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# Anomaly Detection
Aeon provides anomaly detection methods for identifying unusual patterns in time series at both series and collection levels.
## Collection Anomaly Detectors
Detect anomalous time series within a collection:
- `ClassificationAdapter` - Adapts classifiers for anomaly detection
- Train on normal data, flag outliers during prediction
- **Use when**: Have labeled normal data, want classification-based approach
- `OutlierDetectionAdapter` - Wraps sklearn outlier detectors
- Works with IsolationForest, LOF, OneClassSVM
- **Use when**: Want to use sklearn anomaly detectors on collections
## Series Anomaly Detectors
Detect anomalous points or subsequences within a single time series.
### Distance-Based Methods
Use similarity metrics to identify anomalies:
- `CBLOF` - Cluster-Based Local Outlier Factor
- Clusters data, identifies outliers based on cluster properties
- **Use when**: Anomalies form sparse clusters
- `KMeansAD` - K-means based anomaly detection
- Distance to nearest cluster center indicates anomaly
- **Use when**: Normal patterns cluster well
- `LeftSTAMPi` - Left STAMP incremental
- Matrix profile for online anomaly detection
- **Use when**: Streaming data, need online detection
- `STOMP` - Scalable Time series Ordered-search Matrix Profile
- Computes matrix profile for subsequence anomalies
- **Use when**: Discord discovery, motif detection
- `MERLIN` - Matrix profile-based method
- Efficient matrix profile computation
- **Use when**: Large time series, need scalability
- `LOF` - Local Outlier Factor adapted for time series
- Density-based outlier detection
- **Use when**: Anomalies in low-density regions
- `ROCKAD` - ROCKET-based semi-supervised detection
- Uses ROCKET features for anomaly identification
- **Use when**: Have some labeled data, want feature-based approach
### Distribution-Based Methods
Analyze statistical distributions:
- `COPOD` - Copula-Based Outlier Detection
- Models marginal and joint distributions
- **Use when**: Multi-dimensional time series, complex dependencies
- `DWT_MLEAD` - Discrete Wavelet Transform Multi-Level Anomaly Detection
- Decomposes series into frequency bands
- **Use when**: Anomalies at specific frequencies
### Isolation-Based Methods
Use isolation principles:
- `IsolationForest` - Random forest-based isolation
- Anomalies easier to isolate than normal points
- **Use when**: High-dimensional data, no assumptions about distribution
- `OneClassSVM` - Support vector machine for novelty detection
- Learns boundary around normal data
- **Use when**: Well-defined normal region, need robust boundary
- `STRAY` - Streaming Robust Anomaly Detection
- Robust to data distribution changes
- **Use when**: Streaming data, distribution shifts
### External Library Integration
- `PyODAdapter` - Bridges PyOD library to aeon
- Access 40+ PyOD anomaly detectors
- **Use when**: Need specific PyOD algorithm
## Quick Start
```python
from aeon.anomaly_detection import STOMP
import numpy as np
# Create time series with anomaly
y = np.concatenate([
np.sin(np.linspace(0, 10, 100)),
[5.0], # Anomaly spike
np.sin(np.linspace(10, 20, 100))
])
# Detect anomalies
detector = STOMP(window_size=10)
anomaly_scores = detector.fit_predict(y)
# Higher scores indicate more anomalous points
threshold = np.percentile(anomaly_scores, 95)
anomalies = anomaly_scores > threshold
```
## Point vs Subsequence Anomalies
- **Point anomalies**: Single unusual values
- Use: COPOD, DWT_MLEAD, IsolationForest
- **Subsequence anomalies** (discords): Unusual patterns
- Use: STOMP, LeftSTAMPi, MERLIN
- **Collective anomalies**: Groups of points forming unusual pattern
- Use: Matrix profile methods, clustering-based
## Evaluation Metrics
Specialized metrics for anomaly detection:
```python
from aeon.benchmarking.metrics.anomaly_detection import (
range_precision,
range_recall,
range_f_score,
roc_auc_score
)
# Range-based metrics account for window detection
precision = range_precision(y_true, y_pred, alpha=0.5)
recall = range_recall(y_true, y_pred, alpha=0.5)
f1 = range_f_score(y_true, y_pred, alpha=0.5)
```
## Algorithm Selection
- **Speed priority**: KMeansAD, IsolationForest
- **Accuracy priority**: STOMP, COPOD
- **Streaming data**: LeftSTAMPi, STRAY
- **Discord discovery**: STOMP, MERLIN
- **Multi-dimensional**: COPOD, PyODAdapter
- **Semi-supervised**: ROCKAD, OneClassSVM
- **No training data**: IsolationForest, STOMP
## Best Practices
1. **Normalize data**: Many methods sensitive to scale
2. **Choose window size**: For matrix profile methods, window size critical
3. **Set threshold**: Use percentile-based or domain-specific thresholds
4. **Validate results**: Visualize detections to verify meaningfulness
5. **Handle seasonality**: Detrend/deseasonalize before detection

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# Time Series Classification
Aeon provides 13 categories of time series classifiers with scikit-learn compatible APIs.
## Convolution-Based Classifiers
Apply random convolutional transformations for efficient feature extraction:
- `Arsenal` - Ensemble of ROCKET classifiers with varied kernels
- `HydraClassifier` - Multi-resolution convolution with dilation
- `RocketClassifier` - Random convolution kernels with ridge regression
- `MiniRocketClassifier` - Simplified ROCKET variant for speed
- `MultiRocketClassifier` - Combines multiple ROCKET variants
**Use when**: Need fast, scalable classification with strong performance across diverse datasets.
## Deep Learning Classifiers
Neural network architectures optimized for temporal sequences:
- `FCNClassifier` - Fully convolutional network
- `ResNetClassifier` - Residual networks with skip connections
- `InceptionTimeClassifier` - Multi-scale inception modules
- `TimeCNNClassifier` - Standard CNN for time series
- `MLPClassifier` - Multi-layer perceptron baseline
- `EncoderClassifier` - Generic encoder wrapper
- `DisjointCNNClassifier` - Shapelet-focused architecture
**Use when**: Large datasets available, need end-to-end learning, or complex temporal patterns.
## Dictionary-Based Classifiers
Transform time series into symbolic representations:
- `BOSSEnsemble` - Bag-of-SFA-Symbols with ensemble voting
- `TemporalDictionaryEnsemble` - Multiple dictionary methods combined
- `WEASEL` - Word ExtrAction for time SEries cLassification
- `MrSEQLClassifier` - Multiple symbolic sequence learning
**Use when**: Need interpretable models, sparse patterns, or symbolic reasoning.
## Distance-Based Classifiers
Leverage specialized time series distance metrics:
- `KNeighborsTimeSeriesClassifier` - k-NN with temporal distances (DTW, LCSS, ERP, etc.)
- `ElasticEnsemble` - Combines multiple elastic distance measures
- `ProximityForest` - Tree ensemble using distance-based splits
**Use when**: Small datasets, need similarity-based classification, or interpretable decisions.
## Feature-Based Classifiers
Extract statistical and signature features before classification:
- `Catch22Classifier` - 22 canonical time-series characteristics
- `TSFreshClassifier` - Automated feature extraction via tsfresh
- `SignatureClassifier` - Path signature transformations
- `SummaryClassifier` - Summary statistics extraction
- `FreshPRINCEClassifier` - Combines multiple feature extractors
**Use when**: Need interpretable features, domain expertise available, or feature engineering approach.
## Interval-Based Classifiers
Extract features from random or supervised intervals:
- `CanonicalIntervalForestClassifier` - Random interval features with decision trees
