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Hands-On Unsupervised Learning with Python

You're reading from  Hands-On Unsupervised Learning with Python

Product type Book
Published in Feb 2019
Publisher Packt
ISBN-13 9781789348279
Pages 386 pages
Edition 1st Edition
Languages
Author (1):
Giuseppe Bonaccorso Giuseppe Bonaccorso
Profile icon Giuseppe Bonaccorso
Toc

Table of Contents (12) Chapters close

Preface 1. Getting Started with Unsupervised Learning 2. Clustering Fundamentals 3. Advanced Clustering 4. Hierarchical Clustering in Action 5. Soft Clustering and Gaussian Mixture Models 6. Anomaly Detection 7. Dimensionality Reduction and Component Analysis 8. Unsupervised Neural Network Models 9. Generative Adversarial Networks and SOMs 10. Assessments 11. Other Books You May Enjoy

Kernel density estimation (KDE)

The solution to the problem of the discontinuity of histograms can be effectively addressed with a simple method. Given a sample xi ∈ X, it's possible to consider a hypervolume (normally a hypercube or a hypersphere), assuming that we are working with multivariate distributions, whose center is xi. The extension of such a region is defined through a constant h called bandwidth (the name has been chosen to support the meaning of a limited area where the value is positive). However, instead of simply counting the number of samples belonging to the hypervolume, we now approximate this value using a smooth kernel function K(xi; h) with some important features:

Moreover, for statistical and practical reasons, it's also necessary to enforce the following integral constraints (for simplicity, they are shown only for a univariate case...

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