# Time Series Classification with aeon¶

Time Series Classification (TSC) involves training a model from a collection of time series (real valued, ordered, data) in order to predict a target variable. For example, we might want to build a model that can predict whether a patient is sick based on their ECG reading, or a persons type of movement based on the trace of the position of their hand. This notebook gives a quick guide to TSC to get you started using aeon time series classifiers. If you can use scikit-learn, it should be easy, because the basic usage is identical.

## Classification Notebooks¶

This note book gives an overview of TSC. More specific notebooks on TSC are base on the type of representation or transformation they use:

## Data Storage and Problem Types¶

Time series can be univariate (each observation is a single value) or multivariate (each observation is a vector). For example, an ECG reading from a single sensor is a univariate series, but a motion trace of from a smart watch would be multivariate, with at least three dimensions (x,y,z co-ordinates). The image above is a univariate problem: each series has its own label. The dimension of the time series instance is also often called the channel. We recommend storing time series in 3D numpy
array of shape `(n_cases, n_channels, n_timepoints)`

and where possible our single problem loaders will return a 3D numpy. Unequal length classification problems are stored in a list of 2D numpy arrays.

```
[1]:
```

```
# Plotting and data loading imports used in this notebook
import warnings
import matplotlib.pyplot as plt
from aeon.datasets import load_arrow_head, load_basic_motions
warnings.filterwarnings("ignore")
arrow, arrow_labels = load_arrow_head(split="train")
motions, motions_labels = load_basic_motions(split="train")
print(f"ArrowHead series of type {type(arrow)} and shape {arrow.shape}")
print(f"Motions type {type(motions)} of shape {motions_labels.shape}")
```

```
ArrowHead series of type <class 'numpy.ndarray'> and shape (36, 1, 251)
Motions type <class 'numpy.ndarray'> of shape (40,)
```

We tend to use 3D numpy even if the data is univariate, although all classifiers work with shape (instance, time point), currently some transformers do not work correctly with 2D arrays. If your series are unequal length, have missing values or are sampled at irregular time intervals, you should read the note book on data preprocessing.

The UCR/UEA TSC dataset archive contains a large number of example TSC problems that have been used thousands of times in the literature to assess TSC algorithms. These datasets have certain characteristics that influence what data structure we use to store them in memory.

Most datasets in the archive contain time series all the same length. For example, the ArrowHead dataset we have just loaded consists of outlines of the images of arrow heads. The classification of projectile points is an important topic in anthropology.

The shapes of the projectile points are converted into a sequence using the angle-based method as described in this blog post about converting images into time series for data mining.

Each instance consists of a single time series (i.e. the problem is univariate) of equal length and a class label based on shape distinctions such as the presence and location of a notch in the arrow. The data set consists of 210 instances, by default split into 36 train and 175 test instances.

The BasicMotions dataset is an example of a multivariate TSC problem. It was generated as part of a project where four students performed four activities whilst wearing a smartwatch. The watch collects 3D accelerometer and 3D gyroscope data. Each instance involved a subject performing one of four tasks (walking, resting, running and badminton) for ten seconds. Time series in this data set have six dimensions or channels.

```
[2]:
```

```
plt.title(
f"First and second dimensions of the first instance in BasicMotions data, "
f"(student {motions_labels[0]})"
)
plt.plot(motions[0][0])
plt.plot(motions[0][1])
```

```
[2]:
```

```
[<matplotlib.lines.Line2D at 0x14b66e59580>]
```

```
[3]:
```

```
plt.title(f"First instance in ArrowHead data (class {arrow_labels[0]})")
plt.plot(arrow[0, 0])
```

```
[3]:
```

```
[<matplotlib.lines.Line2D at 0x14b66ea58b0>]
```

It is possible to use a standard `sklearn`

classifier for univariate, equal length classification problems, but it is unlikely to perform as well as bespoke time series classifiers, since `sklearn`

classifiers ignore the sequence information in the variables.

