Cluster Analysis Based on Tangles in Abstract Separations Systems

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This patent introduces a computer-implemented method for clustering analysis that uses mathematical structures called abstract separation systems (ASS) and abstract tangles. Unlike traditional clustering methods (like k-means or DBSCAN), this technique does not require predefining the number of clusters, or a distance function between data points. Instead, it identifies 'fuzzy' clusters even in ambiguous or complex data, based on relationships (separations) within the data, configurable consistency requirements, and mathematical properties. The method is flexible and can adapt to a wide range of data types and sources, making clustering more robust and capable of discovering previously unknown or not precisely defined groupings.

Use CasesContent extracted from patent full text and abstract with AI.

• Data mining: discovering meaningful groupings in customer, transaction, or behavioral data without prior assumptions.
• Expert systems and knowledge bases: organizing complex knowledge structures and identifying core themes or concepts.
• Image and signal analysis: segmenting images or signals into meaningful features or regions, like facial features or objects within pictures.
• Internet content analysis: clustering themes, topics, or trends in large sets of documents or webpages, helpful for marketing or trend analysis.
• Survey/poll analysis: identifying groups of respondents with similar or distinct belief sets, even when the answers are ambiguous or overlapping.
• Audio and music classification: grouping audio files or music tracks according to structurally similar patterns.
• Data compression: representing large data sets via their essential cluster structure for more efficient storage or transmission.
• Content comparison: measuring similarity between different data sets based on the structure of their clusters (e.g., comparing images, document sets, or music).
• Fact-checking or fake news detection: identifying clusters of consensus or contentious statements, aiding in narrowing down topics for verification.

BenefitsContent extracted from patent full text and abstract with AI.

• Does not require defining the number of clusters or a distance function, reducing parameter tuning and bias.
• Can identify clusters in ambiguous, overlapping, or indirectly defined data—supporting 'fuzzy' clustering.
• Flexible and adaptable to diverse data types and domains, from images to documents to survey data.
• Capable of detecting new or previously undefined types of clusters, encouraging innovation and discovery.
• Allows post-hoc assessment and quantification of cluster strength, complexity, and visibility within data.
• Supports structure identification—revealing the overall organization and relationships among clusters (e.g., as tree structures).
• Can be used for efficient data compression by summarizing the data with essential clusters and their relations.
• Mathematically rigorous, with well-founded properties ensuring robustness (distinguishing and duality properties).
• Enables similarity measurement between data sources based on their cluster structures, not just raw content.

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Patent Abstract

A computer-implemented method to capture and detect clusters in, or determined by, a set V of discrete digital data comprising; • computing, from the set V, an abstract separation system ASS that consists of a finite set S, whose elements are called separations; of a predetermined transitive, antisymmetric and reflexive order relation ≤ on S; and of an order-reversing involution * : S→ S, that is, a mapping s → s* with the property that, (s*)* = s and that r ≤ s implies s*