翻訳待ち：Stochastic complexity of vectors containing cluster structure

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--> [Submitted on 31 Aug 2026] Title:Stochastic complexity of vectors containing cluster structure View a PDF of the paper titled Stochastic complexity of vectors containing cluster structure, by Daniel Nicorici and 2 other authors View PDF HTML (experimental) Abstract:This paper studies the problem of computing the stochastic probability (shortest code length) of the encoded vectors containing cluster structure using Normalized Maximum Likelihood (NML) model. This is of great theoretical and practical importance in data clustering based on Minimum Description Length (MDL) principle, such as for estimating the best number of clusters and best cluster structure for the data. Straightforward computation of the shortest code length of the vector containing cluster structure based on the NML model requires polynomial time with respect to the size of the vector and number of clusters. We show that this is a tractable problem by introducing a recursion formula for the efficient computation of normalizing constant from the NML model. The time complexity of the new formula is linear opposed to previous polynomial time with respect to the size of the vector and number of clusters. Comments: 8 pages, 2 figures. Originally published in the Proceedings of the International Workshop on Nonlinear Signal and Image Processing (NSIP 2007), Bucharest, Romania, 10-12 September 2007, pp. 164-169 Subjects: Machine Learning (cs.LG); Information Theory (cs.IT); Machine Learning (stat.ML) Cite as: arXiv:2609.00084 [cs.LG] (or arXiv:2609.00084v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.00084 arXiv-issued DOI via DataCite (pending registration) Journal reference: Proceedings of NSIP 2007 - International Workshop on Nonlinear Signal and Image Processing (2007), pp. 164-169 Submission history From: Daniel Nicorici [view email] [v1] Mon, 31 Aug 2026 10:44:21 UTC (91 KB) Full-text links: Access Paper: View a PDF of the paper titled Stochastic complexity of vectors containing cluster structure, by Daniel Nicorici and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs cs.IT math math.IT stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)