Multivariate Digital Display for Hyperspace Class Separation
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Solution Overview
Problem
Current methods for visualizing data sets in hyperspace with multiple classes struggle to maintain separation between classes when reduced to 2D or 3D, leading to overlapping and loss of information, making it difficult to classify and identify unknown data points accurately.
Innovation Solution
A multivariate digital separation and display system that transforms data into a pairs-hyperspace with a number of dimensions equal to the number of class pairs, maximizing separation between classes, allowing for clear visualization and classification without information loss, using a computer processor to construct a pairs-matrix, evaluate separation, and project data into this new space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conventional MVA methods (PCA) are used to reduce hyperspace data to 2D or 3D visualization, then the data can be visualized in lower dimensions, but the separation between classes is significantly lost and classes become overlapped
Solution Approach 1:
The patent transforms the data from original N-dimensional hyperspace into a new M-dimensional space where M equals the number of class pairs (m(m-1)/2). Each dimension in the new space corresponds to a specific pair of classes and represents the separation between them. This dimensionality transformation preserves class separation information while enabling visualization, as the new dimensions are specifically designed to maximize separation between class pairs rather than simply reducing dimensions for visualization purposes.
2Ease of operation
If the hyperspace is reduced down to 2D or 3D for human visualization, then the data becomes visually accessible, but classes become overlapped and encroach on top of each other
Solution Approach 1:
The patent fundamentally changes the parameters used for dimensionality reduction. Instead of using principal components that maximize overall variance (which may not preserve class separation), the patent uses separation-specific parameters where each new dimension corresponds to the separation between a specific pair of classes. This parameter change ensures that when data is projected into 2D or 3D from the new M-dimensional space, the class separation is maximized rather than lost, directly addressing the reliability issue.
3Productivity
If all data points of all classes are used to find principal components, then the method captures overall data dispersion, but it cannot maximize separation between specific class pairs
Solution Approach 1:
The patent segments the overall data analysis task into multiple focused sub-tasks, one for each class pair. Instead of finding a single set of principal components that attempts to capture all variance, the patent creates separate dimensions for each class pair (m(m-1)/2 pairs), where each dimension is optimized specifically for separating that pair. This segmentation allows the method to achieve high measurement precision for class separation while maintaining productivity through systematic processing of each pair.
Data Source
AI summary
A multivariate digital separation of classes and display device and method for generating pictures of data set comprised of points in hyperspace. An input device may include a keyboard, a laboratory instrument such as a mass spectrometer, a reader of computer readable medium, or a network interface device. An output device may include a monitor used in conjunction with either a 2D or 3D printer or both. A computer processor receives data from the input device and performs a series of steps to create a 2D or 3D image of the pairs-hyperspace of all pairs of classes in data set. The resulting image is then produced in a non-transitory medium by at least one of the output devices. The processor steps include the use of maximizing the degree of separation between all classes in the data set as well as transformation of separated data points of all classes into pairs-hyperspace.