Para mongo>=v3.4, veja weekStart. A ideia é substruir milissegundos de um timestamp fornecido
db.raw.aggregate([
// stage 1
{ "$match" : {
"Timestamp":{
"$gte": ISODate("2012-05-30"),
"$lt": ISODate("2014-07-31")
}
}},
// stage 2
{ "$project" : {
ApplicationId: 1,
Country: 1,
week: {$isoWeek: "$Timestamp"},
// [TRICK IS HERE] Timestamp - dayOfWeek * msInOneDay
weekStart: { $dateToString: { format: "%Y-%m-%d", date: { // convert date
$subtract: ["$Timestamp", {$multiply: [ {$subtract:[{$isoDayOfWeek: "$Timestamp"},1]}, 86400000]}]
}}},
// stage 3
{ "$group" : {
"_id":{
"ApplicationId": "$ApplicationId",
"Country": "$Country",
"week": "$week"
},
"Date":{ "$first": "$weekStart" },
"Visits": { "$sum": 1 }
}}
])
