PHATE Manifold Metrics

Manifold-aware semantic and relational affinity metrics using PHATE.

Overview

Compute Semantic Affinity (SA) and Relational Affinity (RA) metrics that leverage manifold geometry to capture non-Euclidean structure in embedding spaces.

Key Features

✨ Multi-scale Analysis: Compare metrics at t=1 (baseline) vs t=5-6 (manifold) ✨ Multiple RA Variants: Euclidean, Geodesic, Diffusion ✨ Clustering-free SA: Distribution-based (no labels required) ✨ Analogy Support: Specialized 4-word analogy methods ✨ Optional Loaders: FastText, LaBSE, Ollama, OpenRouter ✨ Dataset Utilities: CSV loading and parsing

Installation

# Core metrics only
pip install phate-manifold-metrics

# With embedding loaders
pip install phate-manifold-metrics[embeddings]

# Development (includes pytest, black, mypy)
pip install phate-manifold-metrics[all]

Quick Start

import numpy as np
from phate_manifold_metrics import PhateManifoldMetrics

# Load/generate embeddings
embeddings = np.random.randn(100, 384)

# Initialize & fit
metrics = PhateManifoldMetrics(knn=5, t=6)
metrics.fit(embeddings)

# Define word pairs
pairs = [(0,1), (2,3), (4,5)]

# Compute SA
sa = metrics.compute_semantic_affinity(pairs)
print(f"SA: {sa['sa_score']:.3f}")

# Compute RA variants
ra_euc = metrics.compute_relational_affinity_euc(pairs)
ra_geo = metrics.compute_relational_affinity_geo(pairs)
ra_dif = metrics.compute_relational_affinity_dif(pairs)

print(f"RA_euc: {ra_euc['ra_euc_score']:.3f}")
print(f"RA_geo: {ra_geo['ra_geo_score']:.3f}")
print(f"RA_dif: {ra_dif['ra_dif_score']:.3f}")

CLI Usage

# Basic test
phate-metrics --knn 5 --t 6

# Dual-scale analysis
phate-metrics --dual-scale

# Euclidean metric
phate-metrics --metric euclidean

Metrics Explained

Semantic Affinity (SA)

Clustering quality in manifold space:

SA = 1 / (1 + CV)
where CV = std(distances) / mean(distances)

• Range: [0, 1], higher = better clustering
• No labels required

Relational Affinity (RA)

Directional alignment of relational vectors:

Statistical RA (word pairs):

• RA_euc: Euclidean (flat space baseline)
• RA_geo: Geodesic (k-NN graph shortest paths)
• RA_dif: Diffusion (PHATE manifold)
• Range: [-1, 1], higher = stronger alignment

Analogy RA (4-word test cases a:b::c:d):

• RA_euc_analogy: Euclidean parallelogram
• RA_geo_analogy: Geodesic parallelogram
• Range: [0, 1], higher = stronger analogy

Parameters

Parameter	Description	Recommendation
knn	k-Nearest neighbors	5-10 (start with 5)
t	Diffusion time	1 (baseline), 6 (manifold)
metric	Distance metric	'cosine' (normalized), 'euclidean'

Optional: Embedding Loaders

FastText

from phate_manifold_metrics.embeddings import load_fasttext_from_extracted

embeddings = load_fasttext_from_extracted(["cat", "dog"], lang='en')

LaBSE

from phate_manifold_metrics.embeddings import load_labse_embeddings

embeddings = load_labse_embeddings(["hello", "你好", "hola"])

Ollama

from phate_manifold_metrics.embeddings.ollama import get_ollama_embeddings_fixed

embeddings = get_ollama_embeddings_fixed(
    ["cat", "dog"],
    model_name="snowflake-arctic-embed2"
)

OpenRouter API

import os
from phate_manifold_metrics.embeddings.openrouter import load_openrouter_embeddings

os.environ['OPENROUTER_API_KEY'] = 'your-key'
embeddings = load_openrouter_embeddings(
    ["hello", "world"],
    model_path="qwen/qwen3-embedding-8b",
    model_name="Qwen3-8B"
)

Documentation

Full API documentation available in docstrings:

from phate_manifold_metrics import PhateManifoldMetrics
help(PhateManifoldMetrics)

Citation

@software{phate_manifold_metrics,
  title = {PHATE Manifold Metrics},
  author = {Digital Duck},
  year = {2026},
  url = {https://github.com/digital-duck/phate-manifold-metrics}
}

References

• PHATE: Moon et al., Nature Biotechnology 2019
• Diffusion Distance: Coifman & Lafon, Applied and Computational Harmonic Analysis 2006

License

MIT License - Copyright (c) 2026 Digital Duck

Authors

Digital Duck (Wen + Claude Sonnet 4.5 + Google Gemini 2.5)