Derivative Aggregation

A parent pipeline aggregation which calculates the derivative of a specified metric in a parent histogram (or date_histogram) aggregation. The specified metric must be numeric and the enclosing histogram must have min_doc_count set to 0 (default for histogram aggregations).

Syntax

A derivative aggregation looks like this in isolation:

  1. "derivative": {
  2.   "buckets_path": "the_sum"
  3. }

Table 53. derivative Parameters

Parameter NameDescriptionRequiredDefault Value

buckets_path

The path to the buckets we wish to find the derivative for (see buckets_path Syntax for more details)

Required

gap_policy

The policy to apply when gaps are found in the data (see Dealing with gaps in the data for more details)

Optional

skip

format

format to apply to the output value of this aggregation

Optional

null

First Order Derivative

The following snippet calculates the derivative of the total monthly sales:

  1. POST /sales/_search
  2. {
  3.   "size": 0,
  4.   "aggs": {
  5.     "sales_per_month": {
  6.       "date_histogram": {
  7.         "field": "date",
  8.         "calendar_interval": "month"
  9.       },
  10.       "aggs": {
  11.         "sales": {
  12.           "sum": {
  13.             "field": "price"
  14.           }
  15.         },
  16.         "sales_deriv": {
  17.           "derivative": {
  18.             "buckets_path": "sales" 
  19.           }
  20.         }
  21.       }
  22.     }
  23.   }
  24. }

buckets_path instructs this derivative aggregation to use the output of the sales aggregation for the derivative

And the following may be the response:

  1. {
  2.    "took": 11,
  3.    "timed_out": false,
  4.    "_shards": ...,
  5.    "hits": ...,
  6.    "aggregations": {
  7.       "sales_per_month": {
  8.          "buckets": [
  9.             {
  10.                "key_as_string": "2015/01/01 00:00:00",
  11.                "key": 1420070400000,
  12.                "doc_count": 3,
  13.                "sales": {
  14.                   "value": 550.0
  15.                } 
  16.             },
  17.             {
  18.                "key_as_string": "2015/02/01 00:00:00",
  19.                "key": 1422748800000,
  20.                "doc_count": 2,
  21.                "sales": {
  22.                   "value": 60.0
  23.                },
  24.                "sales_deriv": {
  25.                   "value": -490.0 
  26.                }
  27.             },
  28.             {
  29.                "key_as_string": "2015/03/01 00:00:00",
  30.                "key": 1425168000000,
  31.                "doc_count": 2, 
  32.                "sales": {
  33.                   "value": 375.0
  34.                },
  35.                "sales_deriv": {
  36.                   "value": 315.0
  37.                }
  38.             }
  39.          ]
  40.       }
  41.    }
  42. }

No derivative for the first bucket since we need at least 2 data points to calculate the derivative

Derivative value units are implicitly defined by the sales aggregation and the parent histogram so in this case the units would be $/month assuming the price field has units of $.

The number of documents in the bucket are represented by the doc_count

Second Order Derivative

A second order derivative can be calculated by chaining the derivative pipeline aggregation onto the result of another derivative pipeline aggregation as in the following example which will calculate both the first and the second order derivative of the total monthly sales:

  1. POST /sales/_search
  2. {
  3.   "size": 0,
  4.   "aggs": {
  5.     "sales_per_month": {
  6.       "date_histogram": {
  7.         "field": "date",
  8.         "calendar_interval": "month"
  9.       },
  10.       "aggs": {
  11.         "sales": {
  12.           "sum": {
  13.             "field": "price"
  14.           }
  15.         },
  16.         "sales_deriv": {
  17.           "derivative": {
  18.             "buckets_path": "sales"
  19.           }
  20.         },
  21.         "sales_2nd_deriv": {
  22.           "derivative": {
  23.             "buckets_path": "sales_deriv" 
  24.           }
  25.         }
  26.       }
  27.     }
  28.   }
  29. }

buckets_path for the second derivative points to the name of the first derivative

And the following may be the response:

  1. {
  2.    "took": 50,
  3.    "timed_out": false,
  4.    "_shards": ...,
  5.    "hits": ...,
  6.    "aggregations": {
  7.       "sales_per_month": {
  8.          "buckets": [
  9.             {
  10.                "key_as_string": "2015/01/01 00:00:00",
  11.                "key": 1420070400000,
  12.                "doc_count": 3,
  13.                "sales": {
  14.                   "value": 550.0
  15.                } 
  16.             },
  17.             {
  18.                "key_as_string": "2015/02/01 00:00:00",
  19.                "key": 1422748800000,
  20.                "doc_count": 2,
  21.                "sales": {
  22.                   "value": 60.0
  23.                },
  24.                "sales_deriv": {
  25.                   "value": -490.0
  26.                } 
  27.             },
  28.             {
  29.                "key_as_string": "2015/03/01 00:00:00",
  30.                "key": 1425168000000,
  31.                "doc_count": 2,
  32.                "sales": {
  33.                   "value": 375.0
  34.                },
  35.                "sales_deriv": {
  36.                   "value": 315.0
  37.                },
  38.                "sales_2nd_deriv": {
  39.                   "value": 805.0
  40.                }
  41.             }
  42.          ]
  43.       }
  44.    }
  45. }

No second derivative for the first two buckets since we need at least 2 data points from the first derivative to calculate the second derivative

Units

The derivative aggregation allows the units of the derivative values to be specified. This returns an extra field in the response normalized_value which reports the derivative value in the desired x-axis units. In the below example we calculate the derivative of the total sales per month but ask for the derivative of the sales as in the units of sales per day:

  1. POST /sales/_search
  2. {
  3.   "size": 0,
  4.   "aggs": {
  5.     "sales_per_month": {
  6.       "date_histogram": {
  7.         "field": "date",
  8.         "calendar_interval": "month"
  9.       },
  10.       "aggs": {
  11.         "sales": {
  12.           "sum": {
  13.             "field": "price"
  14.           }
  15.         },
  16.         "sales_deriv": {
  17.           "derivative": {
  18.             "buckets_path": "sales",
  19.             "unit": "day" 
  20.           }
  21.         }
  22.       }
  23.     }
  24.   }
  25. }

unit specifies what unit to use for the x-axis of the derivative calculation

And the following may be the response:

  1. {
  2.    "took": 50,
  3.    "timed_out": false,
  4.    "_shards": ...,
  5.    "hits": ...,
  6.    "aggregations": {
  7.       "sales_per_month": {
  8.          "buckets": [
  9.             {
  10.                "key_as_string": "2015/01/01 00:00:00",
  11.                "key": 1420070400000,
  12.                "doc_count": 3,
  13.                "sales": {
  14.                   "value": 550.0
  15.                } 
  16.             },
  17.             {
  18.                "key_as_string": "2015/02/01 00:00:00",
  19.                "key": 1422748800000,
  20.                "doc_count": 2,
  21.                "sales": {
  22.                   "value": 60.0
  23.                },
  24.                "sales_deriv": {
  25.                   "value": -490.0, 
  26.                   "normalized_value": -15.806451612903226 
  27.                }
  28.             },
  29.             {
  30.                "key_as_string": "2015/03/01 00:00:00",
  31.                "key": 1425168000000,
  32.                "doc_count": 2,
  33.                "sales": {
  34.                   "value": 375.0
  35.                },
  36.                "sales_deriv": {
  37.                   "value": 315.0,
  38.                   "normalized_value": 11.25
  39.                }
  40.             }
  41.          ]
  42.       }
  43.    }
  44. }

value is reported in the original units of per month

normalized_value is reported in the desired units of per day