Harmony Batch Correction

Overview

Harmony is a fast, scalable algorithm for batch integration in single-cell data. It takes a PCA embedding (cells × PCs) as input and returns a corrected embedding from which batch effects have been regressed out via iterative soft-clustering and per-cluster linear regression. The corrected embedding is then used to compute neighbors, UMAP, and downstream clustering — the raw count matrix is never modified. Harmony works for single-cell RNA-seq, ATAC-seq, and other omics modalities where a PCA-like embedding is available.

When to Use

• Integrating scRNA-seq datasets from different samples, donors, sequencing runs, or experimental batches that should contain the same cell types
• Removing technical variation (library preparation protocol, 10x chemistry version, sequencing depth, sequencing platform) while preserving biological differences between cell types and conditions
• Performing fast, scalable batch correction on datasets with millions of cells where deep generative model training would be prohibitively slow
• Correcting for multiple confounding variables simultaneously (batch, donor, sequencing platform, tissue processing protocol)
• Preparing a corrected embedding for UMAP visualization, Leiden clustering, or label transfer without modifying the gene expression count matrix
• Use omics-plotting SKILL for generic result-table figures; batch-evaluation UMAPs use scanpy sc.pl.*
• Use scVI/scvi-tools instead when you need probabilistic batch correction with a variational autoencoder (deep learning), differential expression with uncertainty estimates, or multi-modal integration (RNA + protein)
• Use BBKNN instead when you want graph-based integration that avoids constructing a corrected embedding altogether and directly builds a cross-batch nearest-neighbor graph
• Use Seurat Integration / CCA (R) instead when you are already in a Seurat workflow and prefer anchor-based integration methods

Prerequisites

• Python packages: harmonypy, scanpy>=1.10, leidenalg, igraph, anndata, pandas, matplotlib
• R packages (optional): harmony, Seurat>=4.0 (for R workflow in Step 7)
• Data requirements: AnnData object with raw counts, batch/sample metadata in adata.obs, and PCA embedding already computed (adata.obsm["X_pca"])
• Environment: Python 3.9+; 8 GB RAM sufficient for up to ~500k cells; linear memory scaling

pip install harmonypy "scanpy[leiden]" anndata pandas matplotlib

# R installation (for Step 7 / Seurat integration)
install.packages("harmony")
# If using Seurat:
install.packages("Seurat")

Pre-flight Interview

Settle these with the user before writing any analysis code.

decisions:
  - id: D1
    param: batchKey
    kind: required
    source: data
    ask: "Which variable separates samples that were processed apart - donor, run, chemistry, or a combination?"
    default: null

  - id: D2
    param: inputEmbedding
    kind: derived
    source: upstream
    ask: "Which reduced space should be corrected?"
    default: "the PCA embedding computed upstream"

  - id: D3
    param: diversityPenalty
    kind: required
    source: user
    depends_on: [D1]
    ask: "How hard should batches be pushed together? Too hard erases real differences between samples."
    default: "2.0; raise toward 4-6 when batch sizes are very uneven"

  - id: D4
    param: numClusters
    kind: optional_conditional
    source: data
    ask: "Does the dataset contain rare populations that need more soft clusters to survive correction?"
    default: "automatic, min(100, cells/30)"

  - id: D5
    param: maxIterations
    kind: optional_conditional
    source: data
    ask: "Did the correction converge, or does it need more iterations?"
    default: 10

  - id: D6
    param: smallClusterProtection
    kind: optional_conditional
    source: user
    ask: "Are small populations being over-split during correction?"
    default: "off"

  - id: D7
    param: kernelBandwidth
    kind: optional
    source: user
    ask: "Should Harmony use its standard soft-clustering bandwidth, or be tuned for unusually heterogeneous batches?"
    default: 0.1

D3 is where batch correction goes wrong in the direction nobody checks. Under-correction is visible - batches stay separated in the embedding. Over-correction is not: samples mix beautifully because a real treatment effect was removed along with the batch effect. Ask what the batch variable is confounded with before raising it.

