pyriemann.embedding.LocallyLinearEmbedding¶
- class pyriemann.embedding.LocallyLinearEmbedding(n_components=2, n_neighbors=5, metric='riemann', reg=0.001)¶
Locally Linear Embedding (LLE) of SPD matrices.
As proposed in [1], Locally Linear Embedding (LLE) is a non-linear, neighborhood-preserving dimensionality reduction algorithm which consists of three main steps. For each point x,
find its k nearest neighbors KNN(x) and
calculate the best reconstruction of x based on its KNN.
Then calculate a low-dimensional embedding for all points based on the weights in step 2.
This implementation using SPD matrices is based on [2].
- Parameters
- n_componentsint, default=2
Dimensionality of projected space.
- n_neighborsint, default=5
Number of neighbors for reconstruction of each point.
- metric{‘riemann’, ‘logeuclid’, ‘euclid’}, default: ‘riemann’
Metric used for KNN and Kernel estimation.
- regfloat, default=1e-3
Regularization parameter.
Notes
New in version 0.3.
References
- 1
Nonlinear Dimensionality Reduction by Locally Linear Embedding S. Roweis and L. K. Saul, in Science, Vol 290, Issue 5500, pp. 2323-2326, 2000.
- 2
Clustering and dimensionality reduction on Riemannian manifolds A. Goh and R. Vidal, in 2008 IEEE Conference on Computer Vision and Pattern Recognition
- Attributes
- embedding_ndarray, shape (n_matrices, n_components)
Stores the embedding vectors.
- error_float
Reconstruction error associated with embedding_.
- data_ndarray, shape (n_matrices, n_channels, n_channels)
Training data.
- __init__(n_components=2, n_neighbors=5, metric='riemann', reg=0.001)¶
- fit(X, y=None)¶
Fit the model from data in X.
- Parameters
- Xndarray, shape (n_matrices, n_channels, n_channels)
Set of SPD matrices.
- yNone
Not used, here for compatibility with sklearn API.
- Returns
- selfobject
Returns the instance itself.
- fit_transform(X, y=None)¶
Calculate the coordinates of the embedded points.
- Parameters
- Xndarray, shape (n_matrices, n_channels, n_channels)
Set of SPD matrices.
- yNone
Not used, here for compatibility with sklearn API.
- Returns
- X_newndarray, shape (n_matrices, n_components)
Coordinates of embedded matrices.
- get_params(deep=True)¶
Get parameters for this estimator.
- Parameters
- deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
- Returns
- paramsdict
Parameter names mapped to their values.
- set_params(**params)¶
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline). The latter have parameters of the form<component>__<parameter>so that it’s possible to update each component of a nested object.- Parameters
- **paramsdict
Estimator parameters.
- Returns
- selfestimator instance
Estimator instance.
- transform(X, y=None)¶
Calculate embedding coordinates.
Calculate embedding coordinates for new data points based on fitted points.
- Parameters
- Xndarray, shape (n_matrices, n_channels, n_channels)
Set of SPD matrices.
- yNone
Not used, here for compatibility with sklearn API.
- Returns
- X_newndarray, shape (n_matrices, n_components)
Coordinates of embedded matrices.