Even if not explicitly stated, data can be often interpreted in a triadic setting in numerous scenarios of data analysis and processing. Formal Concept Analysis, as the underlying mathematical theory of Conceptual Knowledge Processing gives the possibility to explore the structure of data and to understand its structure. Representing knowledge as conceptual hierarchies becomes increasingly popu...

We propose a data reduction approach for finding a reference set for the nearest neighbour classifier. The approach is based on classifier ensembles. Each ensemble member is given a subset of the training data. Using Wilson’s editing method, the ensemble member produces a reduced reference set. We explored several routes to make use of these reference sets. The results with 10 real and artifici...

The k-nearest neighbours (kNN) is a simple but effective method for classification. Its major drawbacks are (1) low efficiency, and (2) dependency on the selection of a “good value” for k. In this paper, we propose a novel similarity-based data reduction method (SBModel) together with three variants aimed at overcoming these shortcomings. Our method constructs a similarity-based model for the d...

Sparse data and irregular data access patterns are hugely important to many applications, such as molecular dynamics and data analytics. Accelerating applications with these characteristics requires maximizing usable bandwidth at all levels of the memory hierarchy, reducing latency, maximizing reuse of moved data, and minimizing the amount the data is moved in the irst place. Many specialized d...

Dimensionality reduction is one of the basic operations in the toolbox of data-analysts and designers of machine learning and pattern recognition systems. Given a large set of measured variables but few observations, an obvious idea is to reduce the degrees of freedom in the measurements by representing them with a smaller set of more “condensed” variables. Another reason for reducing the dimen...

Data reduction is an important issue in the field of data mining. This article describes a new method for selecting a subset of data from a large dataset. A simplified chi-square criterion is proposed for measuring the goodness-of-fit between the distributions of the reduced and full data sets. Under this criterion, the data reduction problem can be formulated as a binary quadratic program and ...