Quick Start

Minimal pipeline — load preprocessed data, run Harmony via scanpy, produce UMAP:

import scanpy as sc

# Load preprocessed AnnData (counts normalized, HVGs selected, PCA run)
adata = sc.read_h5ad("preprocessed.h5ad")   # must have adata.obs["batch"]

# Run Harmony batch correction (corrects adata.obsm["X_pca"] → "X_pca_harmony")
sc.external.pp.harmony_integrate(adata, key="batch")

# Build neighborhood graph on corrected embedding, then UMAP
sc.pp.neighbors(adata, use_rep="X_pca_harmony")
sc.tl.umap(adata)
sc.tl.leiden(adata, resolution=0.5)

# Visualize
sc.pl.umap(adata, color=["batch", "leiden"], ncols=2)
print(f"Clusters: {adata.obs['leiden'].nunique()} | Cells: {adata.n_obs}")

Workflow

Step 1: Quality Control and Preprocessing

Filter, normalize, select highly variable genes (HVGs), and run PCA. Harmony is applied to the PCA embedding produced here.

import scanpy as sc
import numpy as np

sc.settings.set_figure_params(dpi=80, facecolor="white")

# Load multi-batch data — adata.obs must contain a batch column
adata = sc.read_h5ad("multi_batch_counts.h5ad")
# Alternatively, concatenate multiple AnnData objects:
# adata = sc.concat([adata1, adata2, adata3], label="batch",
#                   keys=["batch1", "batch2", "batch3"])

print(f"Loaded: {adata.n_obs} cells × {adata.n_vars} genes")
print(f"Batches: {adata.obs['batch'].value_counts().to_dict()}")

# QC: annotate mitochondrial genes and filter low-quality cells
adata.var["mt"] = adata.var_names.str.startswith("MT-")
sc.pp.calculate_qc_metrics(adata, qc_vars=["mt"], inplace=True)
sc.pp.filter_cells(adata, min_genes=200)
sc.pp.filter_cells(adata, max_genes=6000)
sc.pp.filter_genes(adata, min_cells=3)
adata = adata[adata.obs["pct_counts_mt"] < 20].copy()
print(f"After QC: {adata.n_obs} cells × {adata.n_vars} genes")

# Normalize and log-transform (store raw counts first)
adata.layers["counts"] = adata.X.copy()
sc.pp.normalize_total(adata, target_sum=1e4)
sc.pp.log1p(adata)

# Select HVGs and compute PCA
sc.pp.highly_variable_genes(adata, n_top_genes=3000, batch_key="batch")
sc.pp.pca(adata, n_comps=50, use_highly_variable=True)
print(f"PCA shape: {adata.obsm['X_pca'].shape}")  # (n_cells, 50)

Step 2: Run Harmony via Scanpy Integration

The scanpy wrapper calls harmonypy under the hood and stores the corrected embedding in adata.obsm["X_pca_harmony"].

import scanpy as sc

# Run Harmony — corrects adata.obsm["X_pca"] in-place and stores result as "X_pca_harmony"
sc.external.pp.harmony_integrate(
    adata,
    key="batch",           # obs column with batch labels
    basis="X_pca",         # source embedding (default)
    adjusted_basis="X_pca_harmony",  # destination key (default)
    max_iter_harmony=20,   # maximum Harmony iterations (default 10; increase for complex batches)
    theta=2.0,             # diversity penalty per batch variable (default 2)
    sigma=0.1,             # width of soft-clustering Gaussian kernel
    random_state=42,
)

print(f"Corrected embedding: {adata.obsm['X_pca_harmony'].shape}")
# Expected: (n_cells, 50) — same shape as X_pca

Step 3: Run Harmony via harmonypy Directly

Use the lower-level harmonypy API when you need finer control, access to the HarmonyObject, or integration outside of scanpy.

import harmonypy
import pandas as pd
import numpy as np

# Extract PCA embedding and metadata
pca_embeddings = adata.obsm["X_pca"]                  # numpy array (n_cells, n_PCs)
meta_data = adata.obs[["batch", "donor"]].copy()       # DataFrame with batch variables

# Run Harmony
ho = harmonypy.run_harmony(
    pca_embeddings,
    meta_data,
    vars_use=["batch"],        # list of columns to correct for
    theta=2.0,                 # diversity penalty strength (per variable)
    sigma=0.1,                 # soft-clustering bandwidth
    nclust=None,               # number of clusters; None → auto (min(100, n_cells/30))
    tau=0,                     # protection against over-clustering small clusters
    block_size=0.05,           # fraction of cells per mini-batch
    max_iter_harmony=20,
    max_iter_kmeans=20,
    epsilon_cluster=1e-5,
    epsilon_harmony=1e-4,
    random_state=42,
    verbose=True,
)

corrected = ho.Z_corr.T   # (n_cells, n_PCs) corrected embedding
adata.obsm["X_pca_harmony"] = corrected
print(f"Harmony converged. Corrected embedding shape: {corrected.shape}")

