Early time series classification (eTSC) is the problem of classifying a time series after as few measurements as possible with the highest possible accuracy. The most critical issue of any eTSC method is to decide when enough data of a time series has been seen to take a decision: Waiting for more data points usually makes the classification problem easier but delays the time in which a classification is made; in contrast, earlier classification has to cope with less input data, often leading to inferior accuracy.
This notebook gives a quick guide to get you started with running eTSC algorithms in aeon.
The UCR/UEA time series classification archive contains a large number of example TSC problems that have been used thousands of times in the literature to assess TSC algorithms. Read the data loading documentation and notebooks for details on the aeon data formats and loading data for aeon.
# Imports used in this notebook
import numpy as np
from aeon.classification.early_classification._teaser import TEASER
from aeon.classification.interval_based import TimeSeriesForestClassifier
from aeon.datasets import load_arrow_head
# Load default train/test splits from aeon/datasets/data
arrow_train_X, arrow_train_y = load_arrow_head(split="train")
arrow_test_X, arrow_test_y = load_arrow_head(split="test")
arrow_test_X.shape
(175, 1, 251)
TEASER [1] is a two-tier model using a base classifier to make predictions and a decision making estimator to decide whether these predictions are safe. As a first tier, TEASER requires a TSC algorithm, such as WEASEL, which produces class probabilities as output. As a second tier an anomaly detector is required, such as a one-class SVM.
teaser = TEASER(
random_state=0,
classification_points=[25, 50, 75, 100, 125, 150, 175, 200, 251],
estimator=TimeSeriesForestClassifier(n_estimators=10, random_state=0),
)
teaser.fit(arrow_train_X, arrow_train_y)
TEASER(classification_points=[25, 50, 75, 100, 125, 150, 175, 200, 251],
estimator=TimeSeriesForestClassifier(n_estimators=10, random_state=0),
random_state=0)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. TEASER(classification_points=[25, 50, 75, 100, 125, 150, 175, 200, 251],
estimator=TimeSeriesForestClassifier(n_estimators=10, random_state=0),
random_state=0)TimeSeriesForestClassifier(n_estimators=10, random_state=0)
TimeSeriesForestClassifier(n_estimators=10, random_state=0)
Commonly accuracy is used to determine the correctness of the predictions, while earliness is used to determine how much of the series is required on average to obtain said accuracy. I.e. for the below values, using just 43% of the full test data, we were able to get an accuracy of 69%.
hm, acc, earl = teaser.score(arrow_test_X, arrow_test_y)
print("Earliness on Test Data %2.2f" % earl)
print("Accuracy on Test Data %2.2f" % acc)
print("Harmonic Mean on Test Data %2.2f" % hm)
--------------------------------------------------------------------------- ValueError Traceback (most recent call last) Cell In[10], line 1 ----> 1 hm, acc, earl = teaser.score(arrow_test_X, arrow_test_y) 2 print("Earliness on Test Data %2.2f" % earl) 3 print("Accuracy on Test Data %2.2f" % acc) File C:\Code\aeon\aeon\classification\early_classification\base.py:314, in BaseEarlyClassifier.score(self, X, y) 311 self.check_is_fitted() 313 # boilerplate input checks for predict-like methods --> 314 self._check_X(X) 315 X = self._convert_X(X) 317 return self._score(X, y) File C:\Code\aeon\aeon\classification\early_classification\base.py:631, in BaseEarlyClassifier._check_X(self, X) 629 def _check_X(self, X): 630 """To follow.""" --> 631 metadata = _get_metadata(X) 632 # Check classifier capabilities for X 633 allow_multivariate = self.get_tag("capability:multivariate") File C:\Code\aeon\aeon\classification\early_classification\base.py:707, in _get_metadata(X) 705 metadata = {} 706 metadata["multivariate"] = not is_univariate(X) --> 707 metadata["missing_values"] = has_missing(X) 708 metadata["unequal_length"] = not is_equal_length(X) 709 metadata["n_cases"] = get_n_cases(X) File C:\Code\aeon\aeon\utils\validation\collection.py:305, in has_missing(X) 303 type = get_type(X) 304 if type == "numpy3D" or type == "numpy2D": --> 305 return np.any(np.isnan(np.min(X))) 306 if type == "np-list": 307 for x in X: File <__array_function__ internals>:180, in amin(*args, **kwargs) File C:\Code\aeon\venv\lib\site-packages\numpy\core\fromnumeric.py:2918, in amin(a, axis, out, keepdims, initial, where) 2802 @array_function_dispatch(_amin_dispatcher) 2803 def amin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, 2804 where=np._NoValue): 2805 """ 2806 Return the minimum of an array or minimum along an axis. 2807 (...) 2916 6 2917 """ -> 2918 return _wrapreduction(a, np.minimum, 'min', axis, None, out, 2919 keepdims=keepdims, initial=initial, where=where) File C:\Code\aeon\venv\lib\site-packages\numpy\core\fromnumeric.py:86, in _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs) 83 else: 84 return reduction(axis=axis, out=out, **passkwargs) ---> 86 return ufunc.reduce(obj, axis, dtype, out, **passkwargs) ValueError: zero-size array to reduction operation minimum which has no identity
print("Earliness on Train Data %2.2f" % teaser._train_earliness)
print("Accuracy on Train Data %2.2f" % teaser._train_accuracy)
Earliness on Train Data 0.31 Accuracy on Train Data 0.69
With the full test data, we would obtain 68% accuracy with the same classifier.
