Compactness Hypothesis, Potential Functions, and Rectifying Linear Space in Machine Learning

Mottl, Vadim; Seredin, Oleg; Krasotkina, Olga

doi:10.1007/978-3-319-99492-5_3

Cited by 3 publications

(2 citation statements)

References 34 publications

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“…Машинне навчання базується на двох постулатах, якi ми вже неявно використовували вище: 1) постулат представлення об'єкта як вектора ознак у векторному просторi i 2) постулат компактностi Авер'янова та Бравермана [28].…”

Section: близькIстьunclassified

A Non-Parametric Approach to Explainable Artificial Intelligence and Its Application in Medicine

Klyushin,

Maistrenko

2023

JNAM

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The paper proposes a non-parametrical approach to explainable artificial intelligence based on the compactness postulate, which states that objects of one class in the feature space are, as a rule, located closer to each other than to objects of other classes. Objects are considered similar if they are located close to each other in the feature space. Meanwhile, the properties of objects in real life are often random values. Such objects are not described by a vector of features, but by a random sample or several samples of features, and the postulate of compactness should be replaced by the postulate of statistical homogeneity. Objects are considered statistically homogeneous if their features obey the same distributions. The paper describes a non-parametric measure of homogeneity and an illustration of its use in medical applications, in particular for the diagnosis of breast cancer within the framework of similarity-based explainable artificial intelligence.For comparison, the results of diagnostics of the same data set using deep learning of an artificial neural network are given. We formulate new statistical postulates of machine learning and propose to consider a machine learning algorithm as explanatory and interpretable if it satisfies these postulates.

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Section: близькIстьunclassified

A Non-Parametric Approach to Explainable Artificial Intelligence and Its Application in Medicine

Klyushin,

Maistrenko

2023

JNAM

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“…Each skeletal model is represented by a vector of real values reflecting the dissimilarity measure of this model with respect to a fixed set of skeletons. The work [27] defines such a fixed data set as a "basic assembly". After that, for each skeletal model in three-dimensional space received from an RGB-D sensor a set of distances (column vector) to each object of the basic assembly is determined.…”

Section: Introductionmentioning

confidence: 99%

The basic assembly of skeletal models in the fall detection problem

Seredin¹,

Kopylov²,

Surkov³

et al. 2023

Computer Optics

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The paper considers the appliance of the featureless approach to the human activity recognition problem, which exclude the direct anthropomorphic and visual characteristics of human figure from further analysis and thus increase the privacy of the monitoring system. A generalized pairwise comparison function of two human skeletal models, invariant to the sensor type, is used to project the object of interest to the secondary feature space, formed by the basic assembly of skeletons. A sequence of such projections in time forms an activity map, which allows an application of deep learning methods based on convolution neural networks for activity recognition. The proper ordering of skeletal models in a basic assembly plays an important role in secondary space design. The study of ordering of the basic assembly by the shortest unclosed path algorithm and correspondent activity maps for video streams from the TST Fall Detection v2 database are presented.

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Potential Functions for Signals and Symbolic Sequences

Sulimova

Mottl

2018

Braverman Readings in Machine Learning. Key Ideas From Inception to Current State

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Compactness Hypothesis, Potential Functions, and Rectifying Linear Space in Machine Learning

Cited by 3 publications

References 34 publications

A Non-Parametric Approach to Explainable Artificial Intelligence and Its Application in Medicine

A Non-Parametric Approach to Explainable Artificial Intelligence and Its Application in Medicine

The basic assembly of skeletal models in the fall detection problem

Potential Functions for Signals and Symbolic Sequences

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