2.2.3.2. Persistence Images
In this section, we provide examples for classification using persistence images. As mentioned in Persistence Images section, we use Persim library to compute persistence images. This library can automatically capture the bounds of the image. Our algorithm implements that option, so user do not need to give boundaries for life time and birth time of the images.
>>> from teaspoon.ML.PD_Classification import getPercentScore
>>> from teaspoon.ML import feature_functions as fF
>>> from teaspoon.ML.Base import ParameterBucket
>>> from teaspoon.MakeData.PointCloud import testSetManifolds
>>> from sklearn.preprocessing import LabelEncoder
>>> from sklearn.svm import SVC
>>> # generate persistence diagrams
>>> DgmsDF = testSetManifolds(numDgms=20, numPts=100)
>>> labels_col='trainingLabel'
>>> dgm_col='Dgm1'
>>> # convert categorical labels into integers
>>> label_encoder = LabelEncoder()
>>> x = DgmsDF[labels_col]
>>> y = label_encoder.fit_transform(x)
>>> DgmsDF[labels_col] = y
>>> # set classification parameters
>>> params = ParameterBucket()
>>> params.feature_function = fF.F_Image
>>> params.k_fold_cv=5
>>> params.clf_model = SVC
>>> # perform classification
>>> c_report_train,c_report_test=getPercentScore(DgmsDF,
>>> labels_col='trainingLabel',
>>> dgm_col='Dgm1',
>>> params=params,
>>> precomputed = False,
>>> saving = False,
>>> saving_path = None)
Beginning experiments
Run Number: 1
Test set acc.: 0.583
Training set acc.: 0.688
------------------------------
Run Number: 2
Test set acc.: 0.750
Training set acc.: 0.823
------------------------------
Run Number: 3
Test set acc.: 0.708
Training set acc.: 0.771
------------------------------
Run Number: 4
Test set acc.: 0.583
Training set acc.: 0.688
------------------------------
Run Number: 5
Test set acc.: 0.625
Training set acc.: 0.708
------------------------------
Finished with training/testing experiments
Test Set
---------
Average accuracy: 0.650
Standard deviation: 0.068
Training Set
---------
Average accuracy: 0.735
Standard deviation: 0.053
For more metrics, see the outputs.
2.2.3.2.1. Transfer learning between two sets of persistence diagrams
User can enable transfer learning option to train and test a classifier using two different sets of persistence diagrams. The first diagram is treated as the training set, while the second diagram is considered as test set. For given two sets of diagrams, algorithm computes their images and generates feature matrices. Then, supervised classification is performed with respect defined parameters.
>>> from teaspoon.ML.PD_Classification import getPercentScore
>>> from teaspoon.ML import feature_functions as fF
>>> from teaspoon.ML.Base import ParameterBucket
>>> from teaspoon.MakeData.PointCloud import testSetManifolds
>>> from sklearn.preprocessing import LabelEncoder
>>> from sklearn.svm import SVC
>>> import numpy as np
>>> # generate persistence diagrams
>>> DgmsDF_train = testSetManifolds(numDgms=20, numPts=100)
>>> DgmsDF_test = testSetManifolds(numDgms=20, numPts=100)
>>> labels_col='trainingLabel'
>>> dgm_col='Dgm1'
>>> # convert categorical labels into integers
>>> label_encoder = LabelEncoder()
>>> x_train,x_test = DgmsDF_train[labels_col],DgmsDF_test[labels_col]
>>> y_train = label_encoder.fit_transform(x_train)
>>> y_test = label_encoder.fit_transform(x_test)
>>> DgmsDF_train[labels_col],DgmsDF_test[labels_col] = y_train,y_test
>>> # set classification parameters
>>> params = ParameterBucket()
>>> params.feature_function = fF.F_Image
>>> params.k_fold_cv=5
>>> params.clf_model = SVC
>>> params.TF_Learning = True
>>> c_report_train,c_report_test=getPercentScore(DgmsDF_train,
>>> labels_col='trainingLabel',
>>> dgm_col='Dgm1',
>>> params=params,
>>> precomputed = False,
>>> saving = False,
>>> saving_path = None,
>>> DgmsDF_test = DgmsDF_test)
Beginning experiments
Run Number: 1
Test set acc.: 0.656
Training set acc.: 0.667
------------------------------
Run Number: 2
Test set acc.: 0.719
Training set acc.: 0.719
------------------------------
Run Number: 3
Test set acc.: 0.833
Training set acc.: 0.844
------------------------------
Run Number: 4
Test set acc.: 0.750
Training set acc.: 0.771
------------------------------
Run Number: 5
Test set acc.: 0.812
Training set acc.: 0.844
------------------------------
Finished with training/testing experiments
Test Set
---------
Average accuracy: 0.754
Standard deviation: 0.064
Training Set
---------
Average accuracy: 0.769
Standard deviation: 0.070
For more metrics, see the outputs.
2.2.3.2.2. Hyperparameter tuning
Our package also provides user with hyperparameter tuning. When it is enabled, user is expected to provide the parameters and their range in a dictionary to tune parameters. Algorithm implements GridSearchCV.
>>> from teaspoon.ML.PD_Classification import getPercentScore
>>> from teaspoon.ML import feature_functions as fF
>>> from teaspoon.ML.Base import ParameterBucket
>>> from teaspoon.MakeData.PointCloud import testSetManifolds
>>> from sklearn.preprocessing import LabelEncoder
>>> from sklearn.svm import SVC
>>> # generate persistence diagrams
>>> DgmsDF = testSetManifolds(numDgms=20, numPts=100)
>>> labels_col='trainingLabel'
>>> dgm_col='Dgm1'
>>> # convert categorical labels into integers
>>> label_encoder = LabelEncoder()
>>> x = DgmsDF[labels_col]
>>> y = label_encoder.fit_transform(x)
>>> DgmsDF[labels_col] = y
>>> # set classification parameters
>>> params = ParameterBucket()
>>> params.feature_function = fF.F_Image
>>> params.k_fold_cv=5
>>> params.clf_model = SVC
>>> params.param_tuning = True
>>> # parameters to tune and their ranges
>>> gamma_range = np.logspace(-3, 3, num=5)
>>> lambda_range = np.logspace(-3, 3, num=5)
>>> params.parToTune = [] # the list that contains the parameters to tune for each classifier
>>> params.parToTune.append({'C': lambda_range,'gamma':gamma_range}) # SVM paramters
>>> # perform classification
>>> c_report_train,c_report_test=getPercentScore(DgmsDF_train,
>>> labels_col='trainingLabel',
>>> dgm_col='Dgm1',
>>> params=params,
>>> precomputed = False,
>>> saving = False,
>>> saving_path = None,
>>> DgmsDF_test = DgmsDF_test)
Beginning experiments
Run Number: 1
Test set acc.: 0.958
Training set acc.: 1.000
------------------------------
Run Number: 2
Test set acc.: 0.958
Training set acc.: 0.990
------------------------------
Run Number: 3
Test set acc.: 1.000
Training set acc.: 0.990
------------------------------
Run Number: 4
Test set acc.: 0.958
Training set acc.: 0.990
------------------------------
Run Number: 5
Test set acc.: 1.000
Training set acc.: 1.000
------------------------------
Finished with training/testing experiments
Test Set
---------
Average accuracy: 0.975
Standard deviation: 0.020
Training Set
---------
Average accuracy: 0.994
Standard deviation: 0.005
For more metrics, see the outputs.