mongodb average arrays across many documents - mongodb

Question

Using mongodb, I have a collection of documents where each document has a fixed length vector of floating point values such as below:
items = [
{"id": "1", "vec": [1, 2, 0]},
{"id": "2", "vec": [6, 4, 1]},
{"id": "3", "vec": [3, 2, 2]},
]
I would like to take the row wise average of these vectors. In this example I would expect the result to return
[ (1 + 6 + 3) / 3, (2 + 4 + 2) / 3, (0 + 1 + 2) / 3 ]
This answer is very close to what I am looking for, but as far as I can tell it will only work on vectors of size 2. mongoDB - average on array values
An answer has been provided that is not very performant for large arrays. For context I am using ~700 dimension vectors.

Answer 1

This should work: https://mongoplayground.net/p/PKXqmmW31nW
[
{
$group: {
_id: null,
a: {
$push: {
$arrayElemAt: ["$vec", 0]
}
},
b: {
$push: {
$arrayElemAt: ["$vec", 1]
}
},
c: {
$push: {
$arrayElemAt: ["$vec", 2]
}
}
}
},
{
$project: {
a: {
$avg: "$a"
},
b: {
$avg: "$b"
},
c: {
$avg: "$c"
}
}
}
]
Which outputs:
[
{
"_id": null,
"a": 3.3333333333333335,
"b": 2.6666666666666665,
"c": 1
}
]
Here's a more efficient without $avg operator. I'll leave other answer up for reference.
https://mongoplayground.net/p/rVERc8YjKZv
db.collection.aggregate([
{
$group: {
_id: null,
a: {
$sum: {
$arrayElemAt: ["$vec", 0]
}
},
b: {
$sum: {
$arrayElemAt: ["$vec", 1]
}
},
c: {
$sum: {
$arrayElemAt: ["$vec", 2]
}
},
totalDocuments: {
$sum: 1
}
}
},
{
$project: {
a: {
$divide: ["$a", "$totalDocuments"]
},
b: {
$divide: ["$b", "$totalDocuments"]
},
c: {
$divide: ["$c", "$totalDocuments"]
}
}
}
])

Answer 2

You can use $unwind to get values into separate documents, the key is to keep the index of the values. Then you can use $group by the index and calculate the average using the $avg operator.
db.collection.aggregate([
{
$unwind: {
path: "$vec",
includeArrayIndex: "i" // unwind and keep index
}
},
{
$group: {
_id: "$i", // group by index
avg: { $avg: "$vec" }
}
}, // at this stage, you already get all the values you need, in separate documents. The following stages will put all the values in an array
{
$sort: { _id: 1 }
},
{
$group: {
_id: null,
avg: { $push: "$avg" }
}
}
])
Mongo Playground