# MLW-gcForest: A Multi-Weighted gcForest Model for Cancer Subtype Classification by Methylation Data
###### Abstract
This model is a new strategy that combines machine learning algorithms and deep learning ideas. The model takes advantage of the multi-layer learning of deep learning and avoids overfitting due to small sample size. The gcForest model consists of two modules: multi-grained scanning and cascade forest modules, as shown in Figure 1. Multi-grained scanning is an approximation of the convolution process of convolutional neural networks. Similar to a convolutional neural network, convolution kernels of different sizes are used to acquire the spatial structure of the pixels in the image and the receptive fields of different scales [29; 30]. When inputting high-dimension sample data, multi-grained scanning can capture different levels of information by cutting the high-dimension sample data into different-scale sequences of features through sliding windows at different scales, enabling gcForest to be contextually or structurally aware. The second model is the cascade forest, which contains multiple-layer random forests. Each layer in the cascade forest receives information processed by the previous layer and transmits information to the next layer. This model can learn more distinct features and provide more accurate predictions. K-fold cross-validation is used to reduce the risk of overfitting when extending a new layer. In detail, the training data is divided into k folds; k-1 folds are selected as the training data in turn, and the remaining fold is used as the validation data. After extending the new layer, the performance of the entire cascade is estimated on the validation data, and if there is no significant gain in performance, the expanding process will be terminated [28]. Therefore, the number of gcForest model cascades is automatically determined. Compared with most deep neural networks, gcForest adaptively determines the model complexity by terminating the training when appropriate so that this model can be applied to data of different sizes, not just large-scale data. The gcForest algorithm performs better than other machine learning algorithms for many applications [31]. However, the gcForest algorithm still has the following limitations regarding small-scale cancer gene data. (1) In the multi-grained scanning module of the standard gcForest algorithm, each random forest contributes equally to the final result, but actually, the classification abilities of different forests differ. Similar to how the multi-scale feature maps generated by convolution kernels of different scales have different effects on the final performance [29; 30], multi-grained scanning produces feature vectors of different scales. When using these differently scaled feature vectors to train random forests and completely random forests, the classification ability of each random forest trained is different. This effect is not considered in the standard gcForest, resulting in the features that are truly useful for classification not receiving the attention that these features deserve; such features are very valuable for classification. We should increase the weight of these features and try to increase their positive impact on the classification results. The weights of features that are less useful for classification should be reduced to avoid negative impacts on classification. (2) Furthermore, different sliding windows make different contributions to the final predictions, but the standard gcForest algorithm does not consider these differences. The class vectors derived from different scanning windows have different effects on the final classification results. Different sliding windows need to be given different weights to capture more complex and diverse features, further enhancing the characterization learning ability and improving the classification performance of the model on small samples. In this paper, we propose an improved gcForest model, called the MLW-gcForest model, to solve the subtype classification problem of in cancer subtype classification. MLW-gcForest mainly includes two innovations.