A linear space adjustment by mapping data into an intermediate space and keeping low level data structures

ABSTRACT

One of the most important assumptions in machine learning tasks is the fact that training data points and test data points are extracted from the same distribution. However, this paper assumes the situation in which this fact does no longer hold. Therefore, a task named space adjustment, through which the distribution of the data points in the training-data space and the distribution of the data points in the test-data space become identical, is inevitable. Hereby, authors propose a linear mapping for the space adjustment task in the paper. It considers four approaches for preserving localities among data samples during the space adjustment. Each approach is defined based on a different locality concept. Considering all locality concepts in an objective function, authors transform the space adjustment into an optimisation problem. The paper proposes to optimise the corresponding objective function by an iterative approach. Empirical study shows that the proposed method outperforms the baseline methods. To do experiments, authors employ a large number of real-world datasets.

KEYWORDS:

• Space Adjustment
• optimisation
• structure Maintenance
• classification

Author Contributions

HP and MM designed the study; HP and MM wrote a draft of the manuscript. MRM and KHP edited with help from MM and HP. MRM and KHP wrote the whole paper with help from MM and HP with the statistical point of view. MRM and MM with the help of HP carried out all the analyses including the statistical analyses. MRM and KHP generated all figures and tables. All authors have read and approved of the final version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.