- `DrCIFClassifier` - Diverse Representation CIF with catch22 features
- `TimeSeriesForestClassifier` - Random intervals with summary statistics
- `RandomIntervalClassifier` - Simple interval-based approach
- `RandomIntervalSpectralEnsembleClassifier` - Spectral features from intervals
- `SupervisedTimeSeriesForest` - Supervised interval selection
**Use when**: Discriminative patterns occur in specific time windows.
## Shapelet-Based Classifiers
Identify discriminative subsequences (shapelets):
- `ShapeletTransformClassifier` - Discovers and uses discriminative shapelets
- `LearningShapeletClassifier` - Learns shapelets via gradient descent
- `SASTClassifier` - Scalable approximate shapelet transform
- `RDSTClassifier` - Random dilated shapelet transform
**Use when**: Need interpretable discriminative patterns or phase-invariant features.
## Hybrid Classifiers
Combine multiple classification paradigms:
- `HIVECOTEV1` - Hierarchical Vote Collective of Transformation-based Ensembles (version 1)
- `HIVECOTEV2` - Enhanced version with updated components
**Use when**: Maximum accuracy required, computational resources available.
## Early Classification
Make predictions before observing entire time series:
- `TEASER` - Two-tier Early and Accurate Series Classifier
- `ProbabilityThresholdEarlyClassifier` - Prediction when confidence exceeds threshold
**Use when**: Real-time decisions needed, or observations have cost.
## Ordinal Classification
Handle ordered class labels:
- `OrdinalTDE` - Temporal dictionary ensemble for ordinal outputs
**Use when**: Classes have natural ordering (e.g., severity levels).
## Composition Tools
Build custom pipelines and ensembles:
- `ClassifierPipeline` - Chain transformers with classifiers
- `WeightedEnsembleClassifier` - Weighted combination of classifiers
- `SklearnClassifierWrapper` - Adapt sklearn classifiers for time series
## Quick Start
```python
from aeon.classification.convolution_based import RocketClassifier
from aeon.datasets import load_classification
# Load data
X_train, y_train = load_classification("GunPoint", split="train")
X_test, y_test = load_classification("GunPoint", split="test")
# Train and predict
clf = RocketClassifier()
clf.fit(X_train, y_train)
accuracy = clf.score(X_test, y_test)
```
## Algorithm Selection
- **Speed priority**: MiniRocketClassifier, Arsenal
- **Accuracy priority**: HIVECOTEV2, InceptionTimeClassifier
- **Interpretability**: ShapeletTransformClassifier, Catch22Classifier
- **Small data**: KNeighborsTimeSeriesClassifier, Distance-based methods
- **Large data**: Deep learning classifiers, ROCKET variants

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# Time Series Clustering
Aeon provides clustering algorithms adapted for temporal data with specialized distance metrics and averaging methods.
## Partitioning Algorithms
Standard k-means/k-medoids adapted for time series:
- `TimeSeriesKMeans` - K-means with temporal distance metrics (DTW, Euclidean, etc.)
- `TimeSeriesKMedoids` - Uses actual time series as cluster centers
- `TimeSeriesKShape` - Shape-based clustering algorithm
- `TimeSeriesKernelKMeans` - Kernel-based variant for nonlinear patterns
**Use when**: Known number of clusters, spherical cluster shapes expected.
## Large Dataset Methods
Efficient clustering for large collections:
- `TimeSeriesCLARA` - Clustering Large Applications with sampling
- `TimeSeriesCLARANS` - Randomized search variant of CLARA
**Use when**: Dataset too large for standard k-medoids, need scalability.
## Elastic Distance Clustering
Specialized for alignment-based similarity:
- `KASBA` - K-means with shift-invariant elastic averaging
- `ElasticSOM` - Self-organizing map using elastic distances
**Use when**: Time series have temporal shifts or warping.
## Spectral Methods
Graph-based clustering:
- `KSpectralCentroid` - Spectral clustering with centroid computation
**Use when**: Non-convex cluster shapes, need graph-based approach.
## Deep Learning Clustering
Neural network-based clustering with auto-encoders:
- `AEFCNClusterer` - Fully convolutional auto-encoder
- `AEResNetClusterer` - Residual network auto-encoder
- `AEDCNNClusterer` - Dilated CNN auto-encoder
- `AEDRNNClusterer` - Dilated RNN auto-encoder
- `AEBiGRUClusterer` - Bidirectional GRU auto-encoder
- `AEAttentionBiGRUClusterer` - Attention-enhanced BiGRU auto-encoder
**Use when**: Large datasets, need learned representations, or complex patterns.
## Feature-Based Clustering
Transform to feature space before clustering:
- `Catch22Clusterer` - Clusters on 22 canonical features
- `SummaryClusterer` - Uses summary statistics
- `TSFreshClusterer` - Automated tsfresh features
**Use when**: Raw time series not informative, need interpretable features.
## Composition
Build custom clustering pipelines:
- `ClustererPipeline` - Chain transformers with clusterers
## Averaging Methods
Compute cluster centers for time series:
- `mean_average` - Arithmetic mean
- `ba_average` - Barycentric averaging with DTW
- `kasba_average` - Shift-invariant averaging
- `shift_invariant_average` - General shift-invariant method
**Use when**: Need representative cluster centers for visualization or initialization.
## Quick Start
```python
from aeon.clustering import TimeSeriesKMeans
from aeon.datasets import load_classification
# Load data (using classification data for clustering)
X_train, _ = load_classification("GunPoint", split="train")
# Cluster time series
clusterer = TimeSeriesKMeans(
n_clusters=3,
distance="dtw", # Use DTW distance
averaging_method="ba" # Barycentric averaging
)
labels = clusterer.fit_predict(X_train)
centers = clusterer.cluster_centers_
```
## Algorithm Selection
- **Speed priority**: TimeSeriesKMeans with Euclidean distance
- **Temporal alignment**: KASBA, TimeSeriesKMeans with DTW
- **Large datasets**: TimeSeriesCLARA, TimeSeriesCLARANS
- **Complex patterns**: Deep learning clusterers
- **Interpretability**: Catch22Clusterer, SummaryClusterer
- **Non-convex clusters**: KSpectralCentroid
## Distance Metrics
Compatible distance metrics include:
- Euclidean, Manhattan, Minkowski (lock-step)
- DTW, DDTW, WDTW (elastic with alignment)
- ERP, EDR, LCSS (edit-based)
- MSM, TWE (specialized elastic)
## Evaluation
Use clustering metrics from sklearn or aeon benchmarking:
- Silhouette score
- Davies-Bouldin index
- Calinski-Harabasz index

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# Datasets and Benchmarking
Aeon provides comprehensive tools for loading datasets and benchmarking time series algorithms.
