Mathematical Introduction to Data Science / by Sven A. Wegner.

Format:

Book

Author/Creator:

Wegner, Sven A., author.

Language:

English

Subjects (All):

Quantitative research.

Artificial intelligence--Data processing.

Artificial intelligence.

Data Analysis and Big Data.

Data Science.

Local Subjects:

Data Analysis and Big Data.

Data Science.

Physical Description:

1 online resource (301 pages)

Edition:

1st ed. 2024.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024.

Summary:

This textbook is intended for students of mathematics who have completed the foundational courses of their undergraduate studies and now want to specialize in Data Science and Machine Learning. It introduces the reader to the most important topics in the latter areas focusing on rigorous proofs and a systematic understanding of the underlying ideas. The textbook comes with 121 classroom-tested exercises. Topics covered include k-nearest neighbors, linear and logistic regression, clustering, best-fit subspaces, principal component analysis, dimensionality reduction, collaborative filtering, perceptron, support vector machines, the kernel method, gradient descent and neural networks. The author Sven A. Wegner earned his PhD in Functional Analysis in 2010. After several international academic positions, he is currently affiliated with the University of Hamburg (Germany).

Contents:

Preface

1 What is Data (Science)?

2 Affine Linear, Polynomial and Logistic Regression

3 k-nearest Neighbors

4 Clustering

5 Graph Clustering

6 Best-Fit Subspaces

7 Singular Value Decomposition

8 Curse and Blessing of High Dimensionality

9 Concentration of Measure

10 Gaussian Random Vectors in High Dimensions

11 Dimensionality Reduction à la Johnson-Lindenstrauss

12 Separation and Fitting of HIgh-Dimensional Gaussians

13 Perceptron

14 Support Vector Machines

15 Kernel Method

16 Neural Networks

17 Gradient Descent for Convex Functions

Appendix: Selected Results of Probability Theory

Bibliography

Index.

Notes:

Includes bibliographical references and index.

ISBN:

3-662-69426-3