Classification of unbalanced data with transparent kernels

Abstract

Two important issues regarding data driven classification are addressed here: Model interpretation and imbalanced data. The aim is to build data driven classifiers that provide good predictive performance for a set of imbalanced data and enhance the understanding of a model by enabling input/output dependencies that exist to be visualised. Here, the classification method is demonstrated on an imbalanced data set that describes fatigue crack initiation in automotive camshafts. To generate interpretable models, the Support vector Parismonious ANalysis Of Variance (SUPANOVA) technique is extended to the classification domain. The technique enables an additive decomposition of low dimensional kernel models to be recovered, enhancing model visualization. The standard averaging technique used to assess the performance of the model is inappropriate for imbalanced data. As such, the Geometric mean (Gmean), which is typically maximal on the Receiver Operating Characteristic (ROC) when the true positive and negative classification is balanced between two classes is used. A conventional SVM produced results of generalisation estimate of 55%. However, introducing a class-dependent misclassification cost into the SVM resulted in an improved performance of 74%. The SU-PANOVA technique produced a reduced performance of 64%, whilst reducing the model space to just 13 com-industries. However, there is a tradeoff between high strength and the number of fatigue cracks [l]. As such, it is important to investigate why cracks are initiated from the graphite nodules within the microstructure. Clearly, in this example the number of graphite nodules which can be classed as "no crack" exceeds the number of "crack" nodules and consequently the data is imbalanced (see Fig. 1). The graphite nodule size and/or distribution morphology can be obtained from Finite Body Tessellation (FBT). These measurements are used as the features for a classifier to learn the characteristics that cause fatigue crack initiation.

On combination of SMOTE and particle swarm optimization based radial basis function classifier for imbalanced problems

“…The first two real data sets were taken from [50], while the third real data set was from [51]. These three real data sets were chosen in the order of increasing imbalance.…”

“…ADI data set: The austempered ductile iron (ADI) material data set was obtained from a study on fatigue cracks from the graphite nodules within the microstructure in an automotive camshaft application [51]. This two-class data set contained 2923 instances in the feature space of dimension m = 9, with 2807 negative instances and 116 positive instances.…”

A Kernel-Based Two-Class Classifier for Imbalanced Data Sets

“…The austempered ductile iron (ADI) material data set for automotive camshaft application [43] is used to study why fatigue cracks are initiated from the graphite nodules within the microstructure. There are nine features and two class labels ("crack" and "no crack").…”

“…The data set is very imbalanced with a total of 2923 samples in which 116 samples are "crack class," and 2807 samples are "no crack class." A cost-sensitive support vector machine (CS-SVM) and a cost-sensitive SUPANOVA model [43] were applied to investigate the data set [43]. The cost-sensitive SUPANOVA model used one-norm regularization to derive a reduced model set trading model interpretability with classification performance.…”

“…We used random drawn data samples consisting of 90 "crack" and 700 "no crack" data samples from the data set, and the process was repeated 16 times to obtain eight pairs of training/testing data set in order to make a comparison with results of [43]. Initially, all nine input features are normalized to the range using the operation: , , , for .…”