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Trajectory mapping: a new nonmetric scaling technique

W Richards¹, J J Koenderink

¹Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge 02139, USA.

|January 1, 1995

Summary

Trajectory mapping is a novel scaling technique that identifies feature parameterizations and paths within data spaces. This method effectively categorizes object samples without assuming a homogeneous or metric space.

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Area of Science:

Data analysis and visualization
Machine learning
Pattern recognition

Background:

Traditional scaling techniques like multidimensional scaling often assume homogeneous or metric feature spaces.
Recovering underlying parameterizations and traversal paths in complex data is challenging.

Purpose of the Study:

Introduce trajectory mapping as a new scaling technique.
Demonstrate its ability to recover parameterizations, axes, and paths in feature spaces.
Showcase its application in categorizing data samples.

Main Methods:

Trajectory mapping technique development.
Application to a set of color data.
Application to a collection of texture data.

Main Results:

Trajectory mapping successfully recovers parameterizations, axes, and paths.
The technique partitions object samples into distinct categories.
It does not require the feature space to be homogeneous or metric.

Conclusions:

Trajectory mapping offers a flexible approach to analyzing feature spaces.
It provides valuable insights into data structure and categorization.
The method is applicable to diverse datasets, including colors and textures.

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