`nid()`¶

Compare two symbolic sequences using an information-distance estimate derived from Normalized Information Distance (NID). Lower values indicate more shared patterns under this measure. Use it for recordings, texts or symbolic trajectories encoded in the same way.

nid(seq1, seq2, partitions=1, alphabet=None, log_base=None, jobs=0) -> float

Parameters¶

Parameter	Default	Behavior
`seq1`	required	First supported sequence input.
`seq2`	required	Second supported sequence input, converted independently of `seq1`.
`partitions`	`1`	Accepted; has no effect.
`alphabet`	`None`	Does not change the returned distance.
`log_base`	`None`	Does not change the returned distance: the ratio uses factor counts.
`jobs`	`0`	Accepted; has no effect. Native workers use Rayon configuration.

Arguments may have different lengths or accepted Python types. They must represent corresponding symbols with the same byte codes. If byte 0 represents a resting state in one sequence, it must represent the same state in the other. Do not create independent codebooks for a comparison.

See parameter types and errors for integer ranges and conversion errors.

Return value¶

Returns a float. The calculation uses the LZ76 counts of each input and both concatenation orders, making the result symmetric: nid(a, b) == nid(b, a). It needs no alignment of individual positions.

The finite-sequence estimate is returned without clipping. Self-distance can be nonzero, so evaluate that baseline before passing the values to a method that requires a zero diagonal.

Compare sequences¶

import lzcomplexity as lz

first = "abcd"
second = "abce"
distance = lz.nid(first, second)

assert distance == 0.25
assert lz.nid(second, first) == distance
assert lz.nid("banana", "banana") == 1 / 3

This comparison concerns recurring patterns in the sequences, rather than a position-by-position mismatch fraction.

Build pairwise comparisons¶

import lzcomplexity as lz

samples = [b"abcd", b"abce", b"wxyz"]
distances = [
    [lz.nid(first, second) for second in samples]
    for first in samples
]

assert distances[0][1] == 0.25
assert all(
    distances[i][j] == distances[j][i]
    for i in range(len(samples))
    for j in range(len(samples))
)

For many sequences, compute each unordered pair once, then fill the symmetric matrix. The batch-distance recipe gives a larger example; the lzdistance binary handles pairwise file collections from the command line.

Input and length choices¶

Use matched preprocessing and, when possible, comparable sample lengths. For text, decide whether symbols represent bytes, characters, words or other tokens before coding them. A single shared codebook is required for tokenized inputs. See input encoding and sequence length.

Empty inputs are accepted. nid("", "") returns 0.0; comparing an empty input with a nonempty one need not give zero. Treat an absent observation separately from an observed sequence when preparing a dataset.

nid()¶