## Dataset Loading
### Task-Specific Loaders
**Classification Datasets**:
```python
from aeon.datasets import load_classification
# Load train/test split
X_train, y_train = load_classification("GunPoint", split="train")
X_test, y_test = load_classification("GunPoint", split="test")
# Load entire dataset
X, y = load_classification("GunPoint")
```
**Regression Datasets**:
```python
from aeon.datasets import load_regression
X_train, y_train = load_regression("Covid3Month", split="train")
X_test, y_test = load_regression("Covid3Month", split="test")
# Bulk download
from aeon.datasets import download_all_regression
download_all_regression() # Downloads Monash TSER archive
```
**Forecasting Datasets**:
```python
from aeon.datasets import load_forecasting
# Load from forecastingdata.org
y, X = load_forecasting("airline", return_X_y=True)
```
**Anomaly Detection Datasets**:
```python
from aeon.datasets import load_anomaly_detection
X, y = load_anomaly_detection("NAB_realKnownCause")
```
### File Format Loaders
**Load from .ts files**:
```python
from aeon.datasets import load_from_ts_file
X, y = load_from_ts_file("path/to/data.ts")
```
**Load from .tsf files**:
```python
from aeon.datasets import load_from_tsf_file
df, metadata = load_from_tsf_file("path/to/data.tsf")
```
**Load from ARFF files**:
```python
from aeon.datasets import load_from_arff_file
X, y = load_from_arff_file("path/to/data.arff")
```
**Load from TSV files**:
```python
from aeon.datasets import load_from_tsv_file
data = load_from_tsv_file("path/to/data.tsv")
```
**Load TimeEval CSV**:
```python
from aeon.datasets import load_from_timeeval_csv_file
X, y = load_from_timeeval_csv_file("path/to/timeeval.csv")
```
### Writing Datasets
**Write to .ts format**:
```python
from aeon.datasets import write_to_ts_file
write_to_ts_file(X, "output.ts", y=y, problem_name="MyDataset")
```
**Write to ARFF format**:
```python
from aeon.datasets import write_to_arff_file
write_to_arff_file(X, "output.arff", y=y)
```
## Built-in Datasets
Aeon includes several benchmark datasets for quick testing:
### Classification
- `ArrowHead` - Shape classification
- `GunPoint` - Gesture recognition
- `ItalyPowerDemand` - Energy demand
- `BasicMotions` - Motion classification
- And 100+ more from UCR/UEA archives
### Regression
- `Covid3Month` - COVID forecasting
- Various datasets from Monash TSER archive
### Segmentation
- Time series segmentation datasets
- Human activity data
- Sensor data collections
### Special Collections
- `RehabPile` - Rehabilitation data (classification & regression)
## Dataset Metadata
Get information about datasets:
```python
from aeon.datasets import get_dataset_meta_data
metadata = get_dataset_meta_data("GunPoint")
print(metadata)
# {'n_train': 50, 'n_test': 150, 'length': 150, 'n_classes': 2, ...}
```
## Benchmarking Tools
### Loading Published Results
Access pre-computed benchmark results:
```python
from aeon.benchmarking import get_estimator_results
# Get results for specific algorithm on dataset
results = get_estimator_results(
estimator_name="ROCKET",
dataset_name="GunPoint"
)
# Get all available estimators for a dataset
estimators = get_available_estimators("GunPoint")
```
### Resampling Strategies
Create reproducible train/test splits:
```python
from aeon.benchmarking import stratified_resample
# Stratified resampling maintaining class distribution
X_train, X_test, y_train, y_test = stratified_resample(
X, y,
random_state=42,
test_size=0.3
)
```
### Performance Metrics
Specialized metrics for time series tasks:
**Anomaly Detection Metrics**:
```python
from aeon.benchmarking.metrics.anomaly_detection import (
range_precision,
range_recall,
range_f_score,
range_roc_auc_score
)
# Range-based metrics for window detection
precision = range_precision(y_true, y_pred, alpha=0.5)
recall = range_recall(y_true, y_pred, alpha=0.5)
f1 = range_f_score(y_true, y_pred, alpha=0.5)
auc = range_roc_auc_score(y_true, y_scores)
```
**Clustering Metrics**:
```python
from aeon.benchmarking.metrics.clustering import clustering_accuracy
# Clustering accuracy with label matching
accuracy = clustering_accuracy(y_true, y_pred)
```
**Segmentation Metrics**:
```python
from aeon.benchmarking.metrics.segmentation import (
count_error,
hausdorff_error
)
# Number of change points difference
count_err = count_error(y_true, y_pred)
# Maximum distance between predicted and true change points
hausdorff_err = hausdorff_error(y_true, y_pred)
```
### Statistical Testing
Post-hoc analysis for algorithm comparison:
```python
from aeon.benchmarking import (
nemenyi_test,
wilcoxon_test
)
# Nemenyi test for multiple algorithms
results = nemenyi_test(scores_matrix, alpha=0.05)
# Pairwise Wilcoxon signed-rank test
stat, p_value = wilcoxon_test(scores_alg1, scores_alg2)
```
## Benchmark Collections
### UCR/UEA Time Series Archives
Access to comprehensive benchmark repositories:
```python
# Classification: 112 univariate + 30 multivariate datasets
X_train, y_train = load_classification("Chinatown", split="train")
# Automatically downloads from timeseriesclassification.com
```
### Monash Forecasting Archive
```python
# Load forecasting datasets
y = load_forecasting("nn5_daily", return_X_y=False)
```
### Published Benchmark Results
Pre-computed results from major competitions:
- 2017 Univariate Bake-off
- 2021 Multivariate Classification
- 2023 Univariate Bake-off
## Workflow Example
Complete benchmarking workflow:
```python
from aeon.datasets import load_classification
from aeon.classification.convolution_based import RocketClassifier
from aeon.benchmarking import get_estimator_results
from sklearn.metrics import accuracy_score
import numpy as np
# Load dataset
dataset_name = "GunPoint"
X_train, y_train = load_classification(dataset_name, split="train")
X_test, y_test = load_classification(dataset_name, split="test")
# Train model
clf = RocketClassifier(n_kernels=10000, random_state=42)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
# Evaluate
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy:.4f}")
# Compare with published results
published = get_estimator_results("ROCKET", dataset_name)
print(f"Published ROCKET accuracy: {published['accuracy']:.4f}")
```
## Best Practices
### 1. Use Standard Splits
For reproducibility, use provided train/test splits:
```python
# Good: Use standard splits
X_train, y_train = load_classification("GunPoint", split="train")
X_test, y_test = load_classification("GunPoint", split="test")
# Avoid: Creating custom splits
X, y = load_classification("GunPoint")
X_train, X_test, y_train, y_test = train_test_split(X, y)
```
### 2. Set Random Seeds
Ensure reproducibility:
```python
clf = RocketClassifier(random_state=42)
results = stratified_resample(X, y, random_state=42)
```
### 3. Report Multiple Metrics
Don't rely on single metric:
```python
from sklearn.metrics import accuracy_score, f1_score, precision_score
accuracy = accuracy_score(y_test, y_pred)
f1 = f1_score(y_test, y_pred, average='weighted')
precision = precision_score(y_test, y_pred, average='weighted')
```
### 4. Cross-Validation
For robust evaluation on small datasets:
```python
from sklearn.model_selection import cross_val_score
scores = cross_val_score(
clf, X_train, y_train,
cv=5,
scoring='accuracy'
)
print(f"CV Accuracy: {scores.mean():.4f} (+/- {scores.std():.4f})")
```
### 5. Compare Against Baselines
Always compare with simple baselines:
```python
from aeon.classification.distance_based import KNeighborsTimeSeriesClassifier
# Simple baseline: 1-NN with Euclidean distance
baseline = KNeighborsTimeSeriesClassifier(n_neighbors=1, distance="euclidean")
baseline.fit(X_train, y_train)
baseline_acc = baseline.score(X_test, y_test)
print(f"Baseline: {baseline_acc:.4f}")
print(f"Your model: {accuracy:.4f}")
```
### 6. Statistical Significance
Test if improvements are statistically significant:
```python
from aeon.benchmarking import wilcoxon_test
# Run on multiple datasets
accuracies_alg1 = [0.85, 0.92, 0.78, 0.88]
accuracies_alg2 = [0.83, 0.90, 0.76, 0.86]
stat, p_value = wilcoxon_test(accuracies_alg1, accuracies_alg2)
if p_value < 0.05:
print("Difference is statistically significant")
```
## Dataset Discovery
Find datasets matching criteria:
```python
# List all available classification datasets
from aeon.datasets import get_available_datasets
datasets = get_available_datasets("classification")
print(f"Found {len(datasets)} classification datasets")
# Filter by properties
univariate_datasets = [
d for d in datasets
if get_dataset_meta_data(d)['n_channels'] == 1
]
```

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# Distance Metrics
Aeon provides specialized distance functions for measuring similarity between time series, compatible with both aeon and scikit-learn estimators.
