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GmdhPy is the Python library with implementation of iterational group method of data handling algorithm with polynomial reference functions. The resulting models are also known self-organizing deep learning polynomial neural network. It is one of the earliest deep learning methods.

GmdhPy uses the following dependencies:

• numpy
• six
• scikit-learn
• matplotlib (optional, required if you use plotting tools)
• graphviz (optional but recommended if you want to plot model graph, requires installation of binaries from http://www.graphviz.org/ as well)

To install GmdhPy:

sudo pip install git+git://github.com/kvoyager/GmdhPy.git

To uninstall GmdhPy:

sudo pip uninstall gmdhpy

from gmdh import Regressor
model = Regressor()
model.fit(data_x, data_y)
predict_y = model.predict(test_x)

where

• data_x - train data, numpy array shape [num_samples, num_features]
• data_y - target values, numpy array of shape [num_samples]
• test_x - test data, numpy array of shape [num_test_samples, num_feature]

data_x will be splitted to train and validate inside fitting

or

from gmdh import Regressor
model = Regressor()
model.fit(train_x, train_y, validation_data=(validate_x, validate_y))
predict_y = model.predict(test_x)

where

• train_x - train data, numpy array shape [num_train_samples, num_features]
• train_y - train target values, numpy array of shape [num_train_samples]
• validate_x - validate data, numpy array shape [num_validate_samples, num_features]
• validate_y - validate target values, numpy array of shape [num_vaidate_samples]
• test_x - test data, numpy array of shape [num_test_samples, num_feature]

from gmdh import Classifier
model = Classifier()
model.fit(data_x, data_y)

or

model.fit(train_x, train_y, validation_data=(validate_x, validate_y))

predict

predicted_scores = model.predict_proba(test_x)
predicted_lables = model.predict(test_x)

where

• predicted_scores - predicted probabilities of classes (scores)
• predicted_lables - predcited class labels

Note: only binary classification is supported

• admix_features - if set to true the original features will be added to the list of features of each layer default value is true

• criterion_type - criterion for selecting best neurons the following criteria are possible: * validate: the default value, neurons are compared on the basis of validate error * bias: neurons are compared on the basis of bias error * validate_bias: combined criterion, neurons are compared on the basis of bias and validate errors * bias_retrain: firstly, neurons are compared on the basis of bias error, then neurons are retrain on the total data set (train and validate) example of using:

      model = Regressor(criterion_type='bias_retrain')

• seq_type - method to split data set to train and validate

  • mode1 - the default value data set is split to train and validate data sets in the following way: ... train validate train validate train validate ... train validate. The last point is chosen to belong to validate set
  • mode2 - data set is split to train and validate data sets in the following way: ... train validate train validate train validate ... validate train. The last point is chosen to belong to train set
  • mode3_1 - data set is split to train and validate data sets in the following way: ... train validate train train validate train train validate ... train train validate. The last point is chosen to belong to validate set
  • mode4_1 - data set is split to train and validate data sets in the following way: ... train validate train train train validate ... validate train train train validate. The last point is chosen to belong to validate set
  • mode3_2 - data set is split to train and validate data sets in the following way: ... train validate validate train validate validate train validate ... validate validate train. The last point is chosen to belong to train set
  • mode4_2 - data set is split to train and validate data sets in the following way: ... train validate validate validate train validate ... train validate validate validate train. The last point is chosen to belong to train set
  • random - Random split data to train and validate

  example of using:

      model = Regressor(seq_type='random')

• max_layer_count - maximum number of layers, the default value is infinite (sys.maxsize)

• criterion_minimum_width - minimum number of layers at the right required to evaluate optimal number of layer (the optimal neuron) according to the minimum of criteria. For example, if it is found that criterion value has minimum at layer with index 10, the algorithm will proceed till the layer with index 15 the default value is 5

• stop_train_epsilon_condition - the threshold to stop train. If the layer relative training error in compare with minimum layer error becomes smaller than stop_train_epsilon_condition the train is stopped. Default value is 0.001

• manual_best_neurons_selection - if this value set to False, the number of best neurons to be selected is determined automatically and it is equal to the number of original features. Otherwise the number of best neurons to be selected is determined as max(original features, min_best_neurons_count) but not more than max_best_neurons_count. min_best_neurons_count (default 5) or max_best_neurons_count (default inf) has to be provided. For example, if you have N=10 features, the number of all generated neurons will be N*(N-1)/2=45, the number of selected best neurons will be 10, but you can increase this number to 20 by setting manual_min_l_count_value = True and min_best_neurons_count = 20. If you have N=100 features, the number of all generated neurons will be N*(N-1)/2=4950, by default the number of partial neurons passed to the second layer is equal to the number of features = 100. If you want to reduce this number for some smaller number, 50 for example, set manual_best_neurons_selection=True and max_best_neurons_count=50. Note: if min_best_neurons_count is larger than number of generated neurons of the layer it will be reduced to that number example of using:

      model = Regressor(manual_best_neurons_selection=True, min_best_neurons_count=20)

  or

      model = Regressor(manual_best_neurons_selection=True, max_best_neurons_count=50)

• ref_function_types - set of reference functions, by default the set contains linear combination of two inputs and covariation: y = w0 + w1x1 + w2x2 + w3x1x2 you can add other reference functions:

  • linear: y = w0 + w1x1 + w2x2
  • linear_cov: y = w0 + w1x1 + w2x2 + w3x1x2
  • quadratic: full polynom of the 2-nd degree
  • cubic: - full polynom of the 3-rd degree examples of using:

  Regressor(ref_functions='linear')
  Regressor(ref_functions=('linear_cov', 'quadratic', 'cubic', 'linear'))
  Regressor(ref_functions=('quadratic', 'linear'))

• normalize - scale and normalize features if set to True. Default value is True

• layer_err_criterion - criterion of layer error calculation: 'top' - the topmost best neuron error is chosen as layer error; 'avg' - the layer error is the average error of the selected best neurons default value is 'top'

• l2 - regularization value used in neuron fit by Ridge regression (see sklearn linear_neuron.Ridge) default value is 0.5

• n_jobs - number of parallel processes(threads) to train model, default 1. Use 'max' to train using all available threads.

params = {
    'ref_functions': 'linear_cov',
    'criterion_type': 'test_bias',
    'feature_names': feature_names,
    'criterion_minimum_width': 5,
    'admix_features': True,
    'max_layer_count': 50,
    'normalize': True,
    'stop_train_epsilon_condition': 0.0001,
    'layer_err_criterion': 'top',
    'alpha': 0.5,
    'n_jobs': 4
}
model = Regressor(**params)

MIT

• Mueller J.A. Lemke F., Self-organising Data Mining, Berlin (2000)
• J. Schmidhuber. Deep Learning in Neural Networks: An Overview. Neural Networks, Volume 61, January 2015, Pages 85-117
• https://en.wikipedia.org/wiki/Group_method_of_data_handling
• http://www.gmdh.net/