geometric_median#
- skfda.exploratory.stats.geometric_median(X, *, tol=1e-08, metric=LpDistance(p=2, vector_norm=None))[source]#
Compute the geometric median.
The sample geometric median is the point that minimizes the \(L_1\) norm of the vector of distances to all observations:
\[\underset{y \in L(\mathcal{T})}{\arg \min} \sum_{i=1}^N \left \| x_i-y \right \|\]The geometric median in the functional case is also described in [1]. Instead of the proposed algorithm, however, the current implementation uses the corrected Weiszfeld algorithm to compute the median.
- Parameters:
X (T) – Object containing different samples of a functional variable.
tol (float) – tolerance used to check convergence.
metric (Metric[T]) – metric used to compute the vector of distances. By default is the \(L_2\) distance.
- Returns:
Object containing the computed geometric median.
- Return type:
T
Example
>>> from skfda import FDataGrid >>> data_matrix = [[0.5, 1, 2, .5], [1.5, 1, 4, .5]] >>> X = FDataGrid(data_matrix) >>> median = geometric_median(X) >>> median.data_matrix[0, ..., 0] array([ 1. , 1. , 3. , 0.5])
See also
References