feat(preprocessing): add optimal shifted CLR (PFlog1pPF) normalization

docs/api/preprocessing.md

@@ -29,6 +29,7 @@ For visual quality control, see {func}`~scanpy.pl.highest_expr_genes` and
    pp.log1p
    pp.pca
    pp.normalize_total
+   pp.normalize_clr
    pp.regress_out
    pp.scale
    pp.sample

docs/references.bib

@@ -111,6 +111,16 @@ @article{Blondel2008
   pages     = {P10008},
 }
 
+@article{Booeshaghi2022,
+  author    = {Booeshaghi, A. Sina and Hallgrímsdóttir, Ingileif B. and Gálvez-Merchán, Ángel and Pachter, Lior},
+  title     = {Depth normalization for single-cell genomics count data},
+  year      = {2026},
+  url       = {https://doi.org/10.1101/2022.05.06.490859},
+  doi       = {10.1101/2022.05.06.490859},
+  publisher = {Cold Spring Harbor Laboratory},
+  journal   = {bioRxiv},
+}
+
 @article{Burczynski2006,
   author    = {Burczynski, Michael E. and Peterson, Ron L. and Twine, Natalie C. and Zuberek, Krystyna A. and Brodeur, Brendan J. and Casciotti, Lori and Maganti, Vasu and Reddy, Padma S. and Strahs, Andrew and Immermann, Fred and Spinelli, Walter and Schwertschlag, Ulrich and Slager, Anna M. and Cotreau, Monette M. and Dorner, Andrew J.},
   title     = {Molecular Classification of Crohn’s Disease and Ulcerative Colitis Patients Using Transcriptional Profiles in Peripheral Blood Mononuclear Cells},

docs/release-notes/4160.feat.md

@@ -0,0 +1 @@
+Add {func}`scanpy.pp.normalize_clr` for shifted centered log-ratio (PFlog1pPF) normalization, a variance-stabilizing, depth-invariant and rank-preserving count transform {cite:p}`Booeshaghi2022` {smaller}`R Baber`

src/scanpy/preprocessing/__init__.py

@@ -7,7 +7,7 @@
 from ._deprecated.sampling import subsample
 from ._harmony import harmony_integrate
 from ._highly_variable_genes import highly_variable_genes
-from ._normalization import normalize_total
+from ._normalization import normalize_clr, normalize_total
 from ._pca import pca
 from ._qc import calculate_qc_metrics
 from ._recipes import recipe_seurat, recipe_weinreb17, recipe_zheng17
@@ -33,6 +33,7 @@
     "highly_variable_genes",
     "log1p",
     "neighbors",
+    "normalize_clr",
     "normalize_total",
     "pca",
     "recipe_seurat",

src/scanpy/preprocessing/_normalization.py

@@ -7,13 +7,16 @@
 import numpy as np
 from fast_array_utils import stats
 from fast_array_utils.numba import njit
+from fast_array_utils.stats import mean_var
 
 from .. import logging as logg
 from .._compat import CSBase, CSCBase, CSRBase, DaskArray, warn
 from .._utils import axis_mul_or_truediv, dematrix, view_to_actual
 from ..get import _get_obs_rep, _set_obs_rep
 
 if TYPE_CHECKING:
+    from typing import Literal
+
     from anndata import AnnData
 
