Choosing an Index

Each cluster validity index emphasizes different properties of a partition. Values from different index families are not on a common scale, so compare candidate partitions with the same index rather than comparing one index’s number directly with another’s.

The following operation support describes the default NumPy backend. Every listed index supports batch evaluation.

Implemented indices

Index	Name	Prefer	Range	Incremental	Remove/merge/split
CH	Calinski–Harabasz	Larger	[0, inf)	Yes	Yes
CONN	Connectivity	Larger	[0, 1]	FuzzyART Backend Only	No
cSIL	Centroid-based Silhouette	Larger	[-1, 1]	Yes	Yes
DB	Davies–Bouldin	Smaller	[0, inf)	Yes	Yes
GD43	Generalized Dunn 43	Larger	[0, inf)	Yes	Yes
GD53	Generalized Dunn 53	Larger	[0, inf)	Yes	Yes
PS	Partition Separation	Larger	[0, 1]	Yes	Yes
rCIP	Representative Cross Information Potential	Smaller	[0, inf)	Yes	Yes
WB	Within/Between	Smaller	[0, inf)	Yes	Yes
XB	Xie–Beni	Smaller	[0, inf)	Yes	Yes

Optional optimization coverage

Index	Numba batch	Numba sample updates	Numba remove/merge	JAX batch	JAX streaming
CH	Yes	Unchanged	Unchanged	Yes	Capacity
CONN	Unavailable	Unavailable	Unavailable	Unavailable	Unavailable
cSIL	Yes	Unchanged	Unchanged	Unavailable	Unavailable
DB	Yes	Distances	Distances	Unavailable	Unavailable
GD43	Yes	Distances	Distances	Unavailable	Unavailable
GD53	Yes	Unchanged	Unchanged	Unavailable	Unavailable
PS	Yes	Distances	Distances	Unavailable	Unavailable
rCIP	Unavailable	Unavailable	Unavailable	Unavailable	Unavailable
WB	Yes	Unchanged	Unchanged	Yes	Capacity
XB	Yes	Distances	Distances	Yes	Capacity

Yes means compiled batch kernels are available; it does not mean that every operation is compiled. Distances means centroid-distance kernels are compiled while other update logic remains in Python/NumPy. Unchanged means the operation is supported with backend="numba" but uses its existing NumPy implementation. Unavailable means the index rejects that numerical backend.

Capacity means JAX sample additions and update_many chunks require a positive capacity at construction. CH, WB, and XB also provide functional JAX batch and streaming APIs. All JAX modes require x64, and none support remove or merge. Numba retains remove/merge support for all eight supported indices, including the operations marked Unchanged.

NumPy remains the default for every index. CONN’s model_type selects its prototype learner separately from numerical backend selection; it does not enable the optional Numba or JAX numerical backends.

See Backends for installation, accelerated kernels, precision rules, and compilation costs. Backend availability does not guarantee a speedup.

CH, DB, GD43, GD53, WB, and XB summarize variants of within-cluster compactness and between-cluster separation. cSIL offers a bounded, centroid-based silhouette measure. PS measures partition separation, while rCIP uses distributional information. CONN is the specialized choice when connectivity between learned prototypes is important; see Using CONN before using it.

The value numpy.nan is used when an index is not yet defined, including many one-cluster states. When monitoring a stream, consider the trajectory only after enough clusters and samples have been observed. An undefined batch evaluation also emits a RuntimeWarning; incremental startup and structural operations remain silent. Use numpy.isnan to test whether a result is undefined. A computed score of 0.0 remains a valid result.

The conditions for a defined value are:

Definition conditions

Index	The score is defined when
CH	There are at least two clusters and within-cluster sum of squares is positive.
CONN	At least two prototypes or ART categories have been learned.
cSIL	There are at least two clusters. A local term with equal zero compactness and separation contributes 0.0.
DB	There are at least two clusters and every pair of centroids has positive separation.
GD43 and GD53	There are at least two clusters and at least one cluster has positive dispersion.
PS	There are at least two clusters and the cluster centroids have positive dispersion.
rCIP	There are at least two clusters.
WB	There are at least two clusters and between-cluster sum of squares is positive.
XB	There are at least two clusters and minimum centroid separation is positive.

The checks use exact zero comparisons. No small value is added to a denominator, so a very small nonzero denominator remains part of the metric’s result.

For example, exclude undefined values when consuming a streaming score:

import cvi
import numpy as np

index = cvi.CH()
for sample, label in zip(samples, labels):
    value = index.get_cvi(sample, label)
    if not np.isnan(value):
        print(value)