Kohonen map-wise regression applied to interval data

Abstract

Kohonen maps, also known as self-organizing maps, is a powerful clustering method which groups data using multiple nodes that converge to clusters. Therefore, it is not necessary to know a priori the exact number of clusters in the data. This paper proposes a clusterwise regression method that combines self-organizing maps and a parametrized linear regression approach for interval data in the framework of Symbolic Data Analysis. The linear regression approach adapts itself to use the best set of points inside intervals to build the regression model, generalizing all approaches that select points of interest, such as center, range, minimum and maximum, to provide linear regression for interval data. Here, self-organizing map nodes are responsible for detecting local linear regression structures and the parametrized linear regression builds local regression models, one for each node. Finally, outputs are given as weighted averages of the local model predictions. Since our model fits the linear models using the map nodes, it avoids weak performances that might arise when clusters are not easily separable. As another contribution, we provide a way to extract predictions from an existing clusterwise regression method. Experiments with synthetic and real data sets show the usefulness of the proposed method.