Step 4: Compute Neighbors and UMAP on Harmony Embedding

Always use use_rep="X_pca_harmony" so that downstream graph construction is based on the corrected embedding, not the original PCA.

import scanpy as sc

# Build k-nearest neighbor graph using corrected embedding
sc.pp.neighbors(
    adata,
    n_neighbors=15,          # number of neighbors (15-30 typical for scRNA-seq)
    n_pcs=None,              # use all PCs in the embedding
    use_rep="X_pca_harmony", # IMPORTANT: use corrected embedding
    random_state=42,
)

# Compute UMAP for visualization
sc.tl.umap(adata, min_dist=0.3, spread=1.0, random_state=42)

print(f"UMAP computed: {adata.obsm['X_umap'].shape}")  # (n_cells, 2)

Step 5: Leiden Clustering on Harmony-Corrected Graph

Clustering is performed on the neighbor graph built from the Harmony-corrected embedding in Step 4.

import scanpy as sc

# Run Leiden community detection at multiple resolutions
for resolution in [0.3, 0.5, 0.8]:
    sc.tl.leiden(adata, resolution=resolution, key_added=f"leiden_{resolution}")

# Select final resolution
adata.obs["leiden"] = adata.obs["leiden_0.5"]

print(f"Clusters at resolution 0.5: {adata.obs['leiden'].nunique()}")
print(adata.obs["leiden"].value_counts().head())

# Find marker genes per cluster
sc.tl.rank_genes_groups(adata, groupby="leiden", method="wilcoxon", n_genes=50)
sc.pl.rank_genes_groups_dotplot(adata, n_genes=5, groupby="leiden")

Step 6: Evaluate Batch Correction

Plot UMAP colored by batch and by cell type / cluster to visually confirm batch effects are removed while biological structure is preserved.

import scanpy as sc
import matplotlib.pyplot as plt

fig, axes = plt.subplots(1, 3, figsize=(18, 5))

# Before correction: color by batch using uncorrected PCA-based UMAP
sc.pp.neighbors(adata, use_rep="X_pca", key_added="uncorrected_neighbors", random_state=42)
sc.tl.umap(adata, neighbors_key="uncorrected_neighbors", random_state=42)
adata.obsm["X_umap_uncorrected"] = adata.obsm["X_umap"].copy()

# Restore Harmony UMAP
sc.pp.neighbors(adata, use_rep="X_pca_harmony", random_state=42)
sc.tl.umap(adata, random_state=42)

# Panel 1: Corrected UMAP colored by batch
sc.pl.umap(adata, color="batch", title="Harmony: colored by batch",
           ax=axes[0], show=False)

# Panel 2: Corrected UMAP colored by leiden cluster
sc.pl.umap(adata, color="leiden", title="Harmony: Leiden clusters",
           ax=axes[1], show=False)

# Panel 3: Uncorrected UMAP colored by batch (for comparison)
sc.pl.embedding(adata, basis="X_umap_uncorrected", color="batch",
                title="Uncorrected PCA: batch separation",
                ax=axes[2], show=False)

plt.tight_layout()
plt.savefig("harmony_batch_evaluation.png", dpi=150, bbox_inches="tight")
plt.show()
print("Batch evaluation figure saved to harmony_batch_evaluation.png")

Step 7: R Integration with Seurat

For users working in R, Harmony integrates directly with Seurat via RunHarmony().

library(Seurat)
library(harmony)

# Load Seurat object with batch metadata in metadata column "batch"
seurat_obj <- readRDS("multi_batch_seurat.rds")

# Ensure PCA is computed
seurat_obj <- NormalizeData(seurat_obj)
seurat_obj <- FindVariableFeatures(seurat_obj, nfeatures = 3000)
seurat_obj <- ScaleData(seurat_obj)
seurat_obj <- RunPCA(seurat_obj, npcs = 50)

# Run Harmony — corrects the "pca" reduction and adds "harmony" reduction
seurat_obj <- RunHarmony(
  seurat_obj,
  group.by.vars = "batch",   # metadata column(s) to correct for
  dims.use = 1:30,           # number of PCs to use
  theta = 2,                 # diversity penalty
  sigma = 0.1,               # soft-clustering bandwidth
  max.iter.harmony = 20,
  plot_convergence = TRUE,   # plot objective function convergence
  verbose = TRUE
)

