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pysrf

Discover interpretable dimensions from representational similarities.

Representational similarity is a widely used tool in cognitive science and machine learning. pysrf decomposes similarity matrices into sparse, non-negative dimensions that reveal the latent structure underlying similarities.

Given a similarity matrix \(S\), pysrf finds a non-negative embedding \(W\) such that \(S \approx WW^\top\). Each column of \(W\) is a dimension, and each row gives for an item a numeric weight alongside each dimension. Because dimensions are non-negative and sparse (for example, many entries drive toward zero), the embedding is an additive, compositional representation where dimensions contribute positively without canceling each other out.

When to use pysrf

pysrf works broadly on any symmetric similarity matrix. These can come from different domains, for example:

  • Behavioral data: any task that yields a measure of similarity between items.
  • Neural data: representational similarity matrices derived from fMRI, electrophysiology, or other neural recordings.
  • Machine learning: similarity matrices from deep neural network activations

Key capabilities

  • Missing data: real-world similarity matrices are sometimes incomplete and some entries \(i,j\) in a similarity matrix not observed. pysrf can handle missing entries naturally.
  • Dimensionality estimation: the number of optimal dimensions can be estimated via cross-validation
  • Fast solver: a Cython-accelerated solver provides 10-50x speedup over pure Python.

Quick example

import numpy as np
from pysrf import SRF

# Your similarity matrix (e.g., from behavioral judgments or neural data)
s = np.random.rand(100, 100)
s = (s + s.T) / 2

# Decompose into 10 interpretable dimensions
model = SRF(rank=10, max_outer=20, random_state=42)
w = model.fit_transform(s)

# Reconstruct the similarity matrix from the dimensions
s_reconstructed = model.reconstruct()

Reference

Mahner, F. P.*, Lam, K. C.*, & Hebart, M. N. (2025). Interpretable dimensions from sparse representational similarities. In preparation.

Next steps