Weighted Quantile Threshold Determination for Time-Series Data
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Solution Overview
Problem
Existing methods for determining dynamic thresholds in time-series data are ineffective in handling outliers and capturing cyclical patterns, leading to inaccurate threshold settings and slow convergence in response to data changes.
Innovation Solution
The method involves transforming time-series data by reducing outliers, dividing it into discrete intervals, applying cycles, weighting the data, and calculating thresholds from the weighted means and variances to ensure accurate and dynamic threshold determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional threshold determination methods are used, then the process is simple, but the thresholds are inaccurate and do not capture cyclical patterns
Solution Approach 1:
The time-series data is divided into discrete time intervals or bins, allowing the analysis to be performed on segmented portions of the data. This segmentation enables the capture of temporal patterns and cycles while maintaining computational tractability through structured processing of divided data sets.
Solution Approach 2:
The threshold determination method dynamically adjusts thresholds based on weighted quantile analysis of time-series data, allowing the thresholds to adapt to changing data patterns and cyclical behaviors. The weighting scheme enables the system to respond dynamically to recent data while incorporating historical patterns.
2Measurement precision
If all time-series data is used for threshold determination, then more data is available for analysis, but outliers significantly impact threshold accuracy
Solution Approach 1:
The method extracts specific quantile portions of the time-series data for threshold determination, effectively separating the relevant data portions from outliers. By focusing on specific quantiles (e.g., 10th percentile for lower threshold, 90th percentile for upper threshold), the method excludes extreme values that would otherwise distort the threshold calculation.
Solution Approach 2:
The weighting scheme converts the potential harm of using all data (including outliers) into a benefit by assigning appropriate weights that diminish the influence of extreme values. The weighted quantile analysis transforms the complete data set into a useful form where recent relevant data has higher impact while historical and extreme data contribute appropriately.
3Adaptability or versatility
If fixed thresholds are used, then the system is stable, but the thresholds cannot adapt to changes in data patterns
Solution Approach 1:
The threshold determination method implements dynamic thresholds through weighted quantile analysis, where the weights allow the system to adapt to changing data patterns while maintaining stability through the structured incorporation of historical data. The dynamic nature is achieved through the weighting scheme that balances recent and historical observations.
Solution Approach 2:
The method incorporates feedback mechanisms by continuously analyzing time-series data and adjusting thresholds based on the weighted quantile results. The systematic re-evaluation of data patterns provides feedback that enables the thresholds to adapt to changing conditions while maintaining stability through the consistent application of the weighting and quantile analysis framework.
Data Source
AI summary
Methods and systems for determination of thresholds for time-series data. Data is transformed by reducing outliers, dividing the time series data into discrete time intervals, and taking parts of the data corresponding to the range that the thresholds will bound. If data cycles are known, they may be applied to the data and the resulting sets are weighted. Thresholds are then derived from the weighted means and variances of the sets of weighted data.