DDRTree-python

AI-assisted Python port of the DDRTree R package — Discriminative Dimensionality Reduction via learning a Tree — from the KDD'15 paper by Qi Mao, Li Wang, Steve Goodison and Yijun Sun.

Tracks the R CRAN release DDRTree 0.1.6 (2026-02-24).

DDRTree simultaneously:

1. Reduces high-dimensional data to a low-dimensional latent space Z,
2. Learns an explicit smooth principal tree graph embedded in that space, and
3. Obtains a soft clustering of points onto the tree nodes.

It is the dimensionality-reduction backbone used by Monocle 2 for single-cell pseudotime / branching-trajectory inference, but is a general-purpose algorithm for any data with a tree-like intrinsic structure.

Installation

# From PyPI (distribution: ddrtree-python, import: ddrtree)
pip install ddrtree-python             # NumPy backend only
pip install ddrtree-python[torch]      # + PyTorch backend (CPU / CUDA)

For local development:

git clone https://github.com/Bio-Babel/DDRTree-python.git
cd DDRTree-python
pip install -e ".[dev]"

The core depends on numpy, scipy, and scikit-learn. The optional torch extra enables the GPU-friendly backend — no C/C++ extensions are built either way.

Quick start

import numpy as np
from ddrtree import DDRTree

# X is a D x N matrix (features x samples), matching the R convention.
rng = np.random.default_rng(0)
X = rng.standard_normal((10, 200))

res = DDRTree(X, dimensions=2, max_iter=20,
              sigma=1e-3, lambda_=None, ncenter=50,
              gamma=10.0, tol=1e-3, verbose=False)

res.Z      # 2 x 200  reduced-dimension embedding
res.Y      # 2 x 50   principal-graph node coordinates
res.W      # 10 x 2   orthogonal projection basis
res.stree  # N x N scipy.sparse MST weights (first K x K block populated)
res.objective_vals  # objective at each iteration

Backends

DDRTree dispatches to one of two computational backends via the backend argument. The public function signature is otherwise unchanged. Backend selection is always explicit — there is no auto-detection.

backend	Executes on	Typical use
"numpy"	CPU (NumPy)	Default. Reference path, aligned with R.
"torch"	CPU / CUDA	GPU acceleration (Borůvka MST, fast BLAS).

# GPU path — requires torch with CUDA
res = DDRTree(X, ncenter=500, backend="torch", device="cuda")

# Half precision (torch backend only). Memory ½, throughput ~1.5–2× on
# CUDA, ~1e-3 relative drift in the converged embedding.
res = DDRTree(X, ncenter=500, backend="torch", device="cuda", dtype="float32")

Torch backend runs a pure-torch parallel Borůvka (O(log K) rounds) for the MST step — no host round trip per iteration. Explicit mst_algorithm="prim" or "kruskal" routes MST through NumPy / SciPy for strict parity testing against the R gold standard; see tests/test_boruvka_integration.py.

Known differences between backends

• PCA initialisation. NumPy uses scipy.sparse.linalg.svds (iterative, Lanczos, matches R's irlba). Torch uses a direct torch.linalg.svd for the truncated branch — identical subspace, small per-iteration numerical drift.
• K-means. Both backends call sklearn.cluster.KMeans on CPU (small K, negligible overhead). No GPU K-means yet.
• Cholesky fallback. When the tmp_M system drifts non-PSD both backends fall back to LU and emit a RuntimeWarning. The Y-update Cholesky is strict in both backends — the (λ/γ)L + Γ system is PSD by construction, any failure there is surfaced rather than masked.

Numerical parity with the R package

The test suite runs the same inputs through the R DDRTree package and compares the results, for both backends. Eigen-vector sign flips (inherent to eigen-decompositions) are handled in tests. See tests/scripts/generate_gold_standard.R, tests/test_ddrtree.py (NumPy) and tests/test_backend_torch_gold.py (Torch).

Reference

Qi Mao, Li Wang, Steve Goodison, Yijun Sun. Dimensionality Reduction via Graph Structure Learning. KDD'15. https://dl.acm.org/doi/10.1145/2783258.2783309