## Distance Categories
### Elastic Distances
Allow flexible temporal alignment between series:
**Dynamic Time Warping Family:**
- `dtw` - Classic Dynamic Time Warping
- `ddtw` - Derivative DTW (compares derivatives)
- `wdtw` - Weighted DTW (penalizes warping by location)
- `wddtw` - Weighted Derivative DTW
- `shape_dtw` - Shape-based DTW
**Edit-Based:**
- `erp` - Edit distance with Real Penalty
- `edr` - Edit Distance on Real sequences
- `lcss` - Longest Common SubSequence
- `twe` - Time Warp Edit distance
**Specialized:**
- `msm` - Move-Split-Merge distance
- `adtw` - Amerced DTW
- `sbd` - Shape-Based Distance
**Use when**: Time series may have temporal shifts, speed variations, or phase differences.
### Lock-Step Distances
Compare time series point-by-point without alignment:
- `euclidean` - Euclidean distance (L2 norm)
- `manhattan` - Manhattan distance (L1 norm)
- `minkowski` - Generalized Minkowski distance (Lp norm)
- `squared` - Squared Euclidean distance
**Use when**: Series already aligned, need computational speed, or no temporal warping expected.
## Usage Patterns
### Computing Single Distance
```python
from aeon.distances import dtw_distance
# Distance between two time series
distance = dtw_distance(x, y)
# With window constraint (Sakoe-Chiba band)
distance = dtw_distance(x, y, window=0.1)
```
### Pairwise Distance Matrix
```python
from aeon.distances import dtw_pairwise_distance
# All pairwise distances in collection
X = [series1, series2, series3, series4]
distance_matrix = dtw_pairwise_distance(X)
# Cross-collection distances
distance_matrix = dtw_pairwise_distance(X_train, X_test)
```
### Cost Matrix and Alignment Path
```python
from aeon.distances import dtw_cost_matrix, dtw_alignment_path
# Get full cost matrix
cost_matrix = dtw_cost_matrix(x, y)
# Get optimal alignment path
path = dtw_alignment_path(x, y)
# Returns indices: [(0,0), (1,1), (2,1), (2,2), ...]
```
### Using with Estimators
```python
from aeon.classification.distance_based import KNeighborsTimeSeriesClassifier
# Use DTW distance in classifier
clf = KNeighborsTimeSeriesClassifier(
n_neighbors=5,
distance="dtw",
distance_params={"window": 0.2}
)
clf.fit(X_train, y_train)
```
## Distance Parameters
### Window Constraints
Limit warping path deviation (improves speed and prevents pathological warping):
```python
# Sakoe-Chiba band: window as fraction of series length
dtw_distance(x, y, window=0.1) # Allow 10% deviation
# Itakura parallelogram: slopes constrain path
dtw_distance(x, y, itakura_max_slope=2.0)
```
### Normalization
Control whether to z-normalize series before distance computation:
```python
# Most elastic distances support normalization
distance = dtw_distance(x, y, normalize=True)
```
### Distance-Specific Parameters
```python
# ERP: penalty for gaps
distance = erp_distance(x, y, g=0.5)
# TWE: stiffness and penalty parameters
distance = twe_distance(x, y, nu=0.001, lmbda=1.0)
# LCSS: epsilon threshold for matching
distance = lcss_distance(x, y, epsilon=0.5)
```
## Algorithm Selection
### By Use Case:
**Temporal misalignment**: DTW, DDTW, WDTW
**Speed variations**: DTW with window constraint
**Shape similarity**: Shape DTW, SBD
**Edit operations**: ERP, EDR, LCSS
**Derivative matching**: DDTW
**Computational speed**: Euclidean, Manhattan
**Outlier robustness**: Manhattan, LCSS
### By Computational Cost:
**Fastest**: Euclidean (O(n))
**Fast**: Constrained DTW (O(nw) where w is window)
**Medium**: Full DTW (O(n²))
**Slower**: Complex elastic distances (ERP, TWE, MSM)
## Quick Reference Table
| Distance | Alignment | Speed | Robustness | Interpretability |
|----------|-----------|-------|------------|------------------|
| Euclidean | Lock-step | Very Fast | Low | High |
| DTW | Elastic | Medium | Medium | Medium |
| DDTW | Elastic | Medium | High | Medium |
| WDTW | Elastic | Medium | Medium | Medium |
| ERP | Edit-based | Slow | High | Low |
| LCSS | Edit-based | Slow | Very High | Low |
| Shape DTW | Elastic | Medium | Medium | High |
## Best Practices
### 1. Normalization
Most distances sensitive to scale; normalize when appropriate:
```python
from aeon.transformations.collection import Normalizer
normalizer = Normalizer()
X_normalized = normalizer.fit_transform(X)
```
### 2. Window Constraints
For DTW variants, use window constraints for speed and better generalization:
```python
# Start with 10-20% window
distance = dtw_distance(x, y, window=0.1)
```
### 3. Series Length
- Equal-length required: Most lock-step distances
- Unequal-length supported: Elastic distances (DTW, ERP, etc.)
### 4. Multivariate Series
Most distances support multivariate time series:
```python
# x.shape = (n_channels, n_timepoints)
distance = dtw_distance(x_multivariate, y_multivariate)
```
### 5. Performance Optimization
- Use numba-compiled implementations (default in aeon)
- Consider lock-step distances if alignment not needed
- Use windowed DTW instead of full DTW
- Precompute distance matrices for repeated use
### 6. Choosing the Right Distance
```python
# Quick decision tree:
if series_aligned:
use_distance = "euclidean"
elif need_speed:
use_distance = "dtw" # with window constraint
elif temporal_shifts_expected:
use_distance = "dtw" or "shape_dtw"
elif outliers_present:
use_distance = "lcss" or "manhattan"
elif derivatives_matter:
use_distance = "ddtw" or "wddtw"
```
## Integration with scikit-learn
Aeon distances work with sklearn estimators:
```python
from sklearn.neighbors import KNeighborsClassifier
from aeon.distances import dtw_pairwise_distance
# Precompute distance matrix
X_train_distances = dtw_pairwise_distance(X_train)
# Use with sklearn
clf = KNeighborsClassifier(metric='precomputed')
clf.fit(X_train_distances, y_train)
```
## Available Distance Functions
Get list of all available distances:
```python
from aeon.distances import get_distance_function_names
print(get_distance_function_names())
# ['dtw', 'ddtw', 'wdtw', 'euclidean', 'erp', 'edr', ...]
```
Retrieve specific distance function:
```python
from aeon.distances import get_distance_function
distance_func = get_distance_function("dtw")
result = distance_func(x, y, window=0.1)
```

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# Time Series Forecasting
Aeon provides forecasting algorithms for predicting future time series values.
## Naive and Baseline Methods
Simple forecasting strategies for comparison:
- `NaiveForecaster` - Multiple strategies: last value, mean, seasonal naive
- Parameters: `strategy` ("last", "mean", "seasonal"), `sp` (seasonal period)
- **Use when**: Establishing baselines or simple patterns
## Statistical Models
Classical time series forecasting methods:
### ARIMA
- `ARIMA` - AutoRegressive Integrated Moving Average
- Parameters: `p` (AR order), `d` (differencing), `q` (MA order)
- **Use when**: Linear patterns, stationary or difference-stationary series
### Exponential Smoothing
- `ETS` - Error-Trend-Seasonal decomposition
- Parameters: `error`, `trend`, `seasonal` types
- **Use when**: Trend and seasonal patterns present
### Threshold Autoregressive
- `TAR` - Threshold Autoregressive model for regime switching
- `AutoTAR` - Automated threshold discovery
- **Use when**: Series exhibits different behaviors in different regimes
### Theta Method
- `Theta` - Classical Theta forecasting
- Parameters: `theta`, `weights` for decomposition
- **Use when**: Simple but effective baseline needed
### Time-Varying Parameter
- `TVP` - Time-varying parameter model with Kalman filtering
- **Use when**: Parameters change over time
## Deep Learning Forecasters
Neural networks for complex temporal patterns:
- `TCNForecaster` - Temporal Convolutional Network
- Dilated convolutions for large receptive fields
- **Use when**: Long sequences, need non-recurrent architecture
- `DeepARNetwork` - Probabilistic forecasting with RNNs
- Provides prediction intervals
- **Use when**: Need probabilistic forecasts, uncertainty quantification
## Regression-Based Forecasting
Apply regression to lagged features:
- `RegressionForecaster` - Wraps regressors for forecasting
- Parameters: `window_length`, `horizon`
- **Use when**: Want to use any regressor as forecaster
## Quick Start
```python
from aeon.forecasting.naive import NaiveForecaster
from aeon.forecasting.arima import ARIMA
import numpy as np
# Create time series
y = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
# Naive baseline
naive = NaiveForecaster(strategy="last")
naive.fit(y)
forecast_naive = naive.predict(fh=[1, 2, 3])
# ARIMA model
arima = ARIMA(order=(1, 1, 1))
arima.fit(y)
forecast_arima = arima.predict(fh=[1, 2, 3])
```
## Forecasting Horizon
The forecasting horizon (`fh`) specifies which future time points to predict:
```python
# Relative horizon (next 3 steps)
fh = [1, 2, 3]
# Absolute horizon (specific time indices)
from aeon.forecasting.base import ForecastingHorizon
fh = ForecastingHorizon([11, 12, 13], is_relative=False)
```
## Model Selection
- **Baseline**: NaiveForecaster with seasonal strategy
- **Linear patterns**: ARIMA
- **Trend + seasonality**: ETS
- **Regime changes**: TAR, AutoTAR
- **Complex patterns**: TCNForecaster
- **Probabilistic**: DeepARNetwork
- **Long sequences**: TCNForecaster
- **Short sequences**: ARIMA, ETS
## Evaluation Metrics
Use standard forecasting metrics:
```python
from aeon.performance_metrics.forecasting import (
mean_absolute_error,
mean_squared_error,
mean_absolute_percentage_error
)
# Calculate error
mae = mean_absolute_error(y_true, y_pred)
mse = mean_squared_error(y_true, y_pred)
mape = mean_absolute_percentage_error(y_true, y_pred)
```
## Exogenous Variables
Many forecasters support exogenous features:
```python
# Train with exogenous variables
forecaster.fit(y, X=X_train)
# Predict requires future exogenous values
y_pred = forecaster.predict(fh=[1, 2, 3], X=X_test)
```
## Base Classes
- `BaseForecaster` - Abstract base for all forecasters
- `BaseDeepForecaster` - Base for deep learning forecasters
Extend these to implement custom forecasting algorithms.

