# Calinski Harabasz Score¶

## Module Interface¶

class torchmetrics.clustering.CalinskiHarabaszScore(**kwargs)[source]

Compute Calinski Harabasz Score (also known as variance ratio criterion) for clustering algorithms.

$CHS(X, L) = \frac{B(X, L) \cdot (n_\text{samples} - n_\text{labels})}{W(X, L) \cdot (n_\text{labels} - 1)}$

where $$B(X, L)$$ is the between-cluster dispersion, which is the squared distance between the cluster centers and the dataset mean, weighted by the size of the clusters, $$n_\text{samples}$$ is the number of samples, $$n_\text{labels}$$ is the number of labels, and $$W(X, L)$$ is the within-cluster dispersion e.g. the sum of squared distances between each samples and its closest cluster center.

This clustering metric is an intrinsic measure, because it does not rely on ground truth labels for the evaluation. Instead it examines how well the clusters are separated from each other. The score is higher when clusters are dense and well separated, which relates to a standard concept of a cluster.

As input to forward and update the metric accepts the following input:

• data (Tensor): float tensor with shape (N,d) with the embedded data. d is the dimensionality of the embedding space.

• labels (Tensor): single integer tensor with shape (N,) with cluster labels

As output of forward and compute the metric returns the following output:

Parameters:

kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Example::
>>> import torch
>>> from torchmetrics.clustering import CalinskiHarabaszScore
>>> _ = torch.manual_seed(42)
>>> data = torch.randn(10, 3)
>>> labels = torch.randint(3, (10,))
>>> metric = CalinskiHarabaszScore()
>>> metric(data, labels)
tensor(3.0053)

plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.clustering import CalinskiHarabaszScore
>>> metric = CalinskiHarabaszScore()
>>> metric.update(torch.randn(10, 3), torch.randint(0, 2, (10,)))
>>> fig_, ax_ = metric.plot(metric.compute())

>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.clustering import CalinskiHarabaszScore
>>> metric = CalinskiHarabaszScore()
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(torch.randn(10, 3), torch.randint(0, 2, (10,))))
>>> fig_, ax_ = metric.plot(values)


## Functional Interface¶

torchmetrics.functional.clustering.calinski_harabasz_score(data, labels)[source]

Compute the Calinski Harabasz Score (also known as variance ratio criterion) for clustering algorithms.

Parameters:
Return type:

Tensor

Returns:

Scalar tensor with the Calinski Harabasz Score

Example

>>> import torch
>>> from torchmetrics.functional.clustering import calinski_harabasz_score
>>> _ = torch.manual_seed(42)
>>> data = torch.randn(10, 3)
>>> labels = torch.randint(0, 2, (10,))
>>> calinski_harabasz_score(data, labels)
tensor(3.4998)