Temporal Clustering of Non-Stationary Data Using Functional Centroids
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Solution Overview
Problem
Current clustering techniques are inadequate for efficiently and accurately processing non-stationary data, as they assume stationary sources and fail to effectively capture temporal changes, limiting their ability to analyze complex modern systems.
Innovation Solution
The method initializes functional centroids that describe linear or polynomial trends and cyclic patterns in non-stationary data, partitioning the data set and iteratively fitting new centroids to minimize energy, allowing for accurate clustering and future distribution prediction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional clustering techniques (k-means) are used on non-stationary data, then computational simplicity is maintained, but clustering accuracy deteriorates because the methods assume stationary sources and cannot capture temporal changes
Solution Approach 1:
The patent transforms static clustering centers into dynamic functional models that evolve over time. Each clustering center is represented by a function (e.g., polynomial or sinusoidal) with parameters that capture temporal patterns. This allows the clustering algorithm to adapt to non-stationary data where statistics change over time, resolving the contradiction between maintaining simplicity and improving accuracy for temporal data.
Solution Approach 2:
The patent changes the parameter representation from fixed values to time-varying functions. Instead of assuming constant clustering centers, the method models them as functions of time with adjustable parameters (coefficients, frequencies, phases). This parameter transformation enables accurate clustering of non-stationary data while maintaining computational tractability through efficient function fitting algorithms.
2Measurement precision
If functional centroids with temporal modeling are used, then clustering accuracy for non-stationary data improves, but computational requirements increase due to iterative fitting and energy minimization
Solution Approach 1:
The patent performs preliminary actions by initializing functional centroids with reasonable guesses based on initial data analysis or simple clustering. This preliminary setup reduces the number of iterative fitting steps needed later, as the optimization starts from a better position. The preliminary action balances accuracy improvement with computational efficiency by avoiding excessive iterations.
Solution Approach 2:
The patent implements feedback through the energy minimization loop, where each iteration computes the energy (error) and uses it to update functional parameters. The feedback mechanism guides the optimization toward better clustering solutions while allowing early termination when convergence is achieved, thus balancing accuracy and processing speed based on actual data characteristics.
3Adaptability or versatility
If a single stochastic source model is used, then model simplicity is maintained, but ability to handle complex non-stationary data deteriorates
Solution Approach 1:
The patent segments the complex non-stationary data into multiple clusters, each governed by its own functional model. Instead of trying to model all complexity in a single source, the data is divided into homogeneous groups where each group can be represented by a simpler functional centroid. This segmentation allows the system to handle complex overall patterns while maintaining simple local models.
Solution Approach 2:
The patent creates a universal functional centroid framework that can model multiple types of temporal patterns (linear trends, polynomial curves, sinusoidal cycles) using a unified approach. The same functional form with different parameters can represent various non-stationary behaviors, providing versatility without proportionally increasing model complexity. This multi-functionality allows handling diverse data patterns with a consistent methodology.
Data Source
AI summary
Techniques for clustering non-stationary data are disclosed. In embodiments, a method is disclosed comprising initializing a plurality of functional centroids; partitioning a non-stationary data set, using the functional centroids, into partitions, the number of partitions being equal to the number of functional centroids; generating a set of fitted functional centroids for each of the partitions; replacing at least one of the functional centroids with a corresponding fitted functional centroid if a computed energy of the corresponding fitted functional centroid is less than an energy of the at least one functional centroid; computing a summation of the energies associated with each of the functional centroids; and outputting the functional centroids upon determining that a termination condition is met.