I am saving face embedding as numpy array in mongodb and using this aggrigate to find distance between to array using euclidean algorithm.
Can someone please help to calculate distance using cosine?
Sample json document is shown below and aggregate should return only those documents whose distance is <= 0.68
{
"_id": {
"$oid": "635ff70a16dfa4cd45f02c43"
},
"img_path": "1_11",
"name": "11",
"embedding": [
0.04153144732117653,
-0.0008036745712161064,
-0.003807373344898224,
-0.11769875884056091,
0.03676579147577286,
0.09997286647558212,
-0.044136010110378265,
-0.1692838966846466,
-0.003151319921016693,
-0.03791208565235138,
-0.010753434151411057,
-0.024590950459241867,
0.29803258180618286,
-0.04285677522420883,
0.20911607146263123,
0.04455781728029251,
0.029769904911518097,
-0.33982840180397034,
0.010117404162883759,
-0.4239773750305176,
-0.005369218066334724,
0.0714929848909378,
0.2586987018585205,
0.007376951165497303,
-0.03157464414834976,
0.11055145412683487,
-0.052830226719379425,
-0.16745653748512268,
0.06054156646132469,
-0.3206060826778412,
0.054714761674404144,
-0.10260075330734253,
0.2717891037464142,
-0.16717249155044556,
0.09896406531333923,
-0.2952454090118408,
0.010972617194056511,
0.24918027222156525,
-0.2690051198005676,
0.2626166343688965,
0.2875710725784302,
0.13260763883590698,
0.12771351635456085,
-0.22898457944393158,
0.18346519768238068,
-0.06396391987800598,
-0.09320224076509476,
0.02307960018515587,
-0.3165799081325531,
0.007051767781376839,
0.06508949398994446,
-0.15390481054782867,
0.07253721356391907,
0.05360442399978638,
0.02317194454371929,
0.2602832019329071,
0.32494112849235535,
0.10228901356458664,
-0.026188479736447334,
0.051889386028051376,
-0.17360231280326843,
0.2001030296087265,
0.11494665592908859,
-0.1468532681465149,
-0.3037929832935333,
0.4243096113204956,
-0.3967720568180084,
-0.1580674648284912,
0.1209937185049057,
-0.3088080883026123,
0.14958013594150543,
-0.1499250829219818,
0.1793043464422226,
0.042404696345329285,
-0.17440882325172424,
0.014482134953141212,
0.17418500781059265,
-0.29781395196914673,
0.3233387768268585,
-0.13625966012477875,
-0.2671341001987457,
0.1924743503332138,
-0.0009934399276971817,
-0.13012878596782684,
0.04334684833884239,
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0.026077959686517715,
0.23131468892097473,
-0.04128192365169525,
0.11939074844121933,
0.2669318914413452,
0.02978256344795227,
-0.07513333857059479,
0.09071725606918335,
0.14345180988311768,
-0.2577393651008606,
-0.1343279629945755,
0.03614958003163338,
0.04753677546977997,
0.4799879491329193,
0.12120816111564636,
0.04913831502199173,
-0.1472567766904831,
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0.0709092766046524,
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-0.06318340450525284,
0.11655210703611374,
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0.13326743245124817,
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0.0984693095088005,
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-0.005599251948297024,
-0.1000245064496994,
0.03078708052635193,
0.2257998287677765,
0.23468151688575745,
0.24614854156970978,
0.057032980024814606,
0.02590012177824974,
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0.024511300027370453,
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0.15368790924549103,
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0.08967467397451401,
0.023094654083251953,
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0.012936883606016636,
0.03222038224339485,
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]
}
Thank you so much in advance. :)
{
"$addFields": {
"target_embedding": target_embedding
}
}
, {"$unwind" : { "path" : "$embedding", "includeArrayIndex": "embedding_index"}}
, {"$unwind" : { "path" : "$target_embedding", "includeArrayIndex": "target_index" }}
, {
"$project": {
"img_path": 1,
"embedding": 1,
"name" : 1,
"target_embedding": 1,
"compare": {
"$cmp": ['$embedding_index', '$target_index']
}
}
}
, {"$match": {"compare": 0}}
, {
"$group": {
"_id": "$img_path",
"name" : { "$first": "$name" },
"distance": {
"$sum": {
"$pow": [{
"$subtract": ['$embedding', '$target_embedding']
}, 2]
}
}
}
}
, {
"$project": {
"name" : 1,
"_id": 1
#, "distance": 1
, "distance": {"$sqrt": "$distance"}
}
}, {
"$project": {
"name" : 1,
"_id": 1
, "distance": 1
, "cond": { "$lte": [ "$distance", 4.15 ] }
}
}
, {"$match": {"cond": True}}
, { "$sort" : { "distance" : 1 } }
] )
CodePudding user response：
I'm not familiar with the facial recognition domain so I don't know the significance of the 0.68 threshold, but it's easy to change the final "$match".
The pipeline below:
- Fetches a generated
"target_embedding"(described below) - Calculates cosine similarity parameters using
"$reduce"- dot product
- sum of squares for document embedding
- sum of squares for target embedding
- Calculates cosine similarity as the dot product divided by the square root of the product of the two sums of squares
- Thresholds using
"$match"
Rather than loading a 512-length array into mongoplayground.net, I used its mgodatagen configuration option to create two collections: "faces" with a hundred documents of embeddings, and "target" with a single document/embedding used as "target_embedding". So, you'll need to change the initial pipeline stages to match your inputs.
db.faces.aggregate([
// go get the target embedding
{
"$lookup": {
"from": "target",
"pipeline": [],
"as": "target"
}
},
{
"$set": {
"target_embedding": {"$first": "$target.embedding"},
"target": "$$REMOVE"
}
},
// done getting target embedding
//
// calculate cosine similarity params
{
"$project": {
"name": 1,
"img_path": 1,
"cos_sim_params": {
"$reduce": {
"input": {"$range": [0, {"$size": "$embedding"}]},
"initialValue": {
"dot_product": 0,
"doc_2_sum": 0,
"target_2_sum": 0
},
"in": {
"$let": {
"vars": {
"doc_elem": {"$arrayElemAt": ["$embedding", "$$this"]},
"target_elem": {"$arrayElemAt": ["$target_embedding", "$$this"]}
},
"in": {
"dot_product": {
"$add": [
"$$value.dot_product",
{"$multiply": ["$$doc_elem", "$$target_elem"]}
]
},
"doc_2_sum": {
"$add": [
"$$value.doc_2_sum",
{"$pow": ["$$doc_elem", 2]}
]
},
"target_2_sum": {
"$add": [
"$$value.target_2_sum",
{"$pow": ["$$target_elem", 2]}
]
}
}
}
}
}
}
}
},
{
"$project": {
"name": 1,
"img_path": 1,
"cos_sim": {
"$divide": [
"$cos_sim_params.dot_product",
{
"$sqrt": {
"$multiply": [
"$cos_sim_params.doc_2_sum",
"$cos_sim_params.target_2_sum"
]
}
}
]
}
}
},
{
"$match": {
"cos_sim": {"$lte": 0.68}
}
}
])
Try it on mongoplayground.net.