max_distance()

max_distance() returns the maximum off-diagonal dissimilarity in a distance matrix. It is used to normalize representativeness: R_i^k = 1 − d(i, k) / d_max.

Function Usage

max_distance(diss)

R / Literature Parameter Mapping

Sequenzo	R / packages	Notes
max_distance(diss)	max(diss[upper.tri(diss)])	Helske et al. (2024) "maximum distance between two sequences"
Condensed input	as.dist / squareform	SciPy condensed vectors are accepted

Entry Parameters

Parameter	Required	Type	Description
diss	✓	ndarray	Square n × n distance matrix, or a 1D condensed distance vector (SciPy layout).

What It Returns

Type	Description
float	Maximum off-diagonal distance. Returns 0.0 when n < 2.

Example

from sequenzo import max_distance, representativeness_matrix

d_max = max_distance(diss)
R = representativeness_matrix(diss, medoids, d_max=d_max)

When d_max=None, representativeness_matrix() calls max_distance internally.

Notes

• Only the upper triangle (pairs i < j) is considered; the diagonal is ignored.
• Square matrices are validated with the same checks as other distance-matrix functions (symmetry, zero diagonal, no NA, nonnegative entries). Condensed vectors are also checked for NA and negative values before conversion.
• If all sequences are identical, d_max is 0 and representativeness is set to 1 for all entries.

Authors

Code: Yuqi Liang

Documentation: Yuqi Liang

References

Helske, S., Helske, J., & Chihaya, G. K. (2024). From sequences to variables: Rethinking the relationship between sequences and outcomes. Sociological Methodology, 54(1), 27–51.