Abstract
The presence of imbalanced classes is more and more common in practical applications and it is known to heavily compromise the learning process. In this paper we propose a new method aimed at addressing this issue in binary supervised classification. Re-balancing the class sizes has turned out to be a fruitful strategy to overcome this problem. Our proposal performs re-balancing through matrix sketching. Matrix sketching is a recently developed data compression technique that is characterized by the property of preserving most of the linear information that is present in the data. Such property is guaranteed by the Johnson-Lindenstrauss’ Lemma (1984) and allows to embed an n-dimensional space into a reduced one without distorting, within an epsilon -size interval, the distances between any pair of points. We propose to use matrix sketching as an alternative to the standard re-balancing strategies that are based on random under-sampling the majority class or random over-sampling the minority one. We assess the properties of our method when combined with linear discriminant analysis (LDA), classification trees (C4.5) and Support Vector Machines (SVM) on simulated and real data. Results show that sketching can represent a sound alternative to the most widely used rebalancing methods.
Highlights
In many practical contexts, observations have to be classified into two classes of remarkably distinct size
As the sketched data are obtained through random linear combinations of the original ones, most of the linear information is preserved after sketching. This means that, in the imbalanced data case, the size of the majority class can be reduced through sketching without incurring the risk of losing linear information
The Gaussian under-sketching with Linear Discriminant Analysis (LDA) proved to behave significantly better than ROSE and US, while the superiority is less evident with Adasyn, SMOTE and Bal-USOS; there is no relevant improvement in terms of area under the curve (AUC) with respect to the imbalanced case and OS
Summary
Observations have to be classified into two classes of remarkably distinct size. According to previous literature results (see, e.g. Domingos 1999; Branco et al 2016), under-sampling the majority class leads to better classifier performance than over-sampling, and combining the two does not produce much improvement with respect to simple under-sampling They design an over-sampling approach which creates synthetic examples (Synthetic Minority Over-sampling Technique - SMOTE) rather than over-sampling with replacement. We propose to address the imbalanced class issue through matrix sketching, a recently developed data transformation technique It allows to reduce the size of the majority class or to increase the size of the minority one, while preserving the linear information that is present in the original data and performing data perturbation at the same time.
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