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# Deep Learning Networks
Aeon provides neural network architectures specifically designed for time series tasks. These networks serve as building blocks for classification, regression, clustering, and forecasting.
## Core Network Architectures
### Convolutional Networks
**FCNNetwork** - Fully Convolutional Network
- Three convolutional blocks with batch normalization
- Global average pooling for dimensionality reduction
- **Use when**: Need simple yet effective CNN baseline
**ResNetNetwork** - Residual Network
- Residual blocks with skip connections
- Prevents vanishing gradients in deep networks
- **Use when**: Deep networks needed, training stability important
**InceptionNetwork** - Inception Modules
- Multi-scale feature extraction with parallel convolutions
- Different kernel sizes capture patterns at various scales
- **Use when**: Patterns exist at multiple temporal scales
**TimeCNNNetwork** - Standard CNN
- Basic convolutional architecture
- **Use when**: Simple CNN sufficient, interpretability valued
**DisjointCNNNetwork** - Separate Pathways
- Disjoint convolutional pathways
- **Use when**: Different feature extraction strategies needed
**DCNNNetwork** - Dilated CNN
- Dilated convolutions for large receptive fields
- **Use when**: Long-range dependencies without many layers
### Recurrent Networks
**RecurrentNetwork** - RNN/LSTM/GRU
- Configurable cell type (RNN, LSTM, GRU)
- Sequential modeling of temporal dependencies
- **Use when**: Sequential dependencies critical, variable-length series
### Temporal Convolutional Network
**TCNNetwork** - Temporal Convolutional Network
- Dilated causal convolutions
- Large receptive field without recurrence
- **Use when**: Long sequences, need parallelizable architecture
### Multi-Layer Perceptron
**MLPNetwork** - Basic Feedforward
- Simple fully-connected layers
- Flattens time series before processing
- **Use when**: Baseline needed, computational limits, or simple patterns
## Encoder-Based Architectures
Networks designed for representation learning and clustering.
### Autoencoder Variants
**EncoderNetwork** - Generic Encoder
- Flexible encoder structure
- **Use when**: Custom encoding needed
**AEFCNNetwork** - FCN-based Autoencoder
- Fully convolutional encoder-decoder
- **Use when**: Need convolutional representation learning
**AEResNetNetwork** - ResNet Autoencoder
- Residual blocks in encoder-decoder
- **Use when**: Deep autoencoding with skip connections
**AEDCNNNetwork** - Dilated CNN Autoencoder
- Dilated convolutions for compression
- **Use when**: Need large receptive field in autoencoder
**AEDRNNNetwork** - Dilated RNN Autoencoder
- Dilated recurrent connections
- **Use when**: Sequential patterns with long-range dependencies
**AEBiGRUNetwork** - Bidirectional GRU
- Bidirectional recurrent encoding
- **Use when**: Context from both directions helpful
**AEAttentionBiGRUNetwork** - Attention + BiGRU
- Attention mechanism on BiGRU outputs
- **Use when**: Need to focus on important time steps
## Specialized Architectures
**LITENetwork** - Lightweight Inception Time Ensemble
- Efficient inception-based architecture
- LITEMV variant for multivariate series
- **Use when**: Need efficiency with strong performance
**DeepARNetwork** - Probabilistic Forecasting
- Autoregressive RNN for forecasting
- Produces probabilistic predictions
- **Use when**: Need forecast uncertainty quantification
## Usage with Estimators
Networks are typically used within estimators, not directly:
```python
from aeon.classification.deep_learning import FCNClassifier
from aeon.regression.deep_learning import ResNetRegressor
from aeon.clustering.deep_learning import AEFCNClusterer
# Classification with FCN
clf = FCNClassifier(n_epochs=100, batch_size=16)
clf.fit(X_train, y_train)
# Regression with ResNet
reg = ResNetRegressor(n_epochs=100)
reg.fit(X_train, y_train)
# Clustering with autoencoder
clusterer = AEFCNClusterer(n_clusters=3, n_epochs=100)
labels = clusterer.fit_predict(X_train)
```
## Custom Network Configuration
Many networks accept configuration parameters:
```python
# Configure FCN layers
clf = FCNClassifier(
n_epochs=200,
batch_size=32,
kernel_size=[7, 5, 3], # Kernel sizes for each layer
n_filters=[128, 256, 128], # Filters per layer
learning_rate=0.001
)
```
## Base Classes
- `BaseDeepLearningNetwork` - Abstract base for all networks
- `BaseDeepRegressor` - Base for deep regression
- `BaseDeepClassifier` - Base for deep classification
- `BaseDeepForecaster` - Base for deep forecasting
Extend these to implement custom architectures.
