How to Remap Similarity Output to [0, 1]

Since v1.1.0, all PyHDC similarity functions return values in [-1, 1]. If your code expects [0, 1], for example when feeding results to scikit-learn metrics or comparing against v1.0.x thresholds, use remap_to_unit.

The remap function

remap_to_unit applies the linear transformation:

\[\text{remapped} = \frac{\text{sim} + 1}{2}\]

This maps −1 → 0, 0 → 0.5, and +1 → 1. It works on scalars, NumPy arrays, and PyTorch tensors.

from pyhdc.components.similarity import remap_to_unit

print(remap_to_unit(-1.0))    # 0.0
print(remap_to_unit(0.0))     # 0.5
print(remap_to_unit(1.0))     # 1.0

Apply it automatically via the encoding

Pass similarity_remap=remap_to_unit to the encoding constructor. Every similarity call on that encoding is automatically remapped:

import pyhdc
from pyhdc.components.similarity import remap_to_unit

enc = pyhdc.BSC(dimension=10_000, similarity_remap=remap_to_unit)
a   = enc.generate()
b   = enc.generate()

print(a.similarity(a))   # 1.0
print(a.similarity(b))   # ~= 0.5  (unrelated; 0.5 in [0,1] means orthogonal)

Apply it manually

If you only need to remap some calls, apply it after the fact:

enc = pyhdc.BSC(dimension=10_000)   # default: no remap
raw      = a.similarity(b)          # [-1, 1]
remapped = remap_to_unit(raw)        # [0, 1]

Custom remap function

The similarity_remap parameter accepts any callable that maps a scalar or array to a scalar or array of the same shape. Examples:

import numpy as np

# Sigmoid remap: maps all [-1, 1] to (0, 1) with smooth S-curve
def sigmoid_remap(x):
    return 1 / (1 + np.exp(-5 * x))   # scale factor 5 sharpens the transition

enc = pyhdc.MAP_C(dimension=10_000, similarity_remap=sigmoid_remap)

# Hard threshold: returns 1 if similar, 0 if not
def threshold_remap(x):
    return (x > 0.3).astype(float)

Batched similarity with remap

Remapping is applied element-wise, so it works correctly with all batched calling conventions:

enc   = pyhdc.MAP_C(dimension=10_000, similarity_remap=remap_to_unit)
batch = enc.generate(size=(10_000, 10))   # (D, N): each column is a hypervector
query = enc.generate()

# Per-column pairs: result[i] = similarity(batch[:, i], other[:, i])
sims = enc.similarity(batch, enc.generate(size=(10_000, 10)))   # shape (10,), all in [0,1]

Migration from v1.0.x

In v1.0.x, HammingDistance and Overlap (used by BSC and BSDC) returned [0, 1]. In v1.1.0 they return [-1, 1]. To restore the old behaviour globally, add similarity_remap=remap_to_unit when constructing any BSC or BSDC encoding.