Multi-class ROC analysis from a multi-objective optimisation perspective

Copyright © 2006 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Pattern Recognition Letters . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition Letters, Vol. 27 Issue 8 (2006), DOI: 10.1016/j.patrec.2005.10.016Notes: Receiver operating characteristics (ROC) are traditionally used for assessing and tuning classifiers discriminating between two classes. This paper is the first to set ROC analysis in a multi-objective optimisation framework and thus generalise ROC curves to any number of classes, showing how multi-objective optimisation may be used to optimise classifier performance. An important new result is that the appropriate measure for assessing overall classifier quality is the Gini coefficient, rather than the volume under the ROC surface as previously thought. The method is currently being exploited in a KTP project with AI Corporation on detecting credit card fraud.The receiver operating characteristic (ROC) has become a standard tool for the analysis and comparison of classifiers when the costs of misclassification are unknown. There has been relatively little work, however, examining ROC for more than two classes. Here we discuss and present an extension to the standard two-class ROC for multi-class problems. We define the ROC surface for the Q-class problem in terms of a multi-objective optimisation problem in which the goal is to simultaneously minimise the Q(Q − 1) misclassification rates, when the misclassification costs and parameters governing the classifier’s behaviour are unknown. We present an evolutionary algorithm to locate the Pareto front—the optimal trade-off surface between misclassifications of different types. The use of the Pareto optimal surface to compare classifiers is discussed and we present a straightforward multi-class analogue of the Gini coefficient. The performance of the evolutionary algorithm is illustrated on a synthetic three class problem, for both k-nearest neighbour and multi-layer perceptron classifiers

Incorporating Deep Learning Techniques into Outcome Modeling in Non-Small Cell Lung Cancer Patients after Radiation Therapy

Radiation therapy (radiotherapy) together with surgery, chemotherapy, and immunotherapy are common modalities in cancer treatment. In radiotherapy, patients are given high doses of ionizing radiation which is aimed at killing cancer cells and shrinking tumors. Conventional radiotherapy usually gives a standard prescription to all the patients, however, as patients are likely to have heterogeneous responses to the treatment due to multiple prognostic factors, personalization of radiotherapy treatment is desirable. Outcome models can serve as clinical decision-making support tools in the personalized treatment, helping evaluate patients’ treatment options before the treatment or during fractionated treatment. It can further provide insights into designing of new clinical protocols. In the outcome modeling, two indices including tumor control probability (TCP) and normal tissue complication probability (NTCP) are usually investigated. Current outcome models, e.g., analytical models and data-driven models, either fail to take into account complex interactions between physical and biological variables or require complicated feature selection procedures. Therefore, in our studies, deep learning (DL) techniques are incorporated into outcome modeling for prediction of local control (LC), which is TCP in our case, and radiation pneumonitis (RP), which is NTCP in our case, in non-small-cell lung cancer (NSCLC) patients after radiotherapy. These techniques can improve the prediction performance of outcomes and simplify model development procedures. Additionally, longitudinal data association, actuarial prediction, and multi-endpoints prediction are considered in our models. These were carried out in 3 consecutive studies. In the first study, a composite architecture consisting of variational auto-encoder (VAE) and multi-layer perceptron (MLP) was investigated and applied to RP prediction. The architecture enabled the simultaneous dimensionality reduction and prediction. The novel VAE-MLP joint architecture with area under receiver operative characteristics (ROC) curve (AUC) [95% CIs] 0.781 [0.737-0.808] outperformed a strategy which involves separate VAEs and classifiers (AUC 0.624 [ 0.577-0.658]). In the second study, composite architectures consisted of 1D convolutional layer/ locally-connected layer and MLP that took into account longitudinal associations were applied to predict LC. Composite architectures convolutional neural network (CNN)-MLP that can model both longitudinal and non-longitudinal data yielded an AUC 0.832 [ 0.807-0.841]. While plain MLP only yielded an AUC 0.785 [CI: 0.752-0.792] in LC control prediction. In the third study, rather than binary classification, time-to-event information was also incorporated for actuarial prediction. DL architectures ADNN-DVH which consider dosimetric information, ADNN-com which further combined biological and imaging data, and ADNN-com-joint which realized multi-endpoints prediction were investigated. Analytical models were also conducted for comparison purposes. Among all the models, ADNN-com-joint performed the best, yielding c-indexes of 0.705 [0.676-0.734] for RP2, 0.740 [0.714-0.765] for LC and an AU-FROC 0.720 [0.671-0.801] for joint prediction. The performance of proposed models was also tested on a cohort of newly-treated patients and multi-institutional RTOG0617 datasets. These studies taken together indicate that DL techniques can be utilized to improve the performance of outcome models and potentially provide guidance to physicians during decision making. Specifically, a VAE-MLP joint architectures can realize simultaneous dimensionality reduction and prediction, boosting the performance of conventional outcome models. A 1D CNN-MLP joint architecture can utilize temporal-associated variables generated during the span of radiotherapy. A DL model ADNN-com-joint can realize multi-endpoint prediction, which allows considering competing risk factors. All of those contribute to a step toward enabling outcome models as real clinical decision support tools.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162923/1/sunan_1.pd

