Traditionally, clinical methods are employed to detect cancers such as ultrasonography, X-Ray, Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) [1]. However, many cancers cannot be distinguished easily using traditional approaches. An alternative approach to improve detection is to use analyze microarray gene profiles. In microarray gene profiles, mRNA samples are used to measure the expression level of genes, which can be in the magnitude of thousands. This in turn makes detection and classification of difficult due to the high dimensionality in data [2], therefore, there is a need for computation methods to help improve the classification of cancers using microarray gene profiles.

Generally, computational methods are used to remove non-contributing and noisy dimensions from data while simultaneously trying to maintain a high classification rate [3]. Additionally, class imbalance is an important consideration in classification of biomedical data, and there are techniques [4] which incorporate class distribution within the classification algorithm. Our approach is different in that we separate the classification from data preprocessing where we assume class imbalance is to be handled.

Feature selection and extraction is a well researched topic in biomedical fields, especially in the areas concerning microarray data [5–7]. Several methods have been discussed relating to feature selection for microarray data [6, 8–17] and they can be broadly categorized into two groups, filter based methods and wrapper based methods. In filter based methods, genes are selected prior to training the classification model whereas wrapper based methods involve gene selection within the classification process [5, 18, 19].

The importance of selecting features from gene subsets or groups has recently become popular topic in microarray research [7, 20]. For instance, top-r feature selection proposed by Sharma et. al [20] does provide very good results based on a small subset of genes, however, it should be noted that it has a few drawbacks. Firstly, it is quite computationally expensive, requiring a total number of search combinations between ^h+1 C ₂×(d/h) and (2 ^h −1)×(d/h), where h is the block size and d is the total number of dimensions [20]. Additionally, initial parameter selection is crucial and it greatly affects the final results. Top-r is sensitive to the selection of block size and number of resulting blocks. Selecting ideal value of h could be a tricky task and final results are dependent on this value [20]. Lastly, it should be noted that top-r does not fully consider the interaction among features but only amongst the top-r features from each block [5].

In this paper, we consider the classification of the small round blue cell tumor (SRBCT) [21] dataset which has been categorized into 4 types of cancers and has 2308 gene expressions. Khan et al. [1], Tibshirani et al. [21] and Kumar et al. [22] have previously worked on this dataset whereby they have all reported 100% classification accuracies with 96, 43 and 13 genes respectively. While Khan et al. [1] and Tibshirani et al. [21] use the fully-fledged dataset with 2308 genes to perform analysis, Kumar et al. [22] begin their analysis from a reduced set of 96 genes (from Khan et al. [1] findings) to obtain results. Kumar et al. [22] do not use all 2308 genes due to the computational complexity of their approach. Our motivation in this paper is to build upon the approach proposed by Kumar et al. [22] and propose a new method that does not suffer from similar limitations. In the proposed method, we propose a wrapper based method where we commence with the entire feature set from the microarray data without any prior need of feature selection and achieve high classification accuracy with as few features as possible.

Furthermore we validate our approach using the mixed-lineage leukemia (MLL) [23] and lung cancer (LC) [24] datasets. MLL dataset comprises of 3 classes, with each sample containing 12,582 gene expressions. Lastly, LC dataset contains 2 cancer types and each sample comprises of 12,533 gene expressions. We applied gene masking with nearest shrunken centroid classifier to significantly reduce the number of dimensions for the datasets while maintaining 100% accuracies during classification.

Gene masking has been derived from genetic algorithm, whereby genetic algorithm is used to search for an optimal gene mask that provides the greatest performance gains while removing the most number of features for the selected classification algorithm. For this study, Nearest Centroid and Nearest Shrunken Centroid classifiers were used for classification.

Gene masking is a technique that incorporates evolutionary techniques to reduce the dimensionality of data within the training phase of the classification model. The basic premise of this technique is to heuristically remove non-contributing features in data while training the classifier. The amount of contribution by a feature is determined by its impact on classification accuracy, whereby non-contribution is attributed to features whose removal and/or existence has minimal effect on classification accuracy. By reducing the dimensionality of data, gene masking helps improve classifier performance and reduces the computational complexity of the problem. Moreover, it can be used as a feature isolation technique that allows for the identification of features which contribute the most towards classification.

Overview

Gene masking, essentially, is a binary encoded genetic algorithm that generates a template used to represent a chromosome, referred to as a mask, while the individual bits at different indices in the chromosome are annotated as genes. This mask can be visualized as a string of binary digits with length equal to the number of features in data. Each binary digit at a particular index (or a gene in terms of the mask) signifies the presence or absence of the corresponding feature in data. For instance, a problem with five features can represented by a feature vector [f1 f2 f3 f4 f5] and a possible gene mask can be [1 0 0 1 1]. This mask indicates that features f2 and f3 are to be removed from the data and the classification model has to be created using a feature vector comprising of [f1 f4 f5], thus, effectively reducing the dimensionality of data. This process has been depicted in Fig. 1.

In gene masking, the GA processes are unmodified and it goes through its basic set of genetic operations. For each generation, fitness is calculated for every mask in the population. These masks are then exposed to the three GA operators; selection, crossover and mutation. Finally, the best performing mask is chosen after the generation limit is reached in GA.

In essence, the basic purpose of GA in gene masking can be viewed as heuristically searching for the optimal gene mask that reduces the most features for a particular problem while maintaining high classification accuracy. The holistic approach taken when applying gene masking is shown in Fig. 2.

Process details

In order to determine the fitness of each mask, a classifier model is created using the masked dataset and its classification accuracy is evaluated using k-fold cross validation. The masked dataset is divided into k number of folds and a model is iteratively built using k-1 folds and while the k ^th fold is isolated for model evaluation, yielding a set containing k classification accuracy values (one for each fold). Then, the fitness of a mask is computed based on its impact on classification accuracy while also considering the effective reduction in dimensionality. The details of fitness evaluation for gene masking is highlighted in Fig. 3, which describes intricacies between the classification algorithm and the masking process.

Upon fitness evaluation, GA goes through its orthodox set of operators, namely selection, crossover and mutation. Selection has been performed using roulette wheel selection, which is biased towards individuals with higher fitness. Crossover is accomplished by performing a random one-point binary crossover to swap the genes and mutation is performed by negating gene values at random locations. However, to preserve the highest performing chromosome between generations, elite selection is used to ensure that a mask with the highest fitness is passed to the next generation unmodified by GA operators.

The actual fitness value provided to GA is measured in terms of a weighted sum of the average classification accuracy from k-fold cross validation and the ratio of features removed from data, which is highlighted in Eq. 6. This sum is weighted using a constant α, called the Accuracy to Elimination Ratio, which is empirically chosen to direct the evolution of GA either towards attaining better classification accuracy or reducing the most number of features. The value of α is optimized within the interval (0, 1], where higher values of α give higher fitness values to masks with better accuracy while lower values of α give higher fitness values to masks with greater number of genes eliminated.

$$ Fitness = (Accuracy \times \alpha) + (1 - \alpha) \times \frac{Genes \; eliminated}{Total \; genes} $$

(6)

This process of performing fitness evaluations and applying genetic operators continues until the number of generations specified during the initial parameter configuration is reached. The best chromosome discovered during the evolution of the population is selected. This chromosome represents the gene mask that yielded the highest fitness value during training. The best evolved gene mask is subsequently used for masking the test dataset during the testing phase.

Primarily, we had considered the SRBCT dataset for gene masking. The following sections provide details on the data, and the experiment and its results.