accuracy = (
TimeSeriesForestClassifier(n_estimators=10, random_state=0)
.fit(arrow_train_X, arrow_train_y)
.score(arrow_test_X, arrow_test_y)
)
print("Accuracy on the full Test Data %2.2f" % accuracy)
Accuracy on the full Test Data 0.67
The main draw of eTSC is the capabilility to make classifications with incomplete time series. aeon eTSC algorithms accept inputs with less time points than the full series length, and output two items: The prediction made and whether the algorithm thinks the prediction is safe. Information about the decision such as the time stamp it was made at can be obtained from the state_info attribute.
X = arrow_test_X[:, :, :50]
probas, _ = teaser.predict_proba(X)
idx = (probas >= 0).all(axis=1)
print("First 10 Finished prediction\n", np.argwhere(idx).flatten()[:10])
print("First 10 Probabilities of finished predictions\n", probas[idx][:10])
First 10 Finished prediction [ 0 1 4 5 9 11 24 30 32 35] First 10 Probabilities of finished predictions [[0.9 0. 0.1] [0.3 0.1 0.6] [0.8 0.1 0.1] [0.7 0.3 0. ] [0.5 0.2 0.3] [0.6 0.2 0.2] [0.1 0.2 0.7] [0.8 0. 0.2] [0.3 0.1 0.6] [0.9 0. 0.1]]
_, acc, _ = teaser.score(X, arrow_test_y)
print("Accuracy with 50 points on Test Data %2.2f" % acc)
Accuracy with 50 points on Test Data 0.57
The rationale is to keep the state info from the previous predictions in the TEASER object and use it whenever new data is available.
test_points = [25, 50, 75, 100, 125, 150, 175, 200, 251]
final_states = np.zeros((arrow_test_X.shape[0], 4), dtype=int)
final_decisions = np.zeros(arrow_test_X.shape[0], dtype=int)
open_idx = np.arange(0, arrow_test_X.shape[0])
teaser.reset_state_info()
for i in test_points:
probas, decisions = teaser.update_predict_proba(arrow_test_X[:, :, :i])
final_states[open_idx] = teaser.get_state_info()
arrow_test_X, open_idx, final_idx = teaser.split_indices_and_filter(
arrow_test_X, open_idx, decisions
)
final_decisions[final_idx] = i
(
hm,
acc,
earliness,
) = teaser.compute_harmonic_mean(final_states, arrow_test_y)
print("Earliness on length %2i is %2.2f" % (i, earliness))
print("Accuracy on length %2i is %2.2f" % (i, acc))
print("Harmonic Mean on length %2i is %2.2f" % (i, hm))
print("...........")
print("Time Stamp of final decisions", final_decisions)
Earliness on length 25 is 0.10 Accuracy on length 25 is 0.50 Harmonic Mean on length 25 is 0.64 ........... Earliness on length 50 is 0.20 Accuracy on length 50 is 0.57 Harmonic Mean on length 50 is 0.67 ........... Earliness on length 75 is 0.27 Accuracy on length 75 is 0.72 Harmonic Mean on length 75 is 0.72 ........... Earliness on length 100 is 0.32 Accuracy on length 100 is 0.62 Harmonic Mean on length 100 is 0.65 ........... Earliness on length 125 is 0.35 Accuracy on length 125 is 0.69 Harmonic Mean on length 125 is 0.67 ........... Earliness on length 150 is 0.37 Accuracy on length 150 is 0.69 Harmonic Mean on length 150 is 0.66 ........... Earliness on length 175 is 0.39 Accuracy on length 175 is 0.68 Harmonic Mean on length 175 is 0.64 ........... Earliness on length 200 is 0.40 Accuracy on length 200 is 0.69 Harmonic Mean on length 200 is 0.65 ........... Earliness on length 251 is 0.40 Accuracy on length 251 is 0.67 Harmonic Mean on length 251 is 0.63 ........... Time Stamp of final decisions [ 50 50 251 75 50 50 175 200 175 50 75 50 75 75 100 251 100 100 125 75 100 100 75 100 50 125 75 100 75 75 50 75 50 125 175 50 50 75 75 125 50 75 75 50 175 100 150 125 75 100 75 75 75 75 50 100 50 175 75 50 200 50 50 50 75 200 75 125 75 125 150 175 125 50 150 50 75 75 50 100 75 251 251 75 50 100 50 150 100 50 75 100 251 50 50 50 200 100 75 50 200 100 50 50 50 50 251 100 75 75 125 50 125 100 100 50 75 175 175 50 50 100 175 150 100 100 50 100 100 100 175 50 50 100 100 175 251 125 125 100 100 125 100 125 100 125 50 175 75 125 100 100 125 50 50 100 125 100 100 100 251 150 50 75 175 125 50 50 125 75 50 100 175 50 100]
[1] Schäfer, P., & Leser, U. (2020). TEASER: early and accurate time series classification. Data mining and knowledge discovery, 34(5), 1336-1362