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# Method for Visualizing High Dimensional Data Via Projection to a Spherical Coordinate System

IP.com Disclosure Number: IPCOM000250198D
Publication Date: 2017-Jun-09
Document File: 3 page(s) / 200K

## Publishing Venue

The IP.com Prior Art Database

## Abstract

Disclosed is a technique for mapping each data point in a high-dimension test set to a ray in the spherical coordinate system. This method visually represents high-dimensional data in a way that does not require sampling or reducing the dimensions.

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Method for Visualizing High Dimensional Data via Projection to a Spherical Coordinate System

When dealing with large amounts of data, the curse of dimensionality often limits the

theories, insights, and inferences gained through analysis. Data visualization is a

common way to gain broad views about trends and patterns in the data sets undergoing

analysis. However, as with other aspects of analysis, visualization becomes more

difficult as the dimensionality of the data increases. Many different visualization

techniques enable users to view high-dimensional data sets. Most approaches involve

either sampling the data or attempting to reduce the number of dimensions being

represented (both prior to display and interactively). Another method is needed to gain

The novel technique described herein visually represents high-dimensional data in a

way that does not require sampling or reducing the dimensions.

Given a high-dimension data set, the technique maps each data point to a ray in the

spherical coordinate system. Related points can be arranged to share angles based on

common properties, and then ordered such that similar profiles share proximity. The

final output of the visualization is a terrain upon which individual input "rows" or

"columns" can be highlighted, cross sections can be viewed, and peaks and valleys can

be analyzed.

The idea is to map each data point into the spherical coordinate system represented by

radial distance (r), polar angle (theta), and azimuthal angle (phi). Data points from the

same column share the same azimuthal angle, or phi. Data points from the same row

will share the same polar angle, or theta. As such, individual data rows consist of points

in a plane that can be connected by line segments or curves and represent a cross

section of the final three-dimensional (3D) terrain at that angle. The polar angles

assigned to these cross sections evenly distribute through the coordinate system range

(0 to 360 degrees), such that the change in terrain elevation fr...