Landmark
landmark is a Python package that constructs a sequence of landmarks $L_k = ({x_1, x_2, \dots, x_k })$ from a point set $X \subset \mathbb{R}^d$ or metric space $(X, d_X)$ via furthest-first traversal:
$$ x_i = \mathop{\mathrm{arg min}}\limits_{x \in X} \mathop{} d_X(x, L_{i − 1}) $$
The resulting landmarks satisfy a number of convenient coverage and packing properties. Below is an example a data set $X$ (blue points), some sample landmarks $L$ (red), along with the coverage (yellow) and packing (orange) properties they obey.
The sequence formed by resulting landmarks, also called the greedy permutation, can be used to approximate a number of classical problems, such as the traveling saleman problem, the metric k-center clustering problem, and various proximity / range searching problems.
Installation
The package can be installed with pip:
python -m pip install scikit-landmark
Usage
Given a point cloud $X \in \mathbb{R}^{n \times d}$ represented as a numpy matrix with $n$ points in $d$ dimensions, the indices of the landmarks can be found with the landmarks function:
from landmark import landmarks
X = np.random.uniform(size=(50,2))
ind = landmarks(X, k = 10) ## Finds the indices of 25 landmarks
The first $k$-indices of ind are equivalent to the $k$-th prefix of the greedy permutation. You can get their covering radii and their predecessors by specifying full_output=True:
ind, info = landmarks(X, k = 10, full_output = True)
print(ind) ## prefix indices
print(info['radii']) ## insertion radii
print(info['predecessors']) ## predecessor map
For other usages, see the documentation.
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Metadata
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Release files for scikit-landmark 0.1.2
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