# kmapper.Cover¶

class kmapper.Cover(n_cubes=10, perc_overlap=0.5, limits=None, verbose=0)[source]

Bases: `object`

Helper class that defines the default covering scheme

It calculates the cover based on the following formula for overlap. (https://arxiv.org/pdf/1706.00204.pdf)

```             |cube[i] intersection cube[i+1]|
overlap = --------------------------------------
|cube[i]|
```
Parameters
• n_cubes (int) – Number of hypercubes along each dimension. Sometimes referred to as resolution.

• perc_overlap (float) – Amount of overlap between adjacent cubes calculated only along 1 dimension.

• limits (Numpy Array (n_dim,2)) – (lower bound, upper bound) for every dimension If a value is set to float(‘inf’), the bound will be assumed to be the min/max value of the dimension Also, if limits == None, the limits are defined by the maximum and minimum value of the lens for all dimensions. i.e. [[min_1, max_1], [min_2, max_2], [min_3, max_3]]

Example

```>>> import numpy as np
>>> from kmapper.cover import Cover
>>> data = np.random.random((100,2))
>>> cov = Cover(n_cubes=15, perc_overlap=0.75)
>>> cube_centers = cov.fit(data)
>>> cov.transform_single(data, cube_centers)
array([[0.3594448 , 0.07428465],
[0.14490332, 0.01395559],
[0.94988668, 0.03983579],
[0.73517978, 0.09420806],
[0.16903735, 0.06901085],
[0.81578595, 0.10708731],
[0.26923572, 0.12216203],
[0.89203167, 0.0711279 ],
[0.80442115, 0.10220901],
[0.33210782, 0.04365007],
[0.52207707, 0.05892861],
[0.26589744, 0.08502856],
[0.02360067, 0.1263653 ],
[0.29855631, 0.01209373]])
>>> hyper_cubes = cov.transform(data, cube_centers)
```
__init__(n_cubes=10, perc_overlap=0.5, limits=None, verbose=0)[source]

Methods

 `__init__`([n_cubes, perc_overlap, limits, ...]) `find`(data_point) Finds the hypercubes that contain the given data point. `fit`(data) Fit a cover on the data. `fit_transform`(data) `transform`(data[, centers]) Find entries of all hypercubes. `transform_single`(data, center[, i]) Compute entries of data in hypercube centered at center
find(data_point)[source]

Finds the hypercubes that contain the given data point.

Parameters

data_point (array-like) – The data point to locate.

Returns

cube_ids (list of int) – list of hypercube indices, empty if the data point is outside the cover.

fit(data)[source]

Fit a cover on the data. This method constructs centers and radii in each dimension given the perc_overlap and n_cube.

Parameters

data (array-like) – Data to apply the cover to. Warning: First column must be an index column.

Returns

centers (list of arrays) – A list of centers for each cube

transform(data, centers=None)[source]

Find entries of all hypercubes. If centers=None, then use self.centers_ as computed in self.fit.

Empty hypercubes are removed from the result

Parameters
• data (array-like) – Data to find in entries in cube. Warning: first column must be index column.

• centers (list of array-like) – Center points for all cubes as returned by self.fit. Default is to use self.centers_.

Returns

hypercubes (list of array-like) – list of entries in each hypercube in data.

transform_single(data, center, i=0)[source]

Compute entries of data in hypercube centered at center

Parameters
• data (array-like) – Data to find in entries in cube. Warning: first column must be index column.

• center (array-like) – Center points for the cube. Cube is found as all data in [center-self.radius_, center+self.radius_]

• i (int, default 0) – Optional counter to aid in verbose debugging.