To apply `sklearn`

classifiers directly, the data needs to be reshaped into a 2D numpy array. We also offer the ability to load univariate TSC problems directly in 2D arrays. Please note that currently, some Transformers treat a single multivariate time series in a numpy array as shape `(n_timepoints, n_channels)`

rather than `(n_channels,n_timepoints)`

do not work correctly with 2D numpy classification problems, so we recommend using 3D numpyof shape `(n_channels, 1, n_timepoints)`

for
univariate series.

```
[4]:
```

```
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score
rand_forest = RandomForestClassifier(n_estimators=100)
arrow2d = arrow.squeeze()
arrow_test, arrow_test_labels = load_arrow_head(split="test", return_type="numpy2d")
rand_forest.fit(arrow2d, arrow_labels)
y_pred = rand_forest.predict(arrow_test)
accuracy_score(arrow_test_labels, y_pred)
```

```
[4]:
```

```
0.68
```

## Time Series Classifiers in aeon¶

`aeon`

contains the state of the art in time series classifiers in the package `classification`

. These are grouped based on the data representation used to find discriminatory features. We provide a separate notebook for each of type: convolution based, deep learning, distance based, dictionary based, feature_based, hybrid, interval
based, and shapelet based. We also provide some standard classifiers not available in scikit learn in the sklearn package. We show the simplest use cases for classifiers and demonstrate how to build bespoke pipelines for time series classification. An accurate and relatively fast classifier is the ROCKET classifier. ROCKET is a convolution based algorithm described in detail in
the convolution based note book.

```
[5]:
```

```
from aeon.classification.convolution_based import RocketClassifier
rocket = RocketClassifier(num_kernels=2000)
rocket.fit(arrow, arrow_labels)
y_pred = rocket.predict(arrow_test)
accuracy_score(arrow_test_labels, y_pred)
```

```
[5]:
```

```
0.7942857142857143
```

Another accurate classifier for time series classification is version 2 of the HIVE-COTE algorithm. (HC2) is described in the hybrid notebook notebook. HC2 is relatively slow on small problems like these examples. However, it can be configured with an approximate maximum run time as follows (it may take a bit longer than 12 seconds to run this cell, very short times are approximate since there is a minimum amount of work the classifier needs to do):

```
[6]:
```

```
from aeon.classification.hybrid import HIVECOTEV2
hc2 = HIVECOTEV2(time_limit_in_minutes=0.2)
hc2.fit(arrow, arrow_labels)
y_pred = hc2.predict(arrow_test)
accuracy_score(arrow_test_labels, y_pred)
```

```
[6]:
```

```
0.84
```

## Multivariate Classification¶

To use `sklearn`

classifiers directly on multivariate data, one option is to flatten the data so that the 3D array `(n_cases, n_channels, n_timepoints)`

becomes a 2D array of shape `(n_cases, n_channels*n_timepoints)`

.

```
[7]:
```

```
motions_test, motions_test_labels = load_basic_motions(split="test")
motions2d = motions.reshape(motions.shape[0], motions.shape[1] * motions.shape[2])
motions2d_test = motions_test.reshape(
motions_test.shape[0], motions_test.shape[1] * motions_test.shape[2]
)
rand_forest.fit(motions2d, motions_labels)
y_pred = rand_forest.predict(motions2d_test)
accuracy_score(motions_test_labels, y_pred)
```

```
[7]:
```

```
0.925
```

However, many `aeon`

classifiers, including ROCKET and HC2, are configured to work with multivariate input. This works exactly like univariate classification. For example:

```
[8]:
```

```
rocket.fit(motions, motions_labels)
y_pred = rocket.predict(motions_test)
accuracy_score(motions_test_labels, y_pred)
```

```
[8]:
```

```
1.0
```

