Linear algebra and optimization for machine learning : a textbook / Charu C. Aggarwal

By:

Aggarwal, Charu C, 1970- [VerfasserIn]

9783030403430
9783030403461

Subject(s):

Additional physical formats: 9783030403447. | Erscheint auch als: Linear Algebra and Optimization for Machine Learning. Online-Ausgabe 1st ed. 2020. Cham : Springer International Publishing, 2020. 1 Online-Ressource(XXI, 495 p. 93 illus., 26 illus. in color.)DDC classification:

006.31 23

RVK: RVK: ST 301 | SK 220Summary: Preface -- 1 Linear Algebra and Optimization: An Introduction -- 2 Linear Transformations and Linear Systems -- 3 Eigenvectors and Diagonalizable Matrices -- 4 Optimization Basics: A Machine Learning View -- 5 Advanced Optimization Solutions -- 6 Constrained Optimization and Duality -- 7 Singular Value Decomposition -- 8 Matrix Factorization -- 9 The Linear Algebra of Similarity -- 10 The Linear Algebra of Graphs -- 11 Optimization in Computational Graphs -- Index.Summary: This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout this text book together with access to a solution’s manual. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.PPN: PPN: 1700175289

Holdings ( 2 )

Holdings
Item type	Home library	Shelving location	Call number	Status	Notes	Date due	Barcode	Item holds
Freihandbestand ausleihbar	Fachbibliothek Mathematik	Bibliothek / frei aufgestellt	Lin. Algeb. / Agg	Available			36619194090
Handbibliothek	Fakultät für Mathematik	Handbibliothek (Ausleihe und Einsicht nicht möglich)	Lin. Algeb. / Agg	Checked out Ausleihe und Einsicht nicht möglich	Standort: FBM-Handapparat 21	06.05.2041	36607230090

Total holds: 0