# Changing the order of the anndata objects in anndata.concat changes the leiden clustering

**URL:** <https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802>\
**Category:** anndata\
**Created:** [September 17, 2025, 10:50am UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802 "2025-09-17T10:50:33Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![osmanmerdan](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/osmanmerdan/32/1097_2.png) [@osmanmerdan](https://discourse.scverse.org/u/osmanmerdan)\
**Post date:** [September 17, 2025, 10:50am UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/1 "2025-09-17T10:50:33Z")

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Hi everyone,

When I change the order of anndata objects in anndata concat, like the following:

```python
adata1 = ad.concat([day1_data, day2_data, day3_data], join='outer')
adata2 = ad.concat([day2_data, day1_data, day3_data], join='outer')

```

And doing basic processing with normalization, PCA, neighbouring graph, UMAP, and leiden clustering, I got the same UMAP (at least no visual differences I can spot) but fairly significant clustering differences. Like some clusters being merged, some new ones pop up, etc. Did anyone else notice a similar thing? Also, I wonder why?

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**Author:** ![ilan-gold](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/ilan-gold/32/1001_2.png) [@ilan-gold](https://discourse.scverse.org/u/ilan-gold)\
**Post date:** [September 22, 2025, 5:35pm UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/2 "2025-09-22T17:35:00Z")

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Hi @osmanmerdan, are you using `igraph` or `leidenalg` ? Could you share an environment listing i.e., `import scanpy; scanpy.logging.print_versions()` for where this happens? From the igraph [R documentation](https://igraph.org/r/html/1.3.5/cluster_leiden.html), I could see the algorithm having this property “The Leiden algorithm consists of three phases: (1) local moving of nodes, (2) refinement of the partition and (3) aggregation of the network based on the refined partition.”

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**Author:** ![osmanmerdan](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/osmanmerdan/32/1097_2.png) [@osmanmerdan](https://discourse.scverse.org/u/osmanmerdan)\
**Post date:** [September 29, 2025, 6:57pm UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/3 "2025-09-29T18:57:14Z")

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Dear @ilan-gold , I have included an example Jupyter notebook using a publicly available dataset. In my case, I was using Scanpy 1.11.0 and anndata 0.11.1, and I saw this behavior using both the `leidenalg` and `igraph` implementations. In the example I have included, I observed that the PCA analysis yielded different floating-point values for the two datasets, which may be the reason for the differing end results. [Google Colab](https://colab.research.google.com/drive/1LPtZx2rg96X7rbbY-8Locw4eOWZ1-vm7?usp=sharing)

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**Author:** ![ilan-gold](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/ilan-gold/32/1001_2.png) [@ilan-gold](https://discourse.scverse.org/u/ilan-gold)\
**Post date:** [September 30, 2025, 8:38am UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/4 "2025-09-30T08:38:50Z")

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Hmm @osmanmerdan this strikes me as a bug with scipy’s PCA, no? Maybe a bug report there would be a good start? I think if you cut down your example to just that final cell with `arpack` using `scipy` directly, you have a great bug report

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**Author:** ![osmanmerdan](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/osmanmerdan/32/1097_2.png) [@osmanmerdan](https://discourse.scverse.org/u/osmanmerdan)\
**Post date:** [October 1, 2025, 5:31pm UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/5 "2025-10-01T17:31:58Z")

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Hi @ilan-gold, I have opened a discussion [here](https://stackoverflow.com/questions/79779783/pca-with-arpack-returns-different-values-when-the-order-of-observations-change?noredirect=1#comment140770632_79779783). And it turns out that the `np.float32` precision in the normalized count matrix, plus how `arpack` works, can cause these kinds of numerical inconsistencies. So, I have converted the `adata.X` data type to `np.float64` and ran the clustering again.

Here is the interesting part for me: now the PCA values are equal within the `1e-12` limits. However, neighbouring/ clustering is still different. `.obsp['distances']` `.obsp['connectivities']` entries are different.

I went further and changed the method to compute connectivities from `method="umap"` to `method="gauss"`. But it also resulted in different connectivity arrays.

Updated notebook: [Google Colab](https://colab.research.google.com/drive/1LPtZx2rg96X7rbbY-8Locw4eOWZ1-vm7?usp=sharing#scrollTo=xBsMmStYtIkd)

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<div class="post-metadata">

**Author:** ![ilan-gold](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/ilan-gold/32/1001_2.png) [@ilan-gold](https://discourse.scverse.org/u/ilan-gold)\
**Post date:** [October 7, 2025, 10:04am UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/6 "2025-10-07T10:04:22Z")

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Hi @osmanmerdan I have a hunch that the `leiden` algorithm is not stable up to ordering. From [wikipedia](https://en.wikipedia.org/wiki/Leiden_algorithm#Algorithm) I see that there is a “ **Local Moving of Nodes** ” phase which I appears to be unstable up to ordering. Does this make sense?

While I don’t know a whole lot about the inner workings of the algorithms underlying `umap` or `neighbors`, I assume given that `neighbors` relies on ANN (specifically, the default is using `PyNNDescentTransformer`), the ordering again matters because of the approximate nature. For example, I notice the there are a factor of 10 more difference in connectivities than distances, which really signals to me that this is down to some sort of tie-breaking that is getting propagated down from the distances to the connectivities (and then to `leiden` and `umap`). So distances are slightly different, which means connectivities are too, which means leiden is even worse etc.

Here’s a quick sample that I think highlights this fact:

```python-repl
import numpy as np
from pynndescent import PyNNDescentTransformer
from sklearn.datasets import make_blobs
from sklearn.utils import shuffle

n_samples = 1000
n_features = 10
n_neighbors = 10
random_state = 42

X, _ = make_blobs(n_samples=n_samples, n_features=n_features, random_state=random_state)

transformer1 = PyNNDescentTransformer(n_neighbors=n_neighbors, random_state=42)
X_nn_1 = transformer1.fit_transform(X)

X_shuffled, indices = shuffle(X, np.arange(len(X)), random_state=123)

transformer2 = PyNNDescentTransformer(n_neighbors=n_neighbors, random_state=42)
X_nn_2 = transformer2.fit_transform(X_shuffled)

inverse_indices = np.zeros_like(indices)
inverse_indices[indices] = np.arange(len(indices))

X_nn_2_mapped = X_nn_2[inverse_indices, :][:, inverse_indices] # reorder both rows and columns

np.testing.assert_equal(X, X_shuffled[inverse_indices]) # should be equal
np.testing.assert_almost_equal(X_nn_1.toarray(), X_nn_2_mapped.toarray()) # off by 174 for me

```

Short of going into the scanpy code to check the output of nndescent output, I think this probably signals the issue really is the ordering, and it starts as soon as you compute neighbors.

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<div class="post-metadata">

**Author:** ![osmanmerdan](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.scverse.org/osmanmerdan/32/1097_2.png) [@osmanmerdan](https://discourse.scverse.org/u/osmanmerdan)\
**Post date:** [October 9, 2025, 7:45am UTC](https://discourse.scverse.org/t/changing-the-order-of-the-anndata-objects-in-anndata-concat-changes-the-leiden-clustering/3802/7 "2025-10-09T07:45:09Z")

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Hi @ilan-gold thank you very much for the detailed explanation and example.🖖 I totally agree. To me, the mystery is somewhat resolved. It is like a snowball effect, tiny differences add up.