Histogram-Based Multivariate Data Analysis for Grouped Observations
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Solution Overview
Problem
Existing data analysis methods struggle to efficiently analyze multivariate data, particularly when observations are grouped into multiple sets of conditions, making it difficult to extract accurate characteristics of observations belonging to different groups.
Innovation Solution
A computer-implemented method for data analysis that involves obtaining a set of observations, constructing a master histogram from these observations, and then creating secondary histograms for each group, where each bin in the secondary histograms represents the count of observations within that group matching specific values in the master histogram.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If traditional statistical summaries (mean, standard deviation, median) are used to analyze multivariate data, then the analysis process is simple, but the information extracted is insufficient and lacks detailed distribution characteristics
Solution Approach 1:
The patent segments the data analysis process into multiple histogram constructions: a first histogram for the entire dataset and multiple second histograms for different groups. Each histogram divides the parameter range into bins, allowing detailed distribution characteristics to be captured without requiring complex analytical methods. This segmentation enables both simple processing and rich information extraction.
2Measurement precision
If detailed distribution analysis is performed on multivariate data grouped into multiple sets of conditions, then accurate characteristics of each group can be extracted, but the analysis complexity and computational burden increase significantly
Solution Approach 1:
The patent divides the multivariate data into multiple groups based on different sets of conditions, and constructs a separate second histogram for each group. This segmentation allows accurate extraction of distribution characteristics for each group while maintaining a systematic and manageable analysis framework that doesn't require overly complex computational methods.
Solution Approach 2:
The patent transforms the analysis from direct multivariate comparison into a histogram-based representation where data is projected onto bins along one or more parameter dimensions. This dimensionality transformation simplifies the comparison between groups while preserving distribution characteristics, making the analysis more tractable without losing important information.
3Loss of information
If comprehensive multivariate data analysis is performed on all observations, then complete information is obtained, but the processing time and computational resources required increase
Solution Approach 1:
The patent segments the comprehensive data analysis into group-specific analyses through separate second histograms. This allows the system to focus computational resources on analyzing each group's characteristics independently, reducing the overall processing time while maintaining complete information extraction across all groups and conditions.
Solution Approach 2:
The patent performs preliminary data organization by grouping observations according to different sets of conditions before conducting detailed analysis. This preliminary action structures the data in a way that facilitates more efficient processing and reduces the computational burden of subsequent histogram construction and comparison operations.
Data Source
AI summary
A computer-implemented method for data analysis comprises obtaining a plurality of first observations, the plurality of first observations including one or more values of one or more first parameters, the plurality of first observations grouped into a plurality of groups; constructing a first histogram using the values of at least one of the one or more first parameters, included in the plurality of first observations; constructing, for each of the plurality of groups, a second histogram having bins corresponding to bins of the first histogram, wherein each of the bins of the second histogram includes a count of the first observations, among the first observations that belong to the one of the plurality of groups, having one or more values corresponding to the one of the bins; and outputting the second histograms constructed for the plurality of groups.