Non-linear Feature Selection Based on Convolution Neural Networks with Sparse Regularization

Abstract

The efficacy of feature selection methods in dimensionality reduction and enhancing the performance of learning algorithms has been well documented. Traditional feature selection algorithms often grapple with delineating non-linear relationships between features and responses. While deep neural networks excel in capturing such non-linearities, their inherent “black-box” nature detracts from their interpretability. Furthermore, the complexity of deep network architectures can give rise to prolonged training durations and the challenge of vanishing gradients. This study aims to refine network structures, hasten network training, and bolster model interpretability without forfeiting accuracy. This paper delves into a sparse-weighted feature selection approach grounded in convolutional neural networks, termed the low-dimensional sparse-weighted feature selection network (LSWFSNet). LSWFSNet integrates a convolutional selection kernel between the input and convolutional layers, facilitating weighted convolutional calculations on input data while imposing sparse constraints on the selection kernel. Features with significant weights in this kernel are earmarked for subsequent operations in the LSWFSNet computational domain, while those with negligible weights are eschewed to diminish model intricacy. By streamlining the network’s input data, LSWFSNet refines the post-convolution feature maps, thus simplifying its structure. Acknowledging the intrinsic interconnections within the data, our study amalgamates diverse sparse constraints into a cohesive objective function. This ensures the convolutional kernel’s sparsity while acknowledging the structural dynamics of the data. Notably, the foundational convolutional network in this method can be substituted with any deep convolutional network, contingent upon suitable adjustments to the convolutional selection kernel in relation to input data dimensions. The LSWFSNet model was tested on human emotion electroencephalography (EEG) datasets curated by Shanghai Jiao Tong University. When various sparse constraint methodologies were employed, the convolutional kernel manifested sparsity. Regions in the convolutional selection kernel with non-zero weights were identified as having strong correlations with emotional responses. The empirical outcomes not only resonate with extant neuroscience insights but also supersede the baseline network in accuracy metrics. LSWFSNet’s applicability extends to pivotal tasks like keypoint recognition, be it the extraction of salient pixels in facial detection models or the isolation of target attributes in object detection frameworks. This study’s significance is anchored in the amalgamation of sparse constraint techniques with deep convolutional networks, supplanting traditional fully connected networks. This fusion amplifies model interpretability and broadens its applicability, notably in image processing arenas.

Appendix

In this paper, seven various types of convolutional networks are used for backbone, namely VGG-16, Alexnet, Googlenet, Resnet-34, Densenet-101, Efficientnet-B0, and Mobilenet-V2.

Backbone with and without sparse constraints are trained with the same feature vectors from the training set that is used to construct the feature subset. For fair comparison under various sparsity constraints, the parameter setting of the model, including learning rate, is kept exactly the same. The algorithm and methodology are described in “Proposed New Architecture Description” section.

Tables 3 and 4 show the comparison of the accuracy of different networks under different sparsity constraints, where the numbers in parentheses in the table represent the proportion of features screened out by the model under that sparsity constraint.

Table 3 Classification accuracy of single-channel EEG signals under different sparsity constraints

From the accuracy of the two tables, it is easy to find that the accuracy achieved by shallow networks, such as VGG16, is significantly higher than deep networks, such as Densenet101. The results show that there is no strong correlation between the model’s depth and the accuracy. In addition, the feedback of the brain is not completely consistent due to other relevant factors such as the physical state of the human subjects. Therefore, the data sampled from the same human subjects at different times are not exactly the same, which leads to the model accuracy not being exactly the same, for example, “JL20140404” and “JL20140419” in Table 3.

From the sparsity in the two tables, the model can reduce the amount of input data up to $30\%$. However, this does not reach the desirable degree of sparsity. This may be due to the fact that emotional feedback is a very complex process, not just an activity which involving a certain part of brain regions. But the method does achieve results in the aspect of input reduction.

Table 4 Classification accuracy of multi-channel EEG signals under different sparsity constraints