Sampling Strategies for Mining in Data-Scarce Domains

TL;DR

This paper introduces a combined bottom-up and top-down sampling mechanism for data mining in domains with scarce data, leveraging physical properties to improve decision-making and interpretability.

Contribution

It presents a novel framework that integrates data-driven mining with domain-informed sampling, applicable to diverse scientific and engineering fields.

Findings

Effective in identifying pockets in spatial data

Assists in qualitative determination of Jordan forms

Enhances interpretability through physical property exploitation

Abstract

Data mining has traditionally focused on the task of drawing inferences from large datasets. However, many scientific and engineering domains, such as fluid dynamics and aircraft design, are characterized by scarce data, due to the expense and complexity of associated experiments and simulations. In such data-scarce domains, it is advantageous to focus the data collection effort on only those regions deemed most important to support a particular data mining objective. This paper describes a mechanism that interleaves bottom-up data mining, to uncover multi-level structures in spatial data, with top-down sampling, to clarify difficult decisions in the mining process. The mechanism exploits relevant physical properties, such as continuity, correspondence, and locality, in a unified framework. This leads to effective mining and sampling decisions that are explainable in terms of domain knowledge and data characteristics. This approach is demonstrated in two diverse applications -- mining pockets in spatial data, and qualitative determination of Jordan forms of matrices.