A relevância do Atlas Search explicada

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[{
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  "$search": {
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    ...
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    "scoreDetails": true
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  }
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},
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{
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  "$project": {
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    ...
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    "scoreDetails": {"$meta": "searchScoreDetails"}
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  }
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}]

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[
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      {
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        "$search": {
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          "compound": {
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            "filter": [
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              {
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                "compound": {
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                  "must": [
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                    {
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                      "text": {
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                        "query": "Drama",
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                        "path": "genres"
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                      }
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                    },
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                    {
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                      "text": {
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                        "query": "Romance",
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                        "path": "genres"
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                      }
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                    }
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                  ]
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                }
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              }
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            ],
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            "must": [
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              {
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                "phrase": {
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                  "query": "keanu reeves",
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                  "path": "cast"
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                }
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              }
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            ]
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          },
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          "scoreDetails": true
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        }
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      },
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      {
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        "$project": {
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          "_id": 0,
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          "title": 1,
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          "cast": 1,
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          "genres": 1,
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          "score": {
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            "$meta": "searchScore"
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          },
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          "scoreDetails": {
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            "$meta": "searchScoreDetails"
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          }
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        }
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      },
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      {
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        "$limit": 10
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      }
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    ]

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"scoreDetails": {
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  "value": 6.011996746063232,
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  "description": "sum of:",
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  "details": [
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    {
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      "value": 0,
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      "description": "match on required clause, product of:",
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      "details": [
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        {
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          "value": 0,
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          "description": "# clause",
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          "details": []
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        },
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        {
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          "value": 1,
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          "description": "+ScoreDetailsWrapped ($type:string/genres:drama) +ScoreDetailsWrapped ($type:string/genres:romance)",
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          "details": []
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        }
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      ]
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    },
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    {
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      "value": 6.011996746063232,
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      "description": "$type:string/cast:\"keanu reeves\" [BM25Similarity], result of:",
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      "details": [
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        {
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          "value": 6.011996746063232,
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          "description": "score(freq=1.0), computed as boost * idf * tf from:",
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          "details": [
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            {
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              "value": 13.083234786987305,
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              "description": "idf, sum of:",
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              "details": [
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                {
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                  "value": 6.735175132751465,
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                  "description": "idf, computed as log(1 + (N - n + 0.5) / (n + 0.5)) from:",
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                  "details": [
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                    {
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                      "value": 27,
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                      "description": "n, number of documents containing term",
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                      "details": []
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                    },
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                    {
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                      "value": 23140,
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                      "description": "N, total number of documents with field",
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                      "details": []
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                    }
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                  ]
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                },
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                {
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                  "value": 6.348059177398682,
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                  "description": "idf, computed as log(1 + (N - n + 0.5) / (n + 0.5)) from:",
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                  "details": [
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                    {
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                      "value": 40,
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                      "description": "n, number of documents containing term",
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                      "details": []
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                    },
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                    {
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                      "value": 23140,
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                      "description": "N, total number of documents with field",
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                      "details": []
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                    }
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                  ]
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                }
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              ]
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            },
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            {
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              "value": 0.4595191478729248,
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              "description": "tf, computed as freq / (freq + k1 * (1 - b + b * dl / avgdl)) from:",
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              "details": [
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                {
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                  "value": 1,
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                  "description": "phraseFreq=1.0",
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                  "details": []
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                },
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                {
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                  "value": 1.2000000476837158,
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                  "description": "k1, term saturation parameter",
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                  "details": []
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                },
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                {
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                  "value": 0.75,
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                  "description": "b, length normalization parameter",
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                  "details": []
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                },
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                {
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                  "value": 8,
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                  "description": "dl, length of field",
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                  "details": []
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                },
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                {
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                  "value": 8.217415809631348,
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                  "description": "avgdl, average length of field",
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                  "details": []
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                }
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              ]
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            }
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          ]
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        }
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      ]
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    }
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  ]
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}

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log(1 + (N - n + 0.5) / (n + 0.5))

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freq / (freq + k1 * (1 - b + b * dl / avgdl))

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function print_score_details(details, indent_level) {
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  if (!indent_level) { indent_level = 0; }
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  spaces = " ".padStart(indent_level);
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  console.log(spaces + details.value + ", " + details.description);
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  details.details.forEach (d => {
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    print_score_details(d, indent_level + 2);
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  });
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}