A list of classifiers capable of handling multivariate classification can be obtained with this code

```
[9]:
```

```
from aeon.registry import all_estimators
all_estimators(
filter_tags={"capability:multivariate": True},
estimator_types="classifier",
as_dataframe=True,
)
```

```
[9]:
```

```
[('Arsenal', aeon.classification.convolution_based._arsenal.Arsenal),
('CNNClassifier', aeon.classification.deep_learning.cnn.CNNClassifier),
('CanonicalIntervalForestClassifier',
aeon.classification.interval_based._cif.CanonicalIntervalForestClassifier),
('Catch22Classifier',
aeon.classification.feature_based._catch22.Catch22Classifier),
('ChannelEnsembleClassifier',
aeon.classification.compose._channel_ensemble.ChannelEnsembleClassifier),
('DrCIFClassifier',
aeon.classification.interval_based._drcif.DrCIFClassifier),
('DummyClassifier', aeon.classification._dummy.DummyClassifier),
('ElasticEnsemble',
aeon.classification.distance_based._elastic_ensemble.ElasticEnsemble),
('EncoderClassifier',
aeon.classification.deep_learning.encoder.EncoderClassifier),
('FCNClassifier', aeon.classification.deep_learning.fcn.FCNClassifier),
('FreshPRINCEClassifier',
aeon.classification.feature_based._fresh_prince.FreshPRINCEClassifier),
('HIVECOTEV2', aeon.classification.hybrid._hivecote_v2.HIVECOTEV2),
('InceptionTimeClassifier',
aeon.classification.deep_learning.inception_time.InceptionTimeClassifier),
('IndividualInceptionClassifier',
aeon.classification.deep_learning.inception_time.IndividualInceptionClassifier),
('IndividualOrdinalTDE',
aeon.classification.ordinal_classification._ordinal_tde.IndividualOrdinalTDE),
('IndividualTDE', aeon.classification.dictionary_based._tde.IndividualTDE),
('IntervalForestClassifier',
aeon.classification.interval_based._interval_forest.IntervalForestClassifier),
('KNeighborsTimeSeriesClassifier',
aeon.classification.distance_based._time_series_neighbors.KNeighborsTimeSeriesClassifier),
('MLPClassifier', aeon.classification.deep_learning.mlp.MLPClassifier),
('MUSE', aeon.classification.dictionary_based._muse.MUSE),
('OrdinalTDE',
aeon.classification.ordinal_classification._ordinal_tde.OrdinalTDE),
('RDSTClassifier', aeon.classification.shapelet_based._rdst.RDSTClassifier),
('RSTSF', aeon.classification.interval_based._rstsf.RSTSF),
('RandomIntervalClassifier',
aeon.classification.interval_based._interval_pipelines.RandomIntervalClassifier),
('RandomIntervalSpectralEnsembleClassifier',
aeon.classification.interval_based._rise.RandomIntervalSpectralEnsembleClassifier),
('ResNetClassifier',
aeon.classification.deep_learning.resnet.ResNetClassifier),
('RocketClassifier',
aeon.classification.convolution_based._rocket_classifier.RocketClassifier),
('ShapeletTransformClassifier',
aeon.classification.shapelet_based._stc.ShapeletTransformClassifier),
('SignatureClassifier',
aeon.classification.feature_based._signature_classifier.SignatureClassifier),
('SummaryClassifier',
aeon.classification.feature_based._summary_classifier.SummaryClassifier),
('SupervisedIntervalClassifier',
aeon.classification.interval_based._interval_pipelines.SupervisedIntervalClassifier),
('SupervisedTimeSeriesForest',
aeon.classification.interval_based._stsf.SupervisedTimeSeriesForest),
('TSFreshClassifier',
aeon.classification.feature_based._tsfresh_classifier.TSFreshClassifier),
('TapNetClassifier',
aeon.classification.deep_learning.tapnet.TapNetClassifier),
('TemporalDictionaryEnsemble',
aeon.classification.dictionary_based._tde.TemporalDictionaryEnsemble),
('TimeSeriesForestClassifier',
aeon.classification.interval_based._tsf.TimeSeriesForestClassifier)]
```

An alternative for MTSC is to build a univariate classifier on each dimension, then ensemble. Dimension ensembling can be easily done via `ColumnEnsembleClassifier`

which fits classifiers independently to specified dimensions, then combines predictions through a voting scheme. The interface is similar to the `ColumnTransformer`

from `sklearn`

. The example below builds a DrCIF classifier on the first channel and a RocketClassifier on the fourth and fifth dimensions, ignoring the second,
third and sixth.

```
[10]:
```

```
from aeon.classification.compose import ChannelEnsembleClassifier
from aeon.classification.interval_based import DrCIFClassifier
cls = ChannelEnsembleClassifier(
estimators=[
("DrCIF0", DrCIFClassifier(n_estimators=5, n_intervals=2), [0]),
("ROCKET3", RocketClassifier(num_kernels=1000), [3, 4]),
]
)
cls.fit(motions, motions_labels)
y_pred = cls.predict(motions_test)
accuracy_score(motions_test_labels, y_pred)
```

```
[10]:
```

```
0.925
```

