# Dunn Index¶

## Module Interface¶

class torchmetrics.clustering.DunnIndex(p=2, **kwargs)[source]

Compute Dunn Index.

$DI_m = \frac{\min_{1\leq i<j\leq m} \delta(C_i,C_j)}{\max_{1\leq k\leq m} \Delta_k}$

Where $$C_i$$ is a cluster of tensors, $$C_j$$ is a cluster of tensors, and $$\delta(C_i,C_j)$$ is the intercluster distance metric for $$m$$ clusters.

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 DunnIndex
>>> data = torch.tensor([[0, 0], [0.5, 0], [1, 0], [0.5, 1]])
>>> labels = torch.tensor([0, 0, 0, 1])
>>> dunn_index = DunnIndex(p=2)
>>> dunn_index(data, labels)
tensor(2.)

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 DunnIndex
>>> data = torch.tensor([[0, 0], [0.5, 0], [1, 0], [0.5, 1]])
>>> labels = torch.tensor([0, 0, 0, 1])
>>> metric = DunnIndex(p=2)
>>> metric.update(data, labels)
>>> fig_, ax_ = metric.plot(metric.compute())

>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.clustering import DunnIndex
>>> metric = DunnIndex(p=2)
>>> 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.dunn_index(data, labels, p=2)[source]

Compute the Dunn index.

Parameters:
Return type:

Tensor

Returns:

scalar tensor with the dunn index

Example

>>> from torchmetrics.functional.clustering import dunn_index
>>> data = torch.tensor([[0, 0], [0.5, 0], [1, 0], [0.5, 1]])
>>> labels = torch.tensor([0, 0, 0, 1])
>>> dunn_index(data, labels)
tensor(2.)