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Possible Tools
Python Tools
SciKit Learn SVM
http://scikit-learn.org/stable/modules/svm.html#svm
It's complexity is between O(n^2) and O(n^3). Seems easy to use. This is not a neural net; it is a support vector machine.
SciKit Learn Neural Net
http://scikit-learn.org/stable/modules/neural_networks_supervised.html
This IS a neural net using back propagation.
It's complexity is listed as: Suppose there are n training samples, m features, k hidden layers, each containing h neurons - for simplicity, and o output neurons. The time complexity of backpropagation is O(n * m * h^k * o * i), where i is the number of iterations. Since backpropagation has a high time complexity, it is advisable to start with smaller number of hidden neurons and few hidden layers for training.
SK Neural Network Package
This is a separate package than listed above. It requires a separate installation. Documentation is provided at:
https://scikit-neuralnetwork.readthedocs.io/en/latest/index.html
We ran into deprecation warnings, and the program would not execute due to a missing g++ drive.