Data Visualization with Category Theory and Geometry
Language: English
Published by Springer, Springer Aug 2025, 2025
- Hardcover
- New
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germanybuchversandmimpf2000
AbeBooks seller since January 23, 2017
Condition: New
£ 47.35
Quantity: 1 available
Add to basketItem description from seller
Seller Inventory # 9783031979729
- Title
- Data Visualization with Category Theory and Geometry
- Author
- Lukas Silvester Barth
- Publisher
- Springer, Springer Aug 2025
- Publication year
- 2025
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 3031979729
- ISBN 13
- 9783031979729
- Item weight
- 598 grams
- Dimensions
- 241x160x22 mm
This open access book provides a robust exposition of the mathematical foundations of data representation, focusing on two essential pillars of dimensionality reduction methods, namely geometry in general and Riemannian geometry in particular, and category theory.
Presenting a list of examples consisting of both geometric objects and empirical datasets, this book provides insights into the different effects of dimensionality reduction techniques on data representation and visualization, with the aim of guiding the reader in understanding the expected results specific to each method in such scenarios.
As a showcase, the dimensionality reduction method of “Uniform Manifold Approximation and Projection” (UMAP) has been used in this book, as it is built on theoretical foundations from all the areas we want to highlight here. Thus, this book also aims to systematically present the details of constructing a metric representation of a locally distorted metric space, which is essentially the problem that UMAP is trying to address, from a more general perspective.
Explaining how UMAP fits into this broader framework, while critically evaluating the underlying ideas, this book finally introduces an alternative algorithm to UMAP. This algorithm, called IsUMap, retains many of the positive features of UMAP, while improving on some of its drawbacks.
"Synopsis" may belong to another edition of this title.
From the Back Cover
This open access book provides a robust exposition of the mathematical foundations of data representation, focusing on two essential pillars of dimensionality reduction methods, namely geometry in general and Riemannian geometry in particular, and category theory.
Presenting a list of examples consisting of both geometric objects and empirical datasets, this book provides insights into the different effects of dimensionality reduction techniques on data representation and visualization, with the aim of guiding the reader in understanding the expected results specific to each method in such scenarios.
As a showcase, the dimensionality reduction method of “Uniform Manifold Approximation and Projection” (UMAP) has been used in this book, as it is built on theoretical foundations from all the areas we want to highlight here. Thus, this book also aims to systematically present the details of constructing a metric representation of a locally distorted metric space, which is essentially the problem that UMAP is trying to address, from a more general perspective.
Explaining how UMAP fits into this broader framework, while critically evaluating the underlying ideas, this book finally introduces an alternative algorithm to UMAP. This algorithm, called IsUMap, retains many of the positive features of UMAP, while improving on some of its drawbacks.
"About the title" may belong to another edition of this title.
buchversandmimpf2000
Emtmannsberg, BAYE, Germany
AbeBooks seller since January 23, 2017
Shipping rates from Germany to U.S.A.
| Item | 60 to 60 business days | 60 to 60 business days |
|---|---|---|
| First item | £ 51.57 | £ 64.46 |
Payment methods
- Check
- Paypal
Store description
Specialty
Modernes Antiquariat - Bücher von 1960 bis heuteSeller's business information
buchversandmimpf2000
Germany
Terms of sale
Impressum
Gesetzliche Anbieterkennung:
Thorsten Retsch
Buchversand Mimpf2000
Oberölschnitz 16
95517 Emtmannsberg
Deutschland
Telefon: 092092023188
E-Mail: order@buchversandmimpf2000.de
USt-IdNr.: DE 235096871
Alternative Streitbeilegung:
Die Europäische Kommission stellt eine Plattform für die außergerichtliche Online-Streitbeilegung (OS-Plattform) bereit, aufrufbar unter http://ec.europa.eu/odr.
Right of withdrawal
If you are a consumer you can withdraw from the contract in accordance with the following. Consumer means any natural person who is acting for purposes which are outside his trade, business, craft or profession.
Information regarding the right of withdrawal
Statutory right to withdraw
You have the right to withdraw from this contract within 14 days without giving any reason.
The withdrawal period will expire after 14 days from the day on which you acquire, or a third party other than the carrier and indicated by you acquires, physical possession of the last good or the last lot or piece.
To exercise the right of withdrawal, electronically fill in and submit a clear statement on our website, under "My Purchases" in "My Account". We will communicate to you an acknowledgement of receipt of such a withdrawal on a durable medium (e.g. by e-mail) without delay.
To meet the withdrawal deadline, it is sufficient for you to send your communication concerning your exercise of the right of withdrawal before the withdrawal period has expired.
Effects of withdrawal
If you withdraw from this contract, we will reimburse to you all payments received from you, including the costs of delivery (except for the supplementary costs arising if you chose a type of delivery other than the least expensive type of standard delivery offered by us).
We may make a deduction from the reimbursement for loss in value of any goods supplied, if the loss is the result of unnecessary handling by you.
We will make the reimbursement without undue delay, and not later than 14 days after the day on which we are informed about your decision to withdraw from this contract.
We will make the reimbursement using the same means of payment as you used for the initial transaction, unless you have expressly agreed otherwise; in any event, you will not incur any fees as a result of such reimbursement.
We may withhold reimbursement until we have received the goods back, or you have supplied evidence of having sent back the goods, whichever is the earliest.
You shall send back the goods or hand them over to buchversandmimpf2000, Emtmannsberg, BAYE, Germany, +49 09209-2023188, without undue delay and in any event not later than 14 days from the day on which you communicate your withdrawal from this contract to us. The deadline is met if you send back the goods before the period of 14 days has expired. You will have to bear the direct cost of returning the goods. You are only liable for any diminished value of the goods resulting from the handling other than what is necessary to establish the nature, characteristics and functioning of the goods.
Exceptions to the right of withdrawal
The right of withdrawal does not apply to:
- The delivery of newspapers, journals or magazines with the exception of subscription contracts; and
- The supply of digital content which is not supplied on a tangible medium (e.g. on a CD or DVD) if you accepted when you placed your order that we could start to deliver it, and that you could not withdraw once delivery had started.
Shipping terms
Soweit in der Artikelbeschreibung keine andere Frist angegeben ist, erfolgt die Lieferung der Ware innerhalb von 3-5 Werktagen nach Vertragsschluss, bei Vorauszahlung erst nach Eingang des vollständigen Kaufpreises und der Versandkosten. Alle Preise inkl. MwSt.