how to search for the most similar array of numbers against a given array.

[tony156]

Hi everyone, I'm new to Neo4j.

Let say I have a graph of spectrum, where each spectrum has intensity (an array of numbers) as its property. I want to search a given spectrum against these spectrum to find the spectrum that is most similar. I'm trying k-nearest neighbor algorithm but it is looking for k-nearest-node for each node in the graph, but I want to find the nearest node to a given node only.

Thank you for your help

[ameyasoft]

Personally, I find this as very interesting project and want to help you.

Q: The spectrum intensity values show 0.0 and some non 0.0 numbers. Your example shows for one node. For other nodes the difference occurs in non 0.0 values only or it depends on the position of non 0.0 numbers in the array. If you can post values from two nodes (full images from node properties), I can try something from my end. Thanks

[tony156]

Hi @ameyasoft , It will depend on the position of the non zeroes numbers. I'm using k-nearest-neighbor algorithm. I'm posting the screen shots of two nodes, but it won't show all the numbers since my array has 1000 elements. So I will attach a file for that, but you can try with fewer elements as well. Thank you, I will be waiting for your kind reply.

[tony156]

Hi @ameyasoft Thanks for your reply.
I'm using cosine similarity of two arrays, so for example similarity between [1,2,3] and [2,0,4] = (1x2 + 2x0 + 3x4) / (sqr(1^2 + 2^2 + 3^2)xsqr(2^2+0^2+4^2)). Here is the algorithm I used to find the similaries:

CALL gds.knn.stream('spectrumGraph', {

topK: 1,

nodeProperties: [{Intensities:'COSINE'}],

randomSeed: 1337,

concurrency: 1,

sampleRate: 1.0,

deltaThreshold: 0.0

})

YIELD node1, node2, similarity

RETURN gds.util.asNode(node1).title AS S1, gds.util.asNode(node2).title AS S2, similarity

ORDER BY similarity DESCENDING, S1, S2

I'm copying here to show properties of two nodes (since my array size is kinda large the neo4j desktop doesn't show full screenshot).

Node 1: <id>: 1
Intensities:

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Node 2: <id>: 1
Intensities: [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0063722641200811584,0.006153010903497263,0.053466462958387126,0.11809743891361771,0.01937084767469783,0.0012389546841883627,0.0016600600684209244,0.0,0.0,0.005216834470781898,0.0,0.0,0.0,0.0,0.003671621325333491,0.0,0.05541538043913287,0.04315460135936994,0.03520232199596992,0.004503391464437476,0.014564677958787357,0.0014651683203463503,0.0018827934947918661,0.0,0.0,0.0,0.0,0.0,0.0030730252419615854,0.0,0.026157256759437458,0.012901137680579385,1.0,0.11479471982571109,0.0517228778550771,0.002902494962396333,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.021368488092462213,0.003998761045315812,0.06760307511336784,0.011679584045326251,0.12340127862907577,0.018124932570935375,0.00956013628501526,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.9085505274257932,0.1672902042535124,0.09603290886374631,0.009640181110117317,0.0017644663620323031,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.007813070971918187,0.0017087830054395678,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.12142451947003365,0.1823351511629121,0.04606405674134036,0.017035626907589987,0.0021264081798850836,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.006838612231545318,0.0013677224463090635,0.0012598359429106386,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.05447920400641751,0.010618120060277233,0.005143750065253933,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]

Thanks for your help!

[ameyasoft]

Sorry for the delay. I was on Thanksgiving break. The intensity lists you posted look identical. Please post another list that is different from the posted one. Thanks.

[ameyasoft]

Here is what I did:

1. Used apoc.coll.dropDuplicateNeighbors to delete duplicate 0.0 values form each node array intensities.

2. Used these truncated arrays to calculate cosine similarity. Since the two arrays above are similar, for my test I moved the first non 0.0 value to the end of the sencond truncated array.
3. Ran cosine similarity

with step 2, I ran the cosine similarity

RETURN gds.similarity.cosine(i1, i2) AS cosineSimilarity

result: 0.17864027595891765

Check and let me know. Thanks

with i1, apoc.coll.dropDuplicateNeighbors(i1) as i2

return size(i1), size(i2), i2

Result:
[0.0, 0.0063722641200811584, 0.006153010903497263, 0.053466462958387126, 0.11809743891361771, 0.01937084767469783, 0.0012389546841883627, 0.0016600600684209244, 0.0, 0.005216834470781898, 0.0, 0.003671621325333491, 0.0, 0.05541538043913287, 0.04315460135936994, 0.03520232199596992, 0.004503391464437476, 0.014564677958787357, 0.0014651683203463503, 0.0018827934947918661, 0.0, 0.0030730252419615854, 0.0, 0.026157256759437458, 0.012901137680579385, 1.0, 0.11479471982571109, 0.0517228778550771, 0.002902494962396333, 0.0, 0.021368488092462213, 0.003998761045315812, 0.06760307511336784, 0.011679584045326251, 0.12340127862907577, 0.018124932570935375, 0.00956013628501526, 0.0, 0.9085505274257932, 0.1672902042535124, 0.09603290886374631, 0.009640181110117317, 0.0017644663620323031, 0.0, 0.007813070971918187, 0.0017087830054395678, 0.0, 0.12142451947003365, 0.1823351511629121, 0.04606405674134036, 0.017035626907589987, 0.0021264081798850836, 0.0, 0.006838612231545318, 0.0013677224463090635, 0.0012598359429106386, 0.0, 0.05447920400641751, 0.010618120060277233, 0.005143750065253933, 0.0].
Originalt size of 1000 reduced to 61

[tony156]

Hi @ameyasoft . Thanks for your answer. Actually we don't need to truncate the zeroes and just apply cosine similarity to the arrays.
Also, is there a way I can compare a node one by one with every node in the database to find the node with the highest similarity score? Is there a way to write procedure in neo4j for that?

[ameyasoft]

Yes, we can do that. I will send you that code. I used that in a different way to calculate the similarities.

[ameyasoft]

I created four nodes with different intensities(i rearranged one value to create four different intensities).

match (a:Spectrum) where a.intensities is not null
match (b:Spectrum) where id(b) < id(a) and b.intensities is not null
with a.title as S1, a.intensities as a1, b.title as S2, b.intensities as b1 
with S1, S2, gds.similarity.cosine(a1, b1) AS cosineSimilarity

with collect ({Title1: S1, Title2:S2, Similarity: cosineSimilarity }) as Similarities 

unwind Similarities as row 

return row.Title1 as S1, row.Title2 as S2, row.Similarity as cosineSimilarity order by cosineSimilarity desc

Result:

[tony156]

Thank you so much. I will give it a try.