynamics by revealing inherent hierarchical structure in data.Building stock dynamics, hierarchical classification, ultrametric methods,

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“…The decimal representation of numbers yields { } [7], where the result is formulated for p -adic ultrametrics.…”

Section: Baire Distancementioning

confidence: 99%

Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data

Bradley¹,

Braun²

2015

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A novel permutation-dependent Baire distance is introduced for multi-channel data. The optimal permutation is given by minimizing the sum of these pairwise distances. It is shown that for most practical cases the minimum is attained by a new gradient descent algorithm introduced in this article. It is of biquadratic time complexity: Both quadratic in number of channels and in size of data. The optimal permutation allows us to introduce a novel Baire-distance kernel Support Vector Machine (SVM). Applied to benchmark hyperspectral remote sensing data, this new SVM produces results which are comparable with the classical linear SVM, but with higher kernel target alignment.

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On p-adic classification

Cited by 18 publications

References 18 publications

p-Adic mathematical physics: the first 30 years

p-Adic mathematical physics: the first 30 years

An ultrametric interpretation of building related event data

Finding the Asymptotically Optimal Baire Distance for Multi-Channel Data

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