 
@@ -304,3 +307,262 @@ def normalize_total(  # noqa: PLR0912
     elif not inplace:
         return dat
     return None
+
+
+# -----------------------------------------------------------------------------
+# Shifted Centered Log-Ratio (PFlogPF) Core Implementation
+#
+# The mathematical logic and sparse matrix optimization ("offset trick")
+# implemented below are adapted from the Pachter Lab reference repository:
+# https://github.com/pachterlab/bhgp_2022
+#
+# Reference Publication:
+# Booeshaghi et al. (2022, 2026) "Depth normalization for single-cell genomics
+# count data" bioRxiv. doi: 10.1101/2022.05.06.490859
+#
+# Copyright (c) 2022, Pachter Lab. All rights reserved.
+# Licensed under the BSD 2-Clause License.
+# -----------------------------------------------------------------------------
+
+
+def _estimate_overdispersion(x: np.ndarray | CSBase | DaskArray) -> float:
+    r"""Estimate the negative-binomial overdispersion :math:`α` from raw counts.
+
+    Fits :math:`\mathrm{Var}_g = μ_g + α \cdot μ_g^2` across genes, where
+    :math:`μ_g` and :math:`\mathrm{Var}_g` are the per-gene mean and (population)
+    variance over cells. The model is linear in :math:`α`, so the ordinary
+    least-squares solution is closed form
+
+    .. math::
+        α = \frac{\sum_g (\mathrm{Var}_g - μ_g) \, μ_g^2}{\sum_g μ_g^4},
+
+    which is exactly the minimizer a non-linear `curve_fit` would converge to,
+    but without the dependency. :func:`~fast_array_utils.stats.mean_var` is
+    dispatched for dense, sparse and dask input alike, so the only dask-specific
+    step is computing the two final scalar sums.
+    """
+    mu, var = mean_var(x, axis=0, correction=0)
+    mu2 = mu**2
+    numerator = np.sum((var - mu) * mu2)
+    denominator = np.sum(mu2 * mu2)
+    if isinstance(x, DaskArray):
+        import dask
+
+        numerator, denominator = dask.compute(numerator, denominator)
+    if denominator == 0.0:
+        msg = (
+            "Cannot estimate overdispersion: every gene has zero mean. "
+            "Pass `alpha` or `target_sum` explicitly."
+        )
+        raise ValueError(msg)
+    return float(numerator / denominator)
+
+
+def _clr_log_center(u: np.ndarray | CSBase) -> np.ndarray:
+    """Apply log1p then per-cell mean-centering to PF-scaled counts; return dense.
+
+    Operates on a full-width block of cells: every gene must be present so the
+    per-cell mean spans the whole row. Used directly for in-memory input, and
+    per row-chunk under :meth:`~dask.array.Array.map_blocks` (after the genes
+    have been rechunked into a single chunk).
+    """
+    n_genes = u.shape[1]
+    if isinstance(u, CSBase):
+        # Sparse "offset trick": store log1p only at the nonzero entries. The
+        # structural zeros already hold log1p(0) = 0, so the per-cell mean is just
+        # the stored row sum / n_genes, and no densification is needed until the
+        # final centering step.
+        u.data = np.log1p(u.data)
+        per_cell_mean = np.asarray(u.sum(axis=1)).ravel() / n_genes
+        dense_log = u.toarray()
+    else:
+        u = np.asarray(u)
+        dense_log = np.log1p(u)
+        per_cell_mean = dense_log.mean(axis=1)
+
+    # Additive centering (the CLR step): map each cell onto the zero-sum
+    # (Aitchison) hyperplane. This is what fills the zeros and densifies the matrix.
+    return dense_log - per_cell_mean[:, None]
+
+
+def _normalize_clr_helper(
+    x: np.ndarray | CSBase | DaskArray,
+    *,
+    target_sum: float | None,
+    alpha: float | Literal["auto"] | None,
+) -> tuple[np.ndarray | DaskArray, np.ndarray | DaskArray]:
+    """Compute the shifted CLR (PFlog1pPF) transform backend logic.
+
+    This function acts as the internal processing engine for `normalize_clr`,
+    adapted from the reference implementations provided by the Pachter Lab
+    (Booeshaghi et al. 2022). It applies initial depth-scaling followed by
+    an optimized sparse log-shift operation before mapping coordinates onto
+    the zero-sum Aitchison hyperplane.
+
+    Returns the dense, per-cell-centered matrix and the raw per-cell depths
+    (the latter is used by the caller to warn about empty cells).
+
+    See `normalize_clr` for the meaning of the parameters.
+    """
+    # Keep the depths lazy for dask; `.ravel()` would otherwise materialize them.
+    cell_depths = stats.sum(x, axis=1)
+    if not isinstance(x, DaskArray):
+        cell_depths = np.asarray(cell_depths).ravel()
+
+    # Resolve `target_sum` (the paper's PF target constant K, Booeshaghi et al.
+    # 2022): the depth the first proportional-fitting step scales every cell to.
+    if alpha is not None:
+        if alpha == "auto":
+            # Estimate the overdispersion from the raw counts (closed-form OLS,
+            # as in the reference implementation).
+            alpha = _estimate_overdispersion(x)
+        if not alpha > 0:
+            msg = (
+                f"`alpha` must be positive to derive K = 4 * alpha * s, got {alpha}. "
+                "The data may be underdispersed; pass `target_sum` explicitly instead."
+            )
+            raise ValueError(msg)
+        # Delta-method calibration: K = 4 * alpha * s, where s is the mean cell
+        # depth. This sets the count-scale pseudocount to the variance-stabilizing
+        # value y0 = 1 / (4 * alpha), and overrides any value passed as `target_sum`.
+        target_sum = 4.0 * alpha * float(cell_depths.mean())
+    elif target_sum is None:
+        # `float(...)` triggers a single blocking `.compute()` for dask input.