## Training Considerations
### Hyperparameters
Key hyperparameters to tune:
- `n_epochs` - Training iterations (50-200 typical)
- `batch_size` - Samples per batch (16-64 typical)
- `learning_rate` - Step size (0.0001-0.01)
- Network-specific: layers, filters, kernel sizes
### Callbacks
Many networks support callbacks for training monitoring:
```python
from tensorflow.keras.callbacks import EarlyStopping, ReduceLROnPlateau
clf = FCNClassifier(
n_epochs=200,
callbacks=[
EarlyStopping(patience=20, restore_best_weights=True),
ReduceLROnPlateau(patience=10, factor=0.5)
]
)
```
### GPU Acceleration
Deep learning networks benefit from GPU:
```python
import os
os.environ['CUDA_VISIBLE_DEVICES'] = '0' # Use first GPU
# Networks automatically use GPU if available
clf = InceptionTimeClassifier(n_epochs=100)
clf.fit(X_train, y_train)
```
## Architecture Selection
### By Task:
**Classification**: InceptionNetwork, ResNetNetwork, FCNNetwork
**Regression**: InceptionNetwork, ResNetNetwork, TCNNetwork
**Forecasting**: TCNNetwork, DeepARNetwork, RecurrentNetwork
**Clustering**: AEFCNNetwork, AEResNetNetwork, AEAttentionBiGRUNetwork
### By Data Characteristics:
**Long sequences**: TCNNetwork, DCNNNetwork (dilated convolutions)
**Short sequences**: MLPNetwork, FCNNetwork
**Multivariate**: InceptionNetwork, FCNNetwork, LITENetwork
**Variable length**: RecurrentNetwork with masking
**Multi-scale patterns**: InceptionNetwork
### By Computational Resources:
**Limited compute**: MLPNetwork, LITENetwork
**Moderate compute**: FCNNetwork, TimeCNNNetwork
**High compute available**: InceptionNetwork, ResNetNetwork
**GPU available**: Any deep network (major speedup)
## Best Practices
### 1. Data Preparation
Normalize input data:
```python
from aeon.transformations.collection import Normalizer
normalizer = Normalizer()
X_train_norm = normalizer.fit_transform(X_train)
X_test_norm = normalizer.transform(X_test)
```
### 2. Training/Validation Split
Use validation set for early stopping:
```python
from sklearn.model_selection import train_test_split
X_train_fit, X_val, y_train_fit, y_val = train_test_split(
X_train, y_train, test_size=0.2, stratify=y_train
)
clf = FCNClassifier(n_epochs=200)
clf.fit(X_train_fit, y_train_fit, validation_data=(X_val, y_val))
```
### 3. Start Simple
Begin with simpler architectures before complex ones:
1. Try MLPNetwork or FCNNetwork first
2. If insufficient, try ResNetNetwork or InceptionNetwork
3. Consider ensembles if single models insufficient
### 4. Hyperparameter Tuning
Use grid search or random search:
```python
from sklearn.model_selection import GridSearchCV
param_grid = {
'n_epochs': [100, 200],
'batch_size': [16, 32],
'learning_rate': [0.001, 0.0001]
}
clf = FCNClassifier()
grid = GridSearchCV(clf, param_grid, cv=3)
grid.fit(X_train, y_train)
```
### 5. Regularization
Prevent overfitting:
- Use dropout (if network supports)
- Early stopping
- Data augmentation (if available)
- Reduce model complexity
### 6. Reproducibility
Set random seeds:
```python
import numpy as np
import random
import tensorflow as tf
seed = 42
np.random.seed(seed)
random.seed(seed)
tf.random.set_seed(seed)
```

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# Time Series Regression
Aeon provides time series regressors across 9 categories for predicting continuous values from temporal sequences.
## Convolution-Based Regressors
Apply convolutional kernels for feature extraction:
- `HydraRegressor` - Multi-resolution dilated convolutions
- `RocketRegressor` - Random convolutional kernels
- `MiniRocketRegressor` - Simplified ROCKET for speed
- `MultiRocketRegressor` - Combined ROCKET variants
- `MultiRocketHydraRegressor` - Merges ROCKET and Hydra approaches
**Use when**: Need fast regression with strong baseline performance.
## Deep Learning Regressors
Neural architectures for end-to-end temporal regression:
- `FCNRegressor` - Fully convolutional network
- `ResNetRegressor` - Residual blocks with skip connections
- `InceptionTimeRegressor` - Multi-scale inception modules
- `TimeCNNRegressor` - Standard CNN architecture
- `RecurrentRegressor` - RNN/LSTM/GRU variants
- `MLPRegressor` - Multi-layer perceptron
- `EncoderRegressor` - Generic encoder wrapper
- `LITERegressor` - Lightweight inception time ensemble
- `DisjointCNNRegressor` - Specialized CNN architecture
**Use when**: Large datasets, complex patterns, or need feature learning.
## Distance-Based Regressors
k-nearest neighbors with temporal distance metrics:
- `KNeighborsTimeSeriesRegressor` - k-NN with DTW, LCSS, ERP, or other distances
**Use when**: Small datasets, local similarity patterns, or interpretable predictions.
## Feature-Based Regressors
Extract statistical features before regression:
- `Catch22Regressor` - 22 canonical time-series characteristics
- `FreshPRINCERegressor` - Pipeline combining multiple feature extractors
- `SummaryRegressor` - Summary statistics features
- `TSFreshRegressor` - Automated tsfresh feature extraction
**Use when**: Need interpretable features or domain-specific feature engineering.
## Hybrid Regressors
Combine multiple approaches:
- `RISTRegressor` - Randomized Interval-Shapelet Transformation
**Use when**: Benefit from combining interval and shapelet methods.
## Interval-Based Regressors
Extract features from time intervals:
- `CanonicalIntervalForestRegressor` - Random intervals with decision trees
- `DrCIFRegressor` - Diverse Representation CIF
- `TimeSeriesForestRegressor` - Random interval ensemble
- `RandomIntervalRegressor` - Simple interval-based approach
- `RandomIntervalSpectralEnsembleRegressor` - Spectral interval features
- `QUANTRegressor` - Quantile-based interval features
**Use when**: Predictive patterns occur in specific time windows.
## Shapelet-Based Regressors
Use discriminative subsequences for prediction:
- `RDSTRegressor` - Random Dilated Shapelet Transform
**Use when**: Need phase-invariant discriminative patterns.
## Composition Tools
Build custom regression pipelines:
- `RegressorPipeline` - Chain transformers with regressors
- `RegressorEnsemble` - Weighted ensemble with learnable weights
- `SklearnRegressorWrapper` - Adapt sklearn regressors for time series
## Utilities
- `DummyRegressor` - Baseline strategies (mean, median)
- `BaseRegressor` - Abstract base for custom regressors
- `BaseDeepRegressor` - Base for deep learning regressors
## Quick Start
```python
from aeon.regression.convolution_based import RocketRegressor
from aeon.datasets import load_regression
# Load data
X_train, y_train = load_regression("Covid3Month", split="train")
X_test, y_test = load_regression("Covid3Month", split="test")
# Train and predict
reg = RocketRegressor()
reg.fit(X_train, y_train)
predictions = reg.predict(X_test)
```
## Algorithm Selection
- **Speed priority**: MiniRocketRegressor
- **Accuracy priority**: InceptionTimeRegressor, MultiRocketHydraRegressor
- **Interpretability**: Catch22Regressor, SummaryRegressor
- **Small data**: KNeighborsTimeSeriesRegressor
- **Large data**: Deep learning regressors, ROCKET variants
- **Interval patterns**: DrCIFRegressor, CanonicalIntervalForestRegressor

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# Time Series Segmentation
Aeon provides algorithms to partition time series into regions with distinct characteristics, identifying change points and boundaries.