Genetic Programming for Classification with Unbalanced Data

In classification,machine learning algorithms can suffer a performance bias when data sets are unbalanced. Binary data sets are unbalanced when one class is represented by only a small number of training examples (called the minority class), while the other class makes up the rest (majority class). In this scenario, the induced classifiers typically have high accuracy on the majority class but poor accuracy on the minority class. As the minority class typically represents the main class-of-interest in many real-world problems, accurately classifying examples from this class can be at least as important as, and in some cases more important than, accurately classifying examples from the majority class. Genetic Programming (GP) is a promising machine learning technique based on the principles of Darwinian evolution to automatically evolve computer programs to solve problems. While GP has shown much success in evolving reliable and accurate classifiers for typical classification tasks with balanced data, GP, like many other learning algorithms, can evolve biased classifiers when data is unbalanced. This is because traditional training criteria such as the overall success rate in the fitness function in GP, can be influenced by the larger number of examples from the majority class. This thesis proposes a GP approach to classification with unbalanced data. The goal is to develop new internal cost-adjustment techniques in GP to improve classification performances on both the minority class and the majority class. By focusing on internal cost-adjustment within GP rather than the traditional databalancing techniques, the unbalanced data can be used directly or "as is" in the learning process. This removes any dependence on a sampling algorithm to first artificially re-balance the input data prior to the learning process. This thesis shows that by developing a number of new methods in GP, genetic program classifiers with good classification ability on the minority and the majority classes can be evolved. This thesis evaluates these methods on a range of binary benchmark classification tasks with unbalanced data. This thesis demonstrates that unlike tasks with multiple balanced classes where some dynamic (non-static) classification strategies perform significantly better than the simple static classification strategy, either a static or dynamic strategy shows no significant difference in the performance of evolved GP classifiers on these binary tasks. For this reason, the rest of the thesis uses this static classification strategy. This thesis proposes several new fitness functions in GP to perform cost adjustment between the minority and the majority classes, allowing the unbalanced data sets to be used directly in the learning process without sampling. Using the Area under the Receiver Operating Characteristics (ROC) curve (also known as the AUC) to measure how well a classifier performs on the minority and majority classes, these new fitness functions find genetic program classifiers with high AUC on the tasks on both classes, and with fast GP training times. These GP methods outperform two popular learning algorithms, namely, Naive Bayes and Support Vector Machines on the tasks, particularly when the level of class imbalance is large, where both algorithms show biased classification performances. This thesis also proposes a multi-objective GP (MOGP) approach which treats the accuracies of the minority and majority classes separately in the learning process. The MOGP approach evolves a good set of trade-off solutions (a Pareto front) in a single run that perform as well as, and in some cases better than, multiple runs of canonical single-objective GP (SGP). In SGP, individual genetic program solutions capture the performance trade-off between the two objectives (minority and majority class accuracy) using an ROC curve; whereas in MOGP, this requirement is delegated to multiple genetic program solutions along the Pareto front. This thesis also shows how multiple Pareto front classifiers can be combined into an ensemble where individual members vote on the class label. Two ensemble diversity measures are developed in the fitness functions which treat the diversity on both the minority and the majority classes as equally important; otherwise, these measures risk being biased toward the majority class. The evolved ensembles outperform their individual members on the tasks due to good cooperation between members. This thesis further improves the ensemble performances by developing a GP approach to ensemble selection, to quickly find small groups of individuals that cooperate very well together in the ensemble. The pruned ensembles use much fewer individuals to achieve performances that are as good as larger (unpruned) ensembles, particularly on tasks with high levels of class imbalance, thereby reducing the total time to evaluate the ensemble