# Build neighbor graph and UMAP using Harmony embedding
seurat_obj <- FindNeighbors(seurat_obj, reduction = "harmony", dims = 1:30)
seurat_obj <- FindClusters(seurat_obj, resolution = 0.5)
seurat_obj <- RunUMAP(seurat_obj, reduction = "harmony", dims = 1:30)

# Visualize
DimPlot(seurat_obj, reduction = "umap", group.by = "batch")
DimPlot(seurat_obj, reduction = "umap", group.by = "seurat_clusters")

cat(sprintf("Clusters: %d | Cells: %d\n",
            length(unique(seurat_obj$seurat_clusters)),
            ncol(seurat_obj)))

Key Parameters

Parameter	Default	Range / Options	Effect
theta	2.0	0–10	Diversity penalty per batch variable. Higher values force more mixing; set to 0 to disable penalty. Increase to 4–6 for very uneven batch sizes.
sigma	0.1	0.01–0.5	Bandwidth of the soft-clustering Gaussian kernel. Smaller values → sharper cluster assignments; larger values → smoother. Rarely needs changing.
nclust	None (auto)	5–200	Number of soft clusters used for correction. Auto-set to min(100, n_cells/30). Increase for datasets with many rare cell types.
max_iter_harmony	10	5–50	Maximum Harmony iterations. Increase to 20–30 for datasets with strong or complex batch effects where convergence is slow.
tau	0	0–10	Overclustering protection. Positive values penalize very small clusters; use tau=5 when tiny populations are over-splitting.
n_neighbors (scanpy)	15	5–50	Number of nearest neighbors for the post-Harmony graph. Increase for larger datasets (>100k cells) to stabilize clusters.
block_size	0.05	0.01–0.1	Fraction of cells per mini-batch for the K-means step. Smaller values are faster but less stable; default is usually appropriate.

Key Concepts

How Harmony Works

Harmony correction proceeds in three repeated phases until convergence:

1. Soft K-means assignment: Each cell is softly assigned to K clusters based on Euclidean distance in PC space, weighted by the batch-diversity penalty theta.
2. Per-cluster linear regression: Within each cluster, a linear correction is estimated for each batch variable and applied to the cluster's cells.
3. Convergence check: The objective function (mixture model likelihood + diversity penalty) is evaluated; iterations stop when improvement < epsilon_harmony.

The corrected embedding lives in the same PC space as the input PCA but with batch-specific directions subtracted. The raw count matrix (adata.X) and all gene-level information are untouched.

PCA Before Harmony

Harmony assumes the input PCA was computed with batch_key awareness. In scanpy, always pass batch_key="batch" to sc.pp.highly_variable_genes() before PCA so that HVGs are selected independently per batch and then intersected, preventing batch-specific HVGs from dominating the embedding.

Embedding Not Counts

Harmony corrects the embedding, not the count matrix. Differential expression analysis should still use the raw or normalized counts (stored in adata.layers["counts"] or adata.raw), not the corrected PCs.

Common Recipes

Recipe: Multi-Variable Correction (Batch + Donor + Platform)

Correct for multiple confounding variables simultaneously by passing a list to vars_use. Each variable gets its own diversity penalty theta.

import harmonypy
import pandas as pd

# Prepare metadata with multiple batch variables
meta_data = adata.obs[["batch", "donor", "platform"]].copy()

# Run Harmony correcting for all three variables
ho = harmonypy.run_harmony(
    adata.obsm["X_pca"],
    meta_data,
    vars_use=["batch", "donor", "platform"],  # correct for all three
    theta=[2.0, 1.0, 2.0],  # per-variable diversity penalty
    # theta can also be a scalar (same for all variables)
    max_iter_harmony=30,
    random_state=42,
    verbose=True,
)

adata.obsm["X_pca_harmony"] = ho.Z_corr.T
print(f"Multi-variable correction complete. Shape: {adata.obsm['X_pca_harmony'].shape}")

# Verify batch mixing improved for all variables
import scanpy as sc
sc.pp.neighbors(adata, use_rep="X_pca_harmony")
sc.tl.umap(adata, random_state=42)
sc.pl.umap(adata, color=["batch", "donor", "platform"], ncols=3)

Recipe: Diagnose Over-Correction with Marker Genes

If Harmony over-corrects (merges biologically distinct populations), canonical marker genes will lose cell-type specificity on the UMAP. Check this before downstream analysis.

