Multivariate Outlier Detection via Wave Series Transformation
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Solution Overview
Problem
Current data mining techniques are inadequate in effectively identifying outliers in a data set population, as they fail to accurately detect deviations in phase or magnitude, which are crucial for determining actions outside of the norm.
Innovation Solution
The method involves transforming state vectors for actors and populations into sampled wave series representations using Andrews' wave transformation, followed by whitening and comparison to identify deviations in phase or magnitude, with cross-correlation functions determining outliers based on threshold levels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current data mining techniques are used for outlier detection, then the process is simple, but the accuracy of identifying deviations in phase or magnitude is insufficient
Solution Approach 1:
The patent transforms state vectors into sampled wave series representations using Andrews' wave transformation, changing the parameter space from raw data to wave domain. This transformation enables detection of phase and magnitude deviations that are not visible in the original data, resolving the contradiction between simple processing and accurate outlier detection.
Solution Approach 2:
The patent adds temporal/dimensional dimensions by transforming multivariate state vectors into time-series wave series representations. This dimensional transformation allows comparison of phase and magnitude across time, enabling detection of outliers that would be invisible in static multivariate analysis.
2Reliability
If wave transformation and whitening operations are applied, then phase and magnitude deviations can be detected, but computational complexity increases
Solution Approach 1:
The patent applies whitening operations as a preliminary step before comparison to remove autoregressive and moving average effects. This preliminary processing ensures that subsequent comparisons are made on cleaned data, improving reliability of deviation detection while the whitening process itself is a standard statistical procedure that manages computational complexity.
Solution Approach 2:
The sampled wave series representation acts as an intermediary between the raw state vectors and the final deviation comparison. This intermediate transformation layer enables reliable phase and magnitude comparison while consolidating the complexity into a single transformable representation rather than requiring complex direct comparison of multivariate data.
3Measurement precision
If multiple transformations and comparisons are performed, then detection accuracy improves, but processing time increases
Solution Approach 1:
The Andrews' wave transformation serves multiple functions simultaneously: it transforms the data into the wave domain, creates the sampled series representation, and prepares the data for phase and magnitude comparison. This multi-functionality reduces the number of separate processing steps, improving precision while managing processing time.
Solution Approach 2:
The patent replaces complex multivariate statistical comparison mechanisms with wave series transformation and comparison. This substitution simplifies the comparison process to phase and magnitude analysis in the wave domain, which is computationally more efficient than direct multivariate outlier detection while maintaining high precision.
Data Source
AI summary
A computer-implemented method of determining actions outside of a norm is provided. The method comprises: generating an actor state vector and a peer group state vector, wherein the actor state vector identifies a characteristic for an actor in each of a plurality of categories and the peer group state vector identifies a characteristic for a peer group in each of the plurality of categories, transforming the actor state vector into a first sampled wave series representation using a first wave series transformation, transforming the population state vector into a second sampled wave series representation using a second wave series transformation, and filtering the first sampled wave series representation and the second sampled wave series representation to identify a deviation of the first wave series representation from the second wave series representation in a phase or a magnitude.