# Synthetic data generation for classification via uni-modal cluster interpolation

## Abstract

The observations used to classify data from real systems often vary as a result of changing operating conditions (e.g. velocity, load, temperature, etc.). Hence, to create accurate classification algorithms for these systems, observations from a large number of operating conditions must be used in algorithm training. This can be an arduous, expensive, and even dangerous task. Treating an operating condition as an inherently metric continuous variable (e.g. velocity, load or temperature) and recognizing that observations at a single operating condition can be viewed as a data cluster enables formulation of interpolation techniques. This paper presents a method that uses data clusters at operating conditions where data has been collected to estimate data clusters at other operating conditions, enabling classification. The mathematical tools that are key to the proposed data cluster interpolation method are Catmull–Rom splines, the Schur decomposition, singular value decomposition, and a special matrix interpolation function. The ability of this method to accurately estimate distribution, orientation and location in the feature space is then shown through three benchmark problems involving 2D feature vectors. The proposed method is applied to empirical data involving vibration-based terrain classification for an autonomous robot using a feature vector of dimension 300, to show that these estimated data clusters are more effective for classification purposes than known data clusters that correspond to different operating conditions. Ultimately, it is concluded that although collecting real data is ideal, these estimated data clusters can improve classification accuracy when it is inconvenient or difficult to collect additional data.

## Keywords

Interpolation Singular value decomposition Terrain classification Data clusters Pattern classification## Notes

### Acknowledgments

This work was prepared through collaborative participation in the Robotics Consortium which is sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD 19-01-2- 0012. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. Funding for this research also provided by the National Science Foundation, Project EEC-0540865.

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