import scanpy as sc
import matplotlib.pyplot as plt

# Define known canonical marker genes for your tissue
marker_genes = {
    "T cells": ["CD3D", "CD3E", "TRAC"],
    "B cells": ["MS4A1", "CD79A", "CD19"],
    "NK cells": ["GNLY", "NKG7", "KLRD1"],
    "Monocytes": ["LYZ", "CD14", "CST3"],
    "Dendritic cells": ["FCER1A", "CLEC10A"],
}

# Plot canonical markers on the Harmony-corrected UMAP
all_markers = [g for genes in marker_genes.values() for g in genes
               if g in adata.var_names]

sc.pl.umap(
    adata,
    color=all_markers[:6],    # plot first 6 markers
    ncols=3,
    vmax="p99",               # clip color scale at 99th percentile
    frameon=False,
    save="_marker_genes.png",
)

# If markers look diffuse or don't separate cell types cleanly,
# reduce theta (e.g., from 2.0 to 1.0) or reduce max_iter_harmony
print("If marker gene expression is diffuse across clusters, reduce theta.")
print("If batch effects remain visible, increase theta or max_iter_harmony.")

Recipe: Save and Reload Harmony-Corrected AnnData

Save the corrected object with all embeddings for downstream analysis without re-running Harmony.

import scanpy as sc

# Save with all embeddings
adata.write_h5ad("harmony_corrected.h5ad", compression="gzip")
print(f"Saved to harmony_corrected.h5ad ({adata.n_obs} cells)")

# Reload and verify
adata_loaded = sc.read_h5ad("harmony_corrected.h5ad")
print(f"Loaded. Keys in obsm: {list(adata_loaded.obsm.keys())}")
# Expected: ['X_pca', 'X_pca_harmony', 'X_umap']

Expected Outputs

Output	Type	Description
adata.obsm["X_pca_harmony"]	np.ndarray (cells × PCs)	Harmony-corrected PCA embedding; input for neighbors/UMAP/clustering
adata.obsm["X_umap"]	np.ndarray (cells × 2)	2D UMAP coordinates from corrected embedding
adata.obs["leiden"]	pd.Categorical	Leiden cluster labels
adata.uns["neighbors"]	dict	KNN graph metadata (connectivities, distances)
adata.uns["rank_genes_groups"]	dict	Per-cluster marker gene statistics (scores, p-values, log fold changes)
harmony_batch_evaluation.png	PNG figure	Side-by-side UMAP panels: batch labels, cluster labels, uncorrected comparison

Troubleshooting

Problem	Cause	Solution
Harmony does not converge (max iterations reached)	Strong batch effects or too few iterations	Increase max_iter_harmony to 30–50; check that PCA was computed with batch_key HVG selection
Batches still separate on UMAP after correction	theta too low or too few PCs	Increase theta to 3–4; use more PCs (40–50); ensure use_rep="X_pca_harmony" is set in sc.pp.neighbors()
Over-correction: biologically distinct populations merge	theta too high or too many iterations	Reduce theta to 1.0; reduce max_iter_harmony; verify marker gene expression is cell-type-specific
KeyError: 'X_pca_harmony' in sc.pp.neighbors()	Step 2 (harmony_integrate) not run yet	Run sc.external.pp.harmony_integrate(adata, key="batch") before calling sc.pp.neighbors()
AttributeError or import error for sc.external.pp.harmony_integrate	harmonypy not installed	Run pip install harmonypy; verify import harmonypy succeeds
ValueError: vars_use not in meta_data columns	Batch column name mismatch	Check adata.obs.columns and confirm the column name passed to key= exists
Memory error on large datasets (>1M cells)	Full PCA matrix loaded into memory	Use harmonypy directly with chunked PCA; consider subsampling to 200k cells for parameter tuning first
Clusters appear identical before and after correction	PCA was not computed with HVGs selected per batch	Re-run sc.pp.highly_variable_genes(adata, batch_key="batch") and sc.pp.pca() before Harmony

References

• Harmony paper — Korsunsky et al., Nature Methods 2019 — original algorithm, benchmarks against MNN, Seurat, BBKNN, Scanorama
• harmonypy (Python) — GitHub — Python port by Kamil Slowikowski
• harmony (R) — GitHub — original R implementation by Immunogenomics Lab
• Harmony documentation — Broad Institute — tutorials and parameter guidance
• Scanpy external API — harmony_integrate — scanpy wrapper documentation
• Single-cell best practices — batch correction chapter — benchmarks and when to use each method