## Segmentation Algorithms
### Binary Segmentation
- `BinSegmenter` - Recursive binary segmentation
- Iteratively splits series at most significant change points
- Parameters: `n_segments`, `cost_function`
- **Use when**: Known number of segments, hierarchical structure
### Classification-Based
- `ClaSPSegmenter` - Classification Score Profile
- Uses classification performance to identify boundaries
- Discovers segments where classification distinguishes neighbors
- **Use when**: Segments have different temporal patterns
### Fast Pattern-Based
- `FLUSSSegmenter` - Fast Low-cost Unipotent Semantic Segmentation
- Efficient semantic segmentation using arc crossings
- Based on matrix profile
- **Use when**: Large time series, need speed and pattern discovery
### Information Theory
- `InformationGainSegmenter` - Information gain maximization
- Finds boundaries maximizing information gain
- **Use when**: Statistical differences between segments
### Gaussian Modeling
- `GreedyGaussianSegmenter` - Greedy Gaussian approximation
- Models segments as Gaussian distributions
- Incrementally adds change points
- **Use when**: Segments follow Gaussian distributions
### Hierarchical Agglomerative
- `EAggloSegmenter` - Bottom-up merging approach
- Estimates change points via agglomeration
- **Use when**: Want hierarchical segmentation structure
### Hidden Markov Models
- `HMMSegmenter` - HMM with Viterbi decoding
- Probabilistic state-based segmentation
- **Use when**: Segments represent hidden states
### Dimensionality-Based
- `HidalgoSegmenter` - Heterogeneous Intrinsic Dimensionality Algorithm
- Detects changes in local dimensionality
- **Use when**: Dimensionality shifts between segments
### Baseline
- `RandomSegmenter` - Random change point generation
- **Use when**: Need null hypothesis baseline
## Quick Start
```python
from aeon.segmentation import ClaSPSegmenter
import numpy as np
# Create time series with regime changes
y = np.concatenate([
np.sin(np.linspace(0, 10, 100)), # Segment 1
np.cos(np.linspace(0, 10, 100)), # Segment 2
np.sin(2 * np.linspace(0, 10, 100)) # Segment 3
])
# Segment the series
segmenter = ClaSPSegmenter()
change_points = segmenter.fit_predict(y)
print(f"Detected change points: {change_points}")
```
## Output Format
Segmenters return change point indices:
```python
# change_points = [100, 200] # Boundaries between segments
# This divides series into: [0:100], [100:200], [200:end]
```
## Algorithm Selection
- **Speed priority**: FLUSSSegmenter, BinSegmenter
- **Accuracy priority**: ClaSPSegmenter, HMMSegmenter
- **Known segment count**: BinSegmenter with n_segments parameter
- **Unknown segment count**: ClaSPSegmenter, InformationGainSegmenter
- **Pattern changes**: FLUSSSegmenter, ClaSPSegmenter
- **Statistical changes**: InformationGainSegmenter, GreedyGaussianSegmenter
- **State transitions**: HMMSegmenter
## Common Use Cases
### Regime Change Detection
Identify when time series behavior fundamentally changes:
```python
from aeon.segmentation import InformationGainSegmenter
segmenter = InformationGainSegmenter(k=3) # Up to 3 change points
change_points = segmenter.fit_predict(stock_prices)
```
### Activity Segmentation
Segment sensor data into activities:
```python
from aeon.segmentation import ClaSPSegmenter
segmenter = ClaSPSegmenter()
boundaries = segmenter.fit_predict(accelerometer_data)
```
### Seasonal Boundary Detection
Find season transitions in time series:
```python
from aeon.segmentation import HMMSegmenter
segmenter = HMMSegmenter(n_states=4) # 4 seasons
segments = segmenter.fit_predict(temperature_data)
```
## Evaluation Metrics
Use segmentation quality metrics:
```python
from aeon.benchmarking.metrics.segmentation import (
count_error,
hausdorff_error
)
# Count error: difference in number of change points
count_err = count_error(y_true, y_pred)
# Hausdorff: maximum distance between predicted and true points
hausdorff_err = hausdorff_error(y_true, y_pred)
```
## Best Practices
1. **Normalize data**: Ensures change detection not dominated by scale
2. **Choose appropriate metric**: Different algorithms optimize different criteria
3. **Validate segments**: Visualize to verify meaningful boundaries
4. **Handle noise**: Consider smoothing before segmentation
5. **Domain knowledge**: Use expected segment count if known
6. **Parameter tuning**: Adjust sensitivity parameters (thresholds, penalties)
## Visualization
```python
import matplotlib.pyplot as plt
plt.figure(figsize=(12, 4))
plt.plot(y, label='Time Series')
for cp in change_points:
plt.axvline(cp, color='r', linestyle='--', label='Change Point')
plt.legend()
plt.show()
```

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# Similarity Search
Aeon provides tools for finding similar patterns within and across time series, including subsequence search, motif discovery, and approximate nearest neighbors.
## Subsequence Nearest Neighbors (SNN)
Find most similar subsequences within a time series.
### MASS Algorithm
- `MassSNN` - Mueen's Algorithm for Similarity Search
- Fast normalized cross-correlation for similarity
- Computes distance profile efficiently
- **Use when**: Need exact nearest neighbor distances, large series
### STOMP-Based Motif Discovery
- `StompMotif` - Discovers recurring patterns (motifs)
- Finds top-k most similar subsequence pairs
- Based on matrix profile computation
- **Use when**: Want to discover repeated patterns
### Brute Force Baseline
- `DummySNN` - Exhaustive distance computation
- Computes all pairwise distances
- **Use when**: Small series, need exact baseline
## Collection-Level Search
Find similar time series across collections.
### Approximate Nearest Neighbors (ANN)
- `RandomProjectionIndexANN` - Locality-sensitive hashing
- Uses random projections with cosine similarity
- Builds index for fast approximate search
- **Use when**: Large collection, speed more important than exactness
## Quick Start: Motif Discovery
```python
from aeon.similarity_search import StompMotif
import numpy as np
# Create time series with repeated patterns
pattern = np.sin(np.linspace(0, 2*np.pi, 50))
y = np.concatenate([
pattern + np.random.normal(0, 0.1, 50),
np.random.normal(0, 1, 100),
pattern + np.random.normal(0, 0.1, 50),
np.random.normal(0, 1, 100)
])
# Find top-3 motifs
motif_finder = StompMotif(window_size=50, k=3)
motifs = motif_finder.fit_predict(y)
# motifs contains indices of motif occurrences
for i, (idx1, idx2) in enumerate(motifs):
print(f"Motif {i+1} at positions {idx1} and {idx2}")
```
## Quick Start: Subsequence Search
```python
from aeon.similarity_search import MassSNN
import numpy as np
# Time series to search within
y = np.sin(np.linspace(0, 20, 500))
# Query subsequence
query = np.sin(np.linspace(0, 2, 50))
# Find nearest subsequences
searcher = MassSNN()
distances = searcher.fit_transform(y, query)
# Find best match
best_match_idx = np.argmin(distances)
print(f"Best match at index {best_match_idx}")
```
## Quick Start: Approximate NN on Collections
```python
from aeon.similarity_search import RandomProjectionIndexANN
from aeon.datasets import load_classification
# Load time series collection
X_train, _ = load_classification("GunPoint", split="train")
# Build index
ann = RandomProjectionIndexANN(n_projections=8, n_bits=4)
ann.fit(X_train)
# Find approximate nearest neighbors
query = X_train[0]
neighbors, distances = ann.kneighbors(query, k=5)
```
## Matrix Profile
The matrix profile is a fundamental data structure for many similarity search tasks:
- **Distance Profile**: Distances from a query to all subsequences
- **Matrix Profile**: Minimum distance for each subsequence to any other
- **Motif**: Pair of subsequences with minimum distance
- **Discord**: Subsequence with maximum minimum distance (anomaly)
```python
from aeon.similarity_search import StompMotif
# Compute matrix profile and find motifs/discords
mp = StompMotif(window_size=50)
mp.fit(y)
# Access matrix profile
profile = mp.matrix_profile_
profile_indices = mp.matrix_profile_index_
# Find discords (anomalies)
discord_idx = np.argmax(profile)
```
## Algorithm Selection
- **Exact subsequence search**: MassSNN
- **Motif discovery**: StompMotif
- **Anomaly detection**: Matrix profile (see anomaly_detection.md)
- **Fast approximate search**: RandomProjectionIndexANN
- **Small data**: DummySNN for exact results
## Use Cases
### Pattern Matching
Find where a pattern occurs in a long series:
```python
# Find heartbeat pattern in ECG data
searcher = MassSNN()
distances = searcher.fit_transform(ecg_data, heartbeat_pattern)
occurrences = np.where(distances < threshold)[0]
```
### Motif Discovery
Identify recurring patterns:
```python
# Find repeated behavioral patterns
motif_finder = StompMotif(window_size=100, k=5)
motifs = motif_finder.fit_predict(activity_data)
```
### Time Series Retrieval
Find similar time series in database:
```python
# Build searchable index
ann = RandomProjectionIndexANN()
ann.fit(time_series_database)
# Query for similar series
neighbors = ann.kneighbors(query_series, k=10)
```
## Best Practices
1. **Window size**: Critical parameter for subsequence methods
- Too small: Captures noise
- Too large: Misses fine-grained patterns
- Rule of thumb: 10-20% of series length
2. **Normalization**: Most methods assume z-normalized subsequences
- Handles amplitude variations
- Focus on shape similarity
3. **Distance metrics**: Different metrics for different needs
- Euclidean: Fast, shape-based
- DTW: Handles temporal warping
- Cosine: Scale-invariant
4. **Exclusion zone**: For motif discovery, exclude trivial matches
- Typically set to 0.5-1.0 × window_size
- Prevents finding overlapping occurrences
5. **Performance**:
- MASS is O(n log n) vs O(n²) brute force
- ANN trades accuracy for speed
- GPU acceleration available for some methods

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# Transformations
Aeon provides extensive transformation capabilities for preprocessing, feature extraction, and representation learning from time series data.
