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Mathematical analysis for machine learning and data mining

Author: Dan A Simovici
Publisher: New Jersey : World Scientific, [2018] ©2018
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Simovici, Dan A.
Mathematical analysis for machine learning and data mining.
New Jersey : World Scientific, [2018]
(DLC) 2018008584
(OCoLC)1000332248
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Dan A Simovici
ISBN: 9789813229693 9813229691
OCLC Number: 1038489411
Description: 1 online resource (xv, 968 pages)
Contents: 2.5 Seminorms and Norms2.6 Linear Functionals in Inner Product Spaces; 2.7 Hyperplanes; Exercises and Supplements; Bibliographical Comments; 3. Algebra of Convex Sets; 3.1 Introduction; 3.2 Convex Sets and Affine Subspaces; 3.3 Operations on Convex Sets; 3.4 Cones; 3.5 Extreme Points; 3.6 Balanced and Absorbing Sets; 3.7 Polytopes and Polyhedra; Exercises and Supplements; Bibliographical Comments; Part II. Topology; 4. Topology; 4.1 Introduction; 4.2 Topologies; 4.3 Closure and Interior Operators in Topological Spaces; 4.4 Neighborhoods; 4.5 Bases; 4.6 Compactness; 4.7 Separation Hierarchy. 4.8 Locally Compact Spaces4.9 Limits of Functions; 4.10 Nets; 4.11 Continuous Functions; 4.12 Homeomorphisms; 4.13 Connected Topological Spaces; 4.14 Products of Topological Spaces; 4.15 Semicontinuous Functions; 4.16 The Epigraph and the Hypograph of a Function; Exercises and Supplements; Bibliographical Comments; 5. Metric Space Topologies; 5.1 Introduction; 5.2 Sequences in Metric Spaces; 5.3 Limits of Functions on Metric Spaces; 5.4 Continuity of Functions between Metric Spaces; 5.5 Separation Properties of Metric Spaces; 5.6 Completeness of Metric Spaces. 5.7 Pointwise and Uniform Convergence5.8 The Stone-Weierstrass Theorem; 5.9 Totally Bounded Metric Spaces; 5.10 Contractions and Fixed Points; 5.11 The HausdorffMetric Hyperspace of Compact Subsets; 5.12 The Topological Space (R, O); 5.13 Series and Schauder Bases; 5.14 Equicontinuity; Exercises and Supplements; Bibliographical Comments; 6. Topological Linear Spaces; 6.1 Introduction; 6.2 Topologies of Linear Spaces; 6.3 Topologies on Inner Product Spaces; 6.4 Locally Convex Linear Spaces; 6.5 Continuous Linear Operators; 6.6 Linear Operators on Normed Linear Spaces. 6.7 Topological Aspects of Convex Sets6.8 The Relative Interior; 6.9 Separation of Convex Sets; 6.10 Theorems of Alternatives; 6.11 The Contingent Cone; 6.12 Extreme Points and Krein-Milman Theorem; Exercises and Supplements; Bibliographical Comments; Part III. Measure and Integration; 7. Measurable Spaces and Measures; 7.1 Introduction; 7.2 Measurable Spaces; 7.3 Borel Sets; 7.4 Measurable Functions; 7.5 Measures and Measure Spaces; 7.6 Outer Measures; 7.7 The Lebesgue Measure on Rn; 7.8 Measures on Topological Spaces; 7.9 Measures in Metric Spaces; 7.10 Signed and Complex Measures.
Responsibility: by Dan Simovici (University of Massachusetts, Boston, USA).

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