Structural Analysis and Optimization of Convolutional Neural Networks with a Small Sample Size

Abstract

Deep neural networks have gained immense popularity in the Big Data problem; however, the availability of training samples can be relatively limited in specific application domains, particularly medical imaging, and consequently leading to overfitting problems. This "Small Data" challenge may need a mindset that is entirely different from the existing Big Data paradigm. Here, under the small data scenarios, we examined whether the network structure has a substantial influence on the performance and whether the optimal structure is predominantly determined by sample size or data nature. to this end, we listed all possible combinations of layers given an upper bound of the Vcdimension to study how structural hyperparameters affected the performance. Our results showed that structural optimization improved accuracy by 27.99%, 16.44%, and 13.11% over random selection for a sample size of 100, 500, and 1,000 in the MNIST dataset, respectively, suggesting that the importance of the network structure increases as the sample size becomes smaller. furthermore, the optimal network structure was mostly determined by the data nature (photographic, calligraphic, or medical images), and less affected by the sample size, suggesting that the optimal network structure is datadriven, not sample size driven. After network structure optimization, the convolutional neural network could achieve 91.13% accuracy with only 500 samples, 93.66% accuracy with only 1000 samples for the MNIST dataset and 94.10% accuracy with only 3300 samples for the Mitosis (microscopic) dataset. these results indicate the primary importance of the network structure and the nature of the data in facing the Small Data challenge. Deep neural networks have regained immense popularity in recent years. With the availability of much more powerful computational resources, such as CPU clusters and GPUs (Graphics Processing Units), studies are now capable of constructing network structures with even more and wider layers than before. The growth of deep neural networks from the 8 layer AlexNet 1 , to the 19-layer VGG 2 , to the 22-layer GoogleNet 3 , followed by the 152-layer ResNet 4 , shows a clear generalization of the idea that deeper networks perform better, and it has been pretty conclusive that the evolution trend of artificial neural networks is in the direction of even deeper or more complicated structures. However, this trend is ubiquitously built upon the assumption of sufficiently high sample size (i.e. Big Data), and the issue of overfitting or under-training can be reasonably ignored. While in numerous real-world applications, the number of samples in a dataset can be relatively limited, and the issues would arise with a generalized method of plain layer stacking in an attempt to improve performance. This "Small Data" challenge would call for a completely different mindset and approach from the existing "Big Data" one. Specifically, In the case of a "Small Data" challenge (e.g. sample < 5,000), the lines are still blurred as to whether the deeper we go, ...

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