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, ...

Background Machine learning (ML) is the application of specialized algorithms to datasets for trend delineation, categorization, or prediction. ML techniques have been traditionally applied to large, highly dimensional databases. Gliomas are a heterogeneous group of primary brain tumors, traditionally graded using histopathologic features. Recently, the World Health Organization proposed a novel grading system for gliomas incorporating molecular characteristics. We aimed to study whether ML could achieve accurate prognostication of 2-year mortality in a small, highly dimensional database of patients with glioma. Methods We applied 3 ML techniques (artificial neural networks [ANNs], decision trees [DTs], and support vector machines [SVMs]) and classical logistic regression (LR) to a dataset consisting of 76 patients with glioma of all grades. We compared the effect of applying the algorithms to the raw database versus a database where only statistically significant features were included into the algorithmic inputs (feature selection). Results Raw input consisted of 21 variables and achieved performance of accuracy/area (C.I.) under the curve of 70.7%/0.70 (49.9–88.5) for ANN, 68%/0.72 (53.4–90.4) for SVM, 66.7%/0.64 (43.6–85.0) for LR, and 65%/0.70 (51.6–89.5) for DT. Feature selected input consisted of 14 variables and achieved performance of 73.4%/0.75 (62.9–87.9) for ANN, 73.3%/0.74 (62.1–87.4) for SVM, 69.3%/0.73 (60.0–85.8) for LR, and 65.2%/0.63 (49.1–76.9) for DT. Conclusions We demonstrate that these techniques can also be applied to small, highly dimensional datasets. Our ML techniques achieved reasonable performance compared with similar studies in the literature. Although local databases may be small versus larger cancer repositories, we demonstrate that ML techniques can still be applied to their analysis; however, traditional statistical methods are of similar benefit.

Deep neural networks have gained immense popularity in the Big Data problem; however, the availability of training samples can be relatively limited in certain 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 setting, 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 VC-dimension 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 data-driven, not sample size driven. After network structure optimization, the conventional convolutional neural network could achieve 91.13% in accuracy with only 500 samples, 93.66% in accuracy with only 1000 samples for the MNIST dataset and 94.10% in 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. Key words: artificial neural network, convolutional neural network, hyperparameter optimization, VC dimension.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 up-on the assumption of a 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. S...