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Search results for “сети Кохонена”

60 results

Machine Learning 1. Lecture 13. Clustering and Semi-Supervised Learning

2026LectureКонстантин Вячеславович Воронцов

The clustering problem and its ill-posedness, the aims of clustering, types of cluster structure, sensitivity to the choice of metric; the problem of semi-supervised learning and transductive learning, why it reduces neither to classification nor to clustering; criteria of clustering quality, the silhouette coefficient, the BCubed measures of precision and recall; the k-means method (Lloyd's algorithm) as a simplification of the EM algorithm for a mixture of Gaussians; the DBSCAN algorithm; agglomerative hierarchical clustering, the Lance–Williams formula and its special cases, the dendrogram, monotonicity, contracting and dilating distances, Ward's distance; semi-supervised learning based on classification: self-training, co-training, co-learning, the transductive SVM, expectation regularisation (XR).
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280

Machine Learning 2. Lecture 5. Topic Modelling

2026LectureКонстантин Вячеславович Воронцов

Probabilistic topic modelling of text document collections: the bag-of-words and conditional independence hypotheses, the maximum likelihood criterion, three interpretations of the problem (soft clustering, stochastic matrix factorisation, autoencoder); the lemma on maximising a function on unit simplices; the ill-posedness of the problem and the additive regularisation of topic models ARTM, the EM algorithm and its interpretation; PLSA and LDA, the Dirichlet distribution, the maximum a posteriori probability and giving up Bayesian inference; smoothing, sparsing, background topics, decorrelation; multimodal and multilingual models, unigrams and bigrams; regularisers for classification and regression on texts, for word co-occurrence in short texts, for links between documents and for topic hierarchies.
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130

Topology 2. Lecture 1

2026LectureФёдор Вылегжанин

Why homology is needed — the fundamental group as a functor, homotopy groups, bordism and its combinatorial approximation; chain complexes and their homology; abstract simplicial complexes, geometric realisation and triangulations; the complex of simplicial chains, the proof of d2=0d^2 = 0, the simplicial homology of a segment, of two points and of the boundary of a triangle; reduced homology.

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470

Machine Learning 1. Lecture 7. Generalizations of Linear Models

2026LectureКонстантин Вячеславович Воронцов

Nonlinear regression: the Newton–Raphson and Gauss–Newton methods as a series of linear regressions; logistic regression and iteratively reweighted least squares (IRLS); the generalized additive model and backfitting; the probabilistic meaning of least squares; the generalized linear model (GLM), the exponential family of distributions and the link function; logistic regression as a special case of GLM; the median, quantile regression and robust loss functions.
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130

Machine Learning 1. Lecture 15. A Short Review of the Semester

2026LectureКонстантин Вячеславович Воронцов

A closing review of the first semester: empirical risk minimisation and gradient methods; underfitting, overfitting, multicollinearity and regularisation; optimisation formulations of supervised learning (regression, classification, ranking) and unsupervised learning (density, mixtures, clustering, one-class classification, semi-supervised learning, PU-learning, principal component analysis, autoencoders); the six scientific schools of machine learning — symbolism, evolutionism, analogism, Bayesianism, connectionism, compositionism — and their Soviet roots; estimate-calculating algorithms; practice: CRISP-DM, data preprocessing, model evaluation and selection, loss analysis, A/B testing, meta-learning and AutoML.
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170

Теория вероятностей, Листок 1

2026Problem sheetСтанислав Шапошников

Задачный листок к курсу теории вероятностей. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.
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270

Machine Learning 1. Lecture 2. Stochastic Gradient and the Linear Classifier

2026LectureКонстантин Вячеславович Воронцов

The general scheme of supervised learning for regression, binary and multiclass classification; the margin and continuous approximations of the threshold loss; the linear classifier as a model of a neuron; the stochastic gradient method, momentum, Nesterov's accelerated gradient and heuristics; multicollinearity and L2 regularization; the maximum likelihood principle, its link to empirical risk minimization and the probabilistic meaning of regularization.
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130

Machine Learning 1. Lecture 1. Basic Concepts and Examples of Applied Problems

2026LectureКонстантин Вячеславович Воронцов

Objects, features and answers; the types of supervised learning problems; parametric models and the learning method; loss functions and empirical risk minimization; the Runge example and overfitting; hold-out, leave-one-out and cross-validation; applied problems from medical diagnosis to sales forecasting; the CRISP-DM standard.
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210

Топология, Листок 2

2026Problem sheetKonstantin Loginov

Задачные листки к курсу топологии. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.
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250

Geometry. Lecture 2

2026LectureФёдор Попеленский

Finite geometries — the Platonic solids. A reminder — right actions, orbits, stabilisers, fundamental domains (corrected definition) and the example of Z+Z\mathbb{Z} + \mathbb{Z} on the plane; the formula ∣G∣=∣Orb⁡(x)∣⋅∣Stab⁡(x)∣|G| = |\operatorname{Orb}(x)| \cdot |\operatorname{Stab}(x)| and the 48 symmetries of the cube; regular polyhedra — Sosinsky's definition and the definition via flags, a stellated counterexample; the five Platonic solids; regular polytopes in R4\mathbb{R}^4 (six) and in Rn\mathbb{R}^n for n≥5n \ge 5 (the cube, the simplex, the hyperoctahedron) with the coordinates of their vertices; why there are no more than five — face angles and the Schläfli symbol; uniqueness of the gluing and the rigidity theorem; Euler's formula; the finite subgroups of SO(3)SO(3) — Zn\mathbb{Z}_n, DnD_n and the rotation groups of the tetrahedron, cube and icosahedron; the duality cube–octahedron, icosahedron–dodecahedron; which figures on the sphere realise Zn\mathbb{Z}_n, DnD_n and Z2\mathbb{Z}_2.

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380

Topology 2. Lecture 3

2026LectureФёдор Вылегжанин

Singular homology — standard simplices and the inclusions of facets, singular simplices and chains, the differential; zeroth homology and path components, the homology of a point, reduced homology; chain maps and maps of homology, functoriality, the chain map induced by a continuous map; chain homotopies and the prism; the homotopy invariance theorem with a full proof via the prism operator; subcomplexes, quotient complexes and the homology of a pair.
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550

Vector calculus. Green's theorem

2026Problem sheetSergey

A contour integral as a double integral: the hypotheses of Green's theorem, orientation of the contour, area as a contour integral, closing an open arc, an annulus, a singular point inside the contour.
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260

Machine Learning 1. Lecture 4. Metric Methods of Classification and Regression

2026LectureКонстантин Вячеславович Воронцов

The continuity and compactness hypotheses; the Minkowski metric and feature-free distances; the generalized metric classifier, the k nearest neighbours method, the Parzen window and the method of potential functions as a linear classifier; complete cross-validation, the compactness profile and the exact CCV formula for the nearest neighbour method; prototype selection; Nadaraya–Watson kernel smoothing, the choice of kernel and bandwidth.
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150