## Transformation Types
Aeon distinguishes between:
- **CollectionTransformers**: Transform multiple time series (collections)
- **SeriesTransformers**: Transform individual time series
## Collection Transformers
### Convolution-Based Feature Extraction
Fast, scalable feature generation using random kernels:
- `RocketTransformer` - Random convolutional kernels
- `MiniRocketTransformer` - Simplified ROCKET for speed
- `MultiRocketTransformer` - Enhanced ROCKET variant
- `HydraTransformer` - Multi-resolution dilated convolutions
- `MultiRocketHydraTransformer` - Combines ROCKET and Hydra
- `ROCKETGPU` - GPU-accelerated variant
**Use when**: Need fast, scalable features for any ML algorithm, strong baseline performance.
### Statistical Feature Extraction
Domain-agnostic features based on time series characteristics:
- `Catch22` - 22 canonical time-series characteristics
- `TSFresh` - Comprehensive automated feature extraction (100+ features)
- `TSFreshRelevant` - Feature extraction with relevance filtering
- `SevenNumberSummary` - Descriptive statistics (mean, std, quantiles)
**Use when**: Need interpretable features, domain-agnostic approach, or feeding traditional ML.
### Dictionary-Based Representations
Symbolic approximations for discrete representations:
- `SAX` - Symbolic Aggregate approXimation
- `PAA` - Piecewise Aggregate Approximation
- `SFA` - Symbolic Fourier Approximation
- `SFAFast` - Optimized SFA
- `SFAWhole` - SFA on entire series (no windowing)
- `BORF` - Bag-of-Receptive-Fields
**Use when**: Need discrete/symbolic representation, dimensionality reduction, interpretability.
### Shapelet-Based Features
Discriminative subsequence extraction:
- `RandomShapeletTransform` - Random discriminative shapelets
- `RandomDilatedShapeletTransform` - Dilated shapelets for multi-scale
- `SAST` - Scalable And Accurate Subsequence Transform
- `RSAST` - Randomized SAST
**Use when**: Need interpretable discriminative patterns, phase-invariant features.
### Interval-Based Features
Statistical summaries from time intervals:
- `RandomIntervals` - Features from random intervals
- `SupervisedIntervals` - Supervised interval selection
- `QUANTTransformer` - Quantile-based interval features
**Use when**: Predictive patterns localized to specific windows.
### Preprocessing Transformations
Data preparation and normalization:
- `MinMaxScaler` - Scale to [0, 1] range
- `Normalizer` - Z-normalization (zero mean, unit variance)
- `Centerer` - Center to zero mean
- `SimpleImputer` - Fill missing values
- `DownsampleTransformer` - Reduce temporal resolution
- `Tabularizer` - Convert time series to tabular format
**Use when**: Need standardization, missing value handling, format conversion.
### Specialized Transformations
Advanced analysis methods:
- `MatrixProfile` - Computes distance profiles for pattern discovery
- `DWTTransformer` - Discrete Wavelet Transform
- `AutocorrelationFunctionTransformer` - ACF computation
- `Dobin` - Distance-based Outlier BasIs using Neighbors
- `SignatureTransformer` - Path signature methods
- `PLATransformer` - Piecewise Linear Approximation
### Class Imbalance Handling
- `ADASYN` - Adaptive Synthetic Sampling
- `SMOTE` - Synthetic Minority Over-sampling
- `OHIT` - Over-sampling with Highly Imbalanced Time series
**Use when**: Classification with imbalanced classes.
### Pipeline Composition
- `CollectionTransformerPipeline` - Chain multiple transformers
## Series Transformers
Transform individual time series (e.g., for preprocessing in forecasting).
### Statistical Analysis
- `AutoCorrelationSeriesTransformer` - Autocorrelation
- `StatsModelsACF` - ACF using statsmodels
- `StatsModelsPACF` - Partial autocorrelation
### Smoothing and Filtering
- `ExponentialSmoothing` - Exponentially weighted moving average
- `MovingAverage` - Simple or weighted moving average
- `SavitzkyGolayFilter` - Polynomial smoothing
- `GaussianFilter` - Gaussian kernel smoothing
- `BKFilter` - Baxter-King bandpass filter
- `DiscreteFourierApproximation` - Fourier-based filtering
**Use when**: Need noise reduction, trend extraction, or frequency filtering.
### Dimensionality Reduction
- `PCASeriesTransformer` - Principal component analysis
- `PlASeriesTransformer` - Piecewise Linear Approximation
### Transformations
- `BoxCoxTransformer` - Variance stabilization
- `LogTransformer` - Logarithmic scaling
- `ClaSPTransformer` - Classification Score Profile
### Pipeline Composition
- `SeriesTransformerPipeline` - Chain series transformers
## Quick Start: Feature Extraction
```python
from aeon.transformations.collection.convolution_based import RocketTransformer
from aeon.classification.sklearn import RotationForest
from aeon.datasets import load_classification
# Load data
X_train, y_train = load_classification("GunPoint", split="train")
X_test, y_test = load_classification("GunPoint", split="test")
# Extract ROCKET features
rocket = RocketTransformer()
X_train_features = rocket.fit_transform(X_train)
X_test_features = rocket.transform(X_test)
# Use with any sklearn classifier
clf = RotationForest()
clf.fit(X_train_features, y_train)
accuracy = clf.score(X_test_features, y_test)
```
## Quick Start: Preprocessing Pipeline
```python
from aeon.transformations.collection import (
MinMaxScaler,
SimpleImputer,
CollectionTransformerPipeline
)
# Build preprocessing pipeline
pipeline = CollectionTransformerPipeline([
('imputer', SimpleImputer(strategy='mean')),
('scaler', MinMaxScaler())
])
X_transformed = pipeline.fit_transform(X_train)
```
## Quick Start: Series Smoothing
```python
from aeon.transformations.series import MovingAverage
# Smooth individual time series
smoother = MovingAverage(window_size=5)
y_smoothed = smoother.fit_transform(y)
```
## Algorithm Selection
### For Feature Extraction:
- **Speed + Performance**: MiniRocketTransformer
- **Interpretability**: Catch22, TSFresh
- **Dimensionality reduction**: PAA, SAX, PCA
- **Discriminative patterns**: Shapelet transforms
- **Comprehensive features**: TSFresh (with longer runtime)
### For Preprocessing:
- **Normalization**: Normalizer, MinMaxScaler
- **Smoothing**: MovingAverage, SavitzkyGolayFilter
- **Missing values**: SimpleImputer
- **Frequency analysis**: DWTTransformer, Fourier methods
### For Symbolic Representation:
- **Fast approximation**: PAA
- **Alphabet-based**: SAX
- **Frequency-based**: SFA, SFAFast
## Best Practices
1. **Fit on training data only**: Avoid data leakage
```python
transformer.fit(X_train)
X_train_tf = transformer.transform(X_train)
X_test_tf = transformer.transform(X_test)
```
2. **Pipeline composition**: Chain transformers for complex workflows
```python
pipeline = CollectionTransformerPipeline([
('imputer', SimpleImputer()),
('scaler', Normalizer()),
('features', RocketTransformer())
])
```
3. **Feature selection**: TSFresh can generate many features; consider selection
```python
from sklearn.feature_selection import SelectKBest
selector = SelectKBest(k=100)
X_selected = selector.fit_transform(X_features, y)
```
4. **Memory considerations**: Some transformers memory-intensive on large datasets
- Use MiniRocket instead of ROCKET for speed
- Consider downsampling for very long series
- Use ROCKETGPU for GPU acceleration
5. **Domain knowledge**: Choose transformations matching domain:
- Periodic data: Fourier-based methods
- Noisy data: Smoothing filters
- Spike detection: Wavelet transforms