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Found 14 papers, 4 papers with code
It is useful to analyze correlation graphs
In 1987, we analyzed the changes in correlation graphs between various features of the organism during stress and adaptation.
Dynamic and Thermodynamic Models of Adaptation
Historically, the first group of models was based on Selye's concept of adaptation energy and used fitness estimates.
Correction of AI systems by linear discriminants: Probabilistic foundations
The new approaches become efficient in high-dimensions, for correction of high-dimensional systems in high-dimensional world (i. e. for processing of essentially high-dimensional data by large systems).
The unreasonable effectiveness of small neural ensembles in high-dimensional brain
Despite the widely-spread consensus on the brain complexity, sprouts of the single neuron revolution emerged in neuroscience in the 1970s.
How deep should be the depth of convolutional neural networks: a backyard dog case study
In relation to the face recognition problem, we formulated an example of such a usecase, the `backyard dog' problem.
Blessing of dimensionality: mathematical foundations of the statistical physics of data
The stochastic separation theorems provide us by such classifiers and a non-iterative (one-shot) procedure for learning.
Stochastic Separation Theorems
Surprisingly, separation of a new image from a very large set of known images is almost always possible even in moderately high dimensions by linear functionals, and coefficients of these functionals can be found explicitly.
Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off.
Robust principal graphs for data approximation
The structure of principal graph is learned from data by application of a topological grammar which in the simplest case leads to the construction of principal curves or trees.
Data Structures and Algorithms
The Five Factor Model of personality and evaluation of drug consumption risk
An exhaustive search was performed to select the most effective subset of input features and data mining methods to classify users and non-users for each drug and pleiad.
Applications
Geometrical complexity of data approximators
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on.
Nonlinear Quality of Life Index
We present details of the analysis of the nonlinear quality of life index for 171 countries.
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach).
Topological Grammars for Data Approximation
The problem of optimal principal complex construction is transformed into a series of minimization problems for quadratic functionals.
