Different latent vectors for same (test)users

Hi,

I created a model for a retailer with 38k customers and 36k articles and a sparsity of 0,55%. One part of the analysis is to find similiar customers, to get the "neighbours" I took the latent features of the users and checked the dot product between them ([similiar to the LightFM example](https://making.lyst.com/lightfm/docs/examples/hybrid_crossvalidated.html)).
In order to get a better understanding of my model I created some test customers and calculated their similarity. Two of those test customers are (besides a different name) exactly the same. Both bought the same (one) article ones and are in the same industry (a user feature).
In my understanding they should have the same vectors and therefore a dot product of 1. But unfortunately the vectors are different and the dot product is -0.057281606.

Does somebody have an explanation how this can happen?

Thanks in advance!

Best,
Moritz

Those are the normalized vectors:
Testuser 1:
```
[ 0.13190027 0.26906827 -0.0822762 0.21407925 0.13211617 0.2566751
0.17467268 0.02340734 0.09154253 0.2269812 -0.26795995 0.06671422
0.08172801 0.1463228 0.21353354 0.12667963 -0.02653628 -0.0790253
0.03541145 0.09163333 0.05831769 0.4006284 0.14730851 0.28267866
-0.05757256 0.1948472 -0.08183019 0.28852767 0.09479482 0.30822176]
```

Testuser 2:
```
[-0.15500401 0.2269293 0.21974853 -0.02541173 -0.16325705 -0.13497874
-0.17643186 0.09408431 0.04687239 0.20745914 0.27600515 0.02616096
-0.24575633 -0.27663186 -0.10878677 0.27803454 0.08667072 0.06445353
0.20262392 0.1274841 0.30217353 -0.04354052 0.29860505 0.30625728
0.0359767 -0.15467772 -0.09467538 -0.12735379 -0.20820434 0.06034918]

```
```
customer1 = "T0000001"
customer2 = "T0000004"
num_user = dataset.interactions_shape()[0]
user_x1 = mappings.kundennummer2row[customer1]
user_x2 = mappings.kundennummer2row[customer2]

user_embeddings_norm = (model.user_embeddings[:num_user].T
/ np.linalg.norm(model.user_embeddings[:num_user], axis=1)).T

similarity = np.dot(user_embeddings_norm[user_x2], user_embeddings_norm[user_x1])
```
That's how I built the dataset:
```
dataset = Dataset()

dataset.fit(items=artikel_meta["Artikelnummer"],
users=kunden_meta["Hauptkundennummer"],
item_features=artikel_meta["Warengruppe"].unique(),
user_features=kunden_meta["Branchenschlüssel"].unique())

(interactions, weights) = dataset.build_interactions([(x['Hauptkundennummer'],
x['Artikelnummer'],
x['Kernumsatz']) for index,x in sales_data_2019_grouped.iterrows()])

def prepare_features_format(data, id, feature_columns):
features = []
for row in range(data.shape[0]):
features.append([data[id][row],[str(data[feature][row]) for feature in feature_columns]])
features = tuple(features)
return features

item_features = dataset.build_item_features(prepare_features_format(artikel_meta,'Artikelnummer',['Warengruppe']))
user_features = dataset.build_user_features(prepare_features_format(kunden_meta,'Hauptkundennummer',['Branchenschlüssel']))

```
_some translation: "Artikelnummer" = "item number", "Hauptkundennummer" = "Customer number", "Warengruppe" = "Product group", "Branchenschlüssel" = "Industry Code"_

Reproduce the comparison using the shown Dataset construction, feature builders, mapping lookups, and model.user_embeddings normalization. Check whether the two customer IDs resolve to the intended rows and whether their interaction and user-feature inputs are identical. Done means explaining the differing vectors or isolating a reproducible defect.

Written by the indexing model from the issue text.