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We propose a Similarity-Based Stratified Splitting (SBSS) technique, which uses both the output and input space information to split the data. The splits are generated using similarity functions among samples to place similar samples in different splits. This approach allows for a better representation of the data in the training phase. This strategy leads to a more realistic performance estimation when used in real-world applications. We evaluate our proposal in twenty-two benchmark datasets with classifiers such as Multi-Layer Perceptron, Support Vector Machine, Random Forest and K-Nearest Neighbors, and five similarity functions Cityblock, Chebyshev, Cosine, Correlation, and Euclidean. According to the Wilcoxon Sign-Rank test, our approach consistently outperformed ordinary stratified 10-fold cross-validation in 75% of the assessed scenarios.

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In this paper we propose a procedure to enable the training of several independent Multilayer Perceptron Neural Networks with a different number of neurons and activation functions in parallel (ParallelMLPs) by exploring the principle of locality and parallelization capabilities of modern CPUs and GPUs. The core idea of this technique is to represent several sub-networks as a single large network and use a Modified Matrix Multiplication that replaces an ordinal matrix multiplication with two simple matrix operations that allow separate and independent paths for gradient flowing. We have assessed our algorithm in simulated datasets varying the number of samples, features and batches using 10,000 different models as well as in the MNIST dataset. We achieved a training speedup from 1 to 4 orders of magnitude if compared to the sequential approach. The code is available online.

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