Coordinate Transformation for Mahalanobis Distance Normalization
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Solution Overview
Problem
The Mahalanobis-Taguchi method is unreliable for determining normality/abnormality when handling items with high nonlinearity or non-normal distributions, as it assumes a normal distribution.
Innovation Solution
A data processing method involving coordinate transformation and standardization to linearize and normalize data, using transformations like SHASH, Yeo-Johnson, Boltzmann, or broken line transformations to calculate Mahalanobis distance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Mahalanobis-Taguchi method is used for abnormality determination, then normality/abnormality can be determined reliably for variables with high linearity, but the reliability is lowered when items with high nonlinearity or non-normal distribution are included
Solution Approach 1:
The patent applies coordinate transformation to change the parameters of the data distribution. By transforming the data through functions like logarithmic, exponential, or power transformations, the data is converted from non-linear/non-normal distribution into a form that approximates normal distribution, thereby enabling the Mahalanobis-Taguchi method to work reliably on previously unsuitable data types
Solution Approach 2:
The patent performs preliminary coordinate transformation and standardization on the data before applying the Mahalanobis-Taguchi method. This preliminary processing step prepares the data by linearizing relationships and normalizing distributions, ensuring that the subsequent abnormality determination can be performed reliably even when the original data contains non-linear or non-normal distributed items
Data Source
AI summary
The present method relates to a data processing method for processing data for calculating a Mahalanobis distance. The present method calculates an objective function for linearizing a combination of items included in unit space data, and calculates coordinate transformation parameters for performing coordinate transformation of the unit space data for each item, in order to minimize the objective function. Then, the calculated coordinate transformation parameters are used to perform coordinate transformation of the unit space data for each item. The unit space data that underwent coordinate transformation is standardized for each item.