Abstract Separation System for Cluster Detection
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Solution Overview
Problem
Existing clustering methods require pre-definition of the number of clusters and a distance function, limiting their ability to handle ambiguous data and identify clusters indirectly described by a data set.
Innovation Solution
The method employs an abstract separation system (ASS) with a partial order and involution, allowing for fuzzy cluster representation and identification without pre-defining the number of clusters or distance function, using separations to split data into overlapping parts and orient them towards features, enabling the detection of clusters in various data types, including indirect descriptions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional clustering methods (k-means, DBSCAN) are used, then clusters can be identified with precise assignments, but the number of clusters and distance function must be pre-defined, limiting adaptability
Solution Approach 1:
The clustering system performs self-service by automatically determining the number of clusters and distance metrics from the data itself, rather than requiring external pre-definition. The system uses the data's intrinsic structure to guide cluster formation, making the clustering process adaptive to different data types without manual configuration.
Solution Approach 2:
The invention dynamically changes clustering parameters (number of clusters, distance functions) based on the specific data being analyzed. Instead of fixed parameters, the system adapts these parameters to match the characteristics of each data set, enabling versatility across different application domains.
2Measurement precision
If precise cluster assignments are enforced, then clear cluster boundaries are achieved, but ambiguous data points cannot be properly handled
Solution Approach 1:
The system applies local quality by allowing different data points to have different degrees of cluster membership based on their individual characteristics. Rather than enforcing uniform precise assignments, the system adapts the precision of assignment to each data point's ambiguity, using probabilistic or fuzzy membership where appropriate.
3Loss of information
If data points are assigned to clusters, then cluster composition is determined, but indirect cluster descriptions (e.g., road signs indicating towns) cannot be identified
Solution Approach 1:
The system uses intermediaries (such as road signs in the example) that indirectly indicate the presence and location of clusters (towns). Rather than requiring direct data about cluster members, the system processes intermediary information that points to cluster locations, enabling identification of clusters described indirectly.
Data Source
AI summary
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*<r* for all r, s∈S; predetermining a set of consistency requirements (CRs), that is, a set F of subsets of S; computing, from the ASS (S,≤, *), one or more abstract tangles, that is, any set T⊆S that contains exactly one of each pair {s, s*} for s∈S, and does not contain any of the forbidden configurations F∈F as a subset; or determining that there is no abstract tangle; and determining that any abstract tangle T represents a cluster in, or determined by, the data set V.