+        target_sum = float(cell_depths.mean())
+    # else: use the `target_sum` passed by the caller.
+
+    # Proportional fitting: rescale each cell so its counts sum to `target_sum` (K).
+    # Dividing by `cell_depths / target_sum` (with allow_divide_by_zero=False)
+    # leaves empty cells as all-zero rows instead of producing invalid infinities.
+    u = axis_mul_or_truediv(
+        x, cell_depths / target_sum, op=truediv, axis=0, allow_divide_by_zero=False
+    )
+
+    if isinstance(x, DaskArray):
+        # Per-cell centering needs the whole row, so collapse the genes into a
+        # single chunk; the transform is then embarrassingly parallel over the
+        # row-chunks. The output is always dense, hence the dense numpy `meta`.
+        u = u.rechunk({1: -1})
+        dense_log = u.map_blocks(
+            _clr_log_center, dtype=np.float64, meta=np.array([], dtype=np.float64)
+        )
+    else:
+        dense_log = _clr_log_center(u)
+
+    return dense_log, cell_depths
+
+
+def normalize_clr(
+    adata: AnnData,
+    *,
+    target_sum: float | None = None,
+    alpha: float | Literal["auto"] | None = None,
+    layer: str | None = None,
+    inplace: bool = True,
+    copy: bool = False,
+) -> AnnData | dict[str, np.ndarray] | None:
+    r"""Normalize counts with the shifted centered log-ratio (PFlog1pPF) transform.
+
+    Computes the shifted centered log-ratio (CLR) transform
+
+    .. math::
+        T(x)_i = \log(u_i + 1) - \frac{1}{D} \sum_{j=1}^D \log(u_j + 1),
+
+    where :math:`u_i = K \, x_i / \sum_j x_j` are the depth-normalized counts
+    (proportional fitting to a target depth :math:`K`) and :math:`D` is the
+    number of genes. Equivalently this is proportional fitting, then
+    :obj:`~numpy.log1p`, then per-cell mean-centering in log space (the
+    centered-log-ratio step). This count transform is simultaneously
+    variance-stabilizing, depth-invariant, and rank-preserving :cite:p:`Booeshaghi2022`.
+
+    Because the per-cell centering fills the zero entries, the output is always
+    dense, and each cell sums to exactly zero.
+
+    .. note::
+        When used with a :class:`~dask.array.Array` in `adata.X`, deriving the
+        proportional-fitting target :math:`K` from the data requires a global
+        reduction and therefore triggers a blocking `.compute()`: once for the
+        default mean-depth target, and once more for `alpha` (including
+        ``alpha="auto"``). Only the scalar reduction is materialized, not the
+        matrix. Passing `target_sum` explicitly avoids this and keeps the whole
+        operation lazy.
+
+    Parameters
+    ----------
+    adata
+        The annotated data matrix of shape `n_obs` × `n_vars`.
+        Rows correspond to cells and columns to genes.
+    target_sum
+        Target depth :math:`K` for the first proportional-fitting step. If `None`
+        (and `alpha` is not given), the empirical mean cell depth is used. Unlike
+        :func:`~scanpy.pp.normalize_total`, this is only an *intermediate* target:
+        cells sum to `target_sum` after proportional fitting, but the subsequent
+        log and centering steps make each cell sum to exactly zero in the output.
+    alpha
+        Negative-binomial overdispersion of the dataset (``var = μ + α·μ²``). When
+        given, it overrides `target_sum` and sets :math:`K = 4 \cdot α \cdot s` by
+        the delta method, where :math:`s` is the mean cell depth, calibrating the
+        count-scale pseudocount to the variance-stabilizing value ``y0 = 1/(4·α)``
+        :cite:p:`Booeshaghi2022`. Pass ``"auto"`` to estimate :math:`α` from the
+        data (closed-form least squares of ``var = μ + α·μ²`` across genes). A
+        :class:`ValueError` is raised if the estimated or supplied :math:`α` is
+        not positive (e.g. underdispersed data); pass `target_sum` instead.
+    layer
+        Layer to normalize instead of `X`.
+    inplace
+        Whether to update `adata` or return a dictionary with the normalized
+        matrix.
+    copy
+        Whether to modify a copied input object. Not compatible with
+        `inplace=False`.
+
+    Returns
+    -------
+    Returns a dictionary with the normalized copy of `adata.X` (key `"X"`) or
+    updates `adata` with the normalized matrix, depending on `inplace`.
+
+    Example
+    -------
+    >>> import numpy as np
+    >>> from anndata import AnnData
+    >>> import scanpy as sc
+    >>> adata = AnnData(np.array([[1, 2, 3], [4, 5, 6]], dtype="float32"))
+    >>> sc.pp.normalize_clr(adata)
+    >>> np.allclose(adata.X.sum(axis=1), 0, atol=1e-6)
+    True
+    """
+    if copy:
+        if not inplace:
+            msg = "`copy=True` cannot be used with `inplace=False`."
+            raise ValueError(msg)
+        adata = adata.copy()
+
+    view_to_actual(adata)
+
+    x = _get_obs_rep(adata, layer=layer)
+    if isinstance(x, CSCBase):
+        x = x.tocsr()
+    if issubclass(x.dtype.type, int | np.integer):
+        x = x.astype(np.float64)
+
+    start = logg.info("normalizing counts per cell via shifted CLR")
+
+    x, cell_depths = _normalize_clr_helper(x, target_sum=target_sum, alpha=alpha)
+
+    if not isinstance(cell_depths, DaskArray) and not np.all(cell_depths > 0):
+        warn("Some cells have zero counts", UserWarning)
+
+    dat = dict(X=x)
+    if inplace:
+        _set_obs_rep(adata, dat["X"], layer=layer)
+
+    logg.info(
+        "    finished ({time_passed})",
+        time=start,
+    )
+
+    if copy:
+        return adata
+    elif not inplace:
+        return dat
+    return None