Modular Machine Learning Methods for Computer-Aided Diagnosis of Breast Cancer

The purpose of this study was to improve breast cancer diagnosis by reducing the number of benign biopsies performed. To this end, we investigated modular and ensemble systems of machine learning methods for computer-aided diagnosis (CAD) of breast cancer. A modular system partitions the input space into smaller domains, each of which is handled by a local model. An ensemble system uses multiple models for the same cases and combines the models\u27 predictions. Five supervised machine learning techniques (LDA, SVM, BP-ANN, CBR, CART) were trained to predict the biopsy outcome from mammographic findings (BIRADS™) and patient age based on a database of 2258 cases mixed from multiple institutions. The generalization of the models was tested on second set of 2177 cases. Clusters were identified in the database using a priori knowledge and unsupervised learning methods (agglomerative hierarchical clustering followed by K-Means, SOM, AutoClass). The performance of the global models over the clusters was examined and local models were trained for clusters. While some local models were superior to some global models, we were unable to build a modular CAD system that was better than the global BP-ANN model. The ensemble systems based on simplistic combination schemes did not result in significant improvements and more complicated combination schemes were found to be unduly optimistic. One of the most striking results of this dissertation was that CAD systems trained on a mixture of lesion types performed much better on masses than on calcifications. Our study of the institutional effects suggests that models built on cases mixed between institutions may overcome some of the weaknesses of models built on cases from a single institution. It was suggestive that each of the unsupervised methods identified a cluster of younger women with well-circumscribed or obscured, oval-shaped masses that accounted for the majority of the BP-ANN’s recommendations for follow up. From the cluster analysis and the CART models, we determined a simple diagnostic rule that performed comparably to the global BP-ANN. Approximately 98% sensitivity could be maintained while providing approximately 26% specificity. This should be compared to the clinical status quo of 100% sensitivity and 0% specificity on this database of indeterminate cases already referred to biopsy

Machine learning for network based intrusion detection: an investigation into discrepancies in findings with the KDD cup '99 data set and multi-objective evolution of neural network classifier ensembles from imbalanced data.

For the last decade it has become commonplace to evaluate machine learning techniques for network based intrusion detection on the KDD Cup '99 data set. This data set has served well to demonstrate that machine learning can be useful in intrusion detection. However, it has undergone some criticism in the literature, and it is out of date. Therefore, some researchers question the validity of the findings reported based on this data set. Furthermore, as identified in this thesis, there are also discrepancies in the findings reported in the literature. In some cases the results are contradictory. Consequently, it is difficult to analyse the current body of research to determine the value in the findings. This thesis reports on an empirical investigation to determine the underlying causes of the discrepancies. Several methodological factors, such as choice of data subset, validation method and data preprocessing, are identified and are found to affect the results significantly. These findings have also enabled a better interpretation of the current body of research. Furthermore, the criticisms in the literature are addressed and future use of the data set is discussed, which is important since researchers continue to use it due to a lack of better publicly available alternatives. Due to the nature of the intrusion detection domain, there is an extreme imbalance among the classes in the KDD Cup '99 data set, which poses a significant challenge to machine learning. In other domains, researchers have demonstrated that well known techniques such as Artificial Neural Networks (ANNs) and Decision Trees (DTs) often fail to learn the minor class(es) due to class imbalance. However, this has not been recognized as an issue in intrusion detection previously. This thesis reports on an empirical investigation that demonstrates that it is the class imbalance that causes the poor detection of some classes of intrusion reported in the literature. An alternative approach to training ANNs is proposed in this thesis, using Genetic Algorithms (GAs) to evolve the weights of the ANNs, referred to as an Evolutionary Neural Network (ENN). When employing evaluation functions that calculate the fitness proportionally to the instances of each class, thereby avoiding a bias towards the major class(es) in the data set, significantly improved true positive rates are obtained whilst maintaining a low false positive rate. These findings demonstrate that the issues of learning from imbalanced data are not due to limitations of the ANNs; rather the training algorithm. Moreover, the ENN is capable of detecting a class of intrusion that has been reported in the literature to be undetectable by ANNs. One limitation of the ENN is a lack of control of the classification trade-off the ANNs obtain. This is identified as a general issue with current approaches to creating classifiers. Striving to create a single best classifier that obtains the highest accuracy may give an unfruitful classification trade-off, which is demonstrated clearly in this thesis. Therefore, an extension of the ENN is proposed, using a Multi-Objective GA (MOGA), which treats the classification rate on each class as a separate objective. This approach produces a Pareto front of non-dominated solutions that exhibit different classification trade-offs, from which the user can select one with the desired properties. The multi-objective approach is also utilised to evolve classifier ensembles, which yields an improved Pareto front of solutions. Furthermore, the selection of classifier members for the ensembles is investigated, demonstrating how this affects the performance of the resultant ensembles. This is a key to explaining why some classifier combinations fail to give fruitful solutions