Interesting phenomenon

[dstaehler]

Hello Cleora team, a very interesting and clever solution for creating embeddings. However, I noticed a behavior that I cannot explain. When creating embeddings with one column (a category of a single node type) that contains both a start and an end node (simple edge list), nodes that are further away from each other generate a vector that is closer to each other. E.g .: (a) -> (b) -> (c) -> (d)

as Edge List:
a b
b c
c d

The vectors a and d are closer together than the vectors a and b (by Cosin value)

Volume: approx. 5.5 million nodes and 41 million edges

I created the embeddings with the following call:

--columns = 'complex :: reflexive :: nodes' -d = 128 -i = 'node.edgelist' -n = 4

As I understand the pattern, the reflexive relationship in a column of a single type (complex) should cover an edge list with a category of node types. What am I doing wrong with the configuration or is this an issue?

A short tip would be very appreciated.

Best

[barbara3430]

Hello @dstaehler ! Your method of running Cleora seems fine. In order to investigate this phenomenon let's do the following:

• please double check if you're using cosine similarity for distance computation
• if yes, this behavior seems strange. Are you sure there are no hidden cycles in your data? E.g. node A could be linked to D futher in the dataset by a direct or at least closer connection.
• you could try with smaller -n. With too large -n all vectors will eventually get very similar to each other. We usually use -n of 1 to 4 and larger -d - usually 1024.

Let us know how it goes :)
Best, Barbara

[dstaehler]

Hello Barbara,

Thanks for your response. I use cosine similarity for the comparison of the vectors. There may be (very likely) connections in the form of A -> C and C -> D somewhere in the dataset. But I have checked the near vector space for the examples where the strange effects occur by a shortest path scan of the whole dataset. The results are: e.g. two nodes that have a shortest path of 3 edges deliver a higher cosine similarity than a node pair where the shortest path is 1 edge. This occurs for almost all examples I checked. What I haven’t done so far is taken the node degree into account. But this would require a full degree scan of the dataset upfront. Skipped this due to scanning complexity. I checked the reduction of n as well (n = 2). Same effect. And I tried the increase of the dimensions as well (d = 512). Didn’t do 1024 but 512 produced the same results. So far I‘m a bit lost what else I cloud do.

best

Doug

[barbara3430]

Dear Doug,
Could you possibly provide us with a slice of your data where this is happening (anonymized if privacy is of concern)? Even a very small one (dozens-hundreds of lines).

Another option is that maybe your graph is bipartite. We have a discussion about such graphs here, with an explanation what to do: #29

Best!
Barbara

[dstaehler]

Hello Barbara,

thank for your replay and the offer to have a look at the dataset. The graph is not bipartite. All the nodes belong to the same entity type. Regarding the example dataset I'll drop you an email.

best

Doug