## sklearn Compatibility¶

`aeon`

classifiers are compatible with `sklearn`

model selection and composition tools using `aeon`

data formats. For example, cross-validation can be performed using the `sklearn`

`cross_val_score`

and `KFold`

functionality:

```
[11]:
```

```
from sklearn.model_selection import KFold, cross_val_score
cross_val_score(rocket, arrow, y=arrow_labels, cv=KFold(n_splits=4))
```

```
[11]:
```

```
array([0.88888889, 0.66666667, 0.88888889, 0.77777778])
```

Parameter tuning can be done using `sklearn`

`GridSearchCV`

. For example, we can tune the *k* and distance measure for a K-NN classifier:

```
[12]:
```

```
from sklearn.model_selection import GridSearchCV
from aeon.classification.distance_based import KNeighborsTimeSeriesClassifier
knn = KNeighborsTimeSeriesClassifier()
param_grid = {"n_neighbors": [1, 5], "distance": ["euclidean", "dtw"]}
parameter_tuning_method = GridSearchCV(knn, param_grid, cv=KFold(n_splits=4))
parameter_tuning_method.fit(arrow, arrow_labels)
y_pred = parameter_tuning_method.predict(arrow_test)
accuracy_score(arrow_test_labels, y_pred)
```

```
[12]:
```

```
0.8
```

Probability calibration is possible with the `sklearn`

`CalibratedClassifierCV`

:

```
[13]:
```

```
from sklearn.calibration import CalibratedClassifierCV
from aeon.classification.interval_based import DrCIFClassifier
calibrated_drcif = CalibratedClassifierCV(
estimator=DrCIFClassifier(n_estimators=10, n_intervals=5), cv=4
)
calibrated_drcif.fit(arrow, arrow_labels)
y_pred = calibrated_drcif.predict(arrow_test)
accuracy_score(arrow_test_labels, y_pred)
```

```
[13]:
```

```
0.7714285714285715
```

### Background info and references for classifiers used here¶

#### KNeighborsTimeSeriesClassifier¶

One nearest neighbour (1-NN) classification with Dynamic Time Warping (DTW) is one of the oldest TSC approaches, and is commonly used as a performance benchmark.

#### RocketClassifier¶

The RocketClassifier is based on a pipeline combination of the ROCKET transformation (transformations.panel.rocket) and the sklearn RidgeClassifierCV classifier. The RocketClassifier is configurable to use variants MiniRocket and MultiRocket. ROCKET is based on generating random convolutional kernels. A large number are generated, then a linear classifier is built on the output.

[1] Dempster, Angus, François Petitjean, and Geoffrey I. Webb. “Rocket: exceptionally fast and accurate time series classification using random convolutional kernels.” Data Mining and Knowledge Discovery (2020) arXiv version DAMI 2020

#### DrCIF¶

The Diverse Representation Canonical Interval Forest Classifier (DrCIF) is an interval based classifier. The algorithm takes multiple randomised intervals from each series and extracts a range of features. These features are used to build a decision tree, which in turn are ensembled into a decision tree forest, in the style of a random forest.

Original CIF classifier: [2] Matthew Middlehurst and James Large and Anthony Bagnall. “The Canonical Interval Forest (CIF) Classifier for Time Series Classification.” IEEE International Conference on Big Data (2020) arXiv version IEEE BigData (2020)

The DrCIF adjustment was proposed in [3].

#### HIVE-COTE 2.0 (HC2)¶

The HIerarchical VotE Collective of Transformation-based Ensembles is a meta ensemble that combines classifiers built on different representations. Version 2 combines DrCIF, TDE, an ensemble of RocketClassifiers called the Arsenal and the ShapeletTransformClassifier. It is one of the most accurate classifiers on the UCR and UEA time series archives.

[3] Middlehurst, Matthew, James Large, Michael Flynn, Jason Lines, Aaron Bostrom, and Anthony Bagnall. “HIVE-COTE 2.0: a new meta ensemble for time series classification.” Machine Learning (2021) ML 2021

#### Catch22¶

The CAnonical Time-series CHaracteristics (Catch22) are a set of 22 informative and low redundancy features extracted from time series data. The features were filtered from 4791 features in the `hctsa`

toolkit.

[4] Lubba, Carl H., Sarab S. Sethi, Philip Knaute, Simon R. Schultz, Ben D. Fulcher, and Nick S. Jones. “catch22: Canonical time-series characteristics.” Data Mining and Knowledge Discovery (2019) DAMI 2019

Generated using nbsphinx. The Jupyter notebook can be found here.