crankshaft/doc/18_outliers.md

Outlier Detection

This set of functions detects the presence of outliers. There are three functions for finding outliers from non-spatial data:

1. Static Outliers
2. Percentage Outliers
3. Standard Deviation Outliers

CDB_StaticOutlier(column_value numeric, threshold numeric)

Arguments

Name	Type	Description
column_value	numeric	The column of values on which to apply the threshold
threshold	numeric	The static threshold which is used to indicate whether a column_value is an outlier or not

Returns

Returns a boolean (true/false) depending on whether a value is above or below (or equal to) the threshold

Name	Type	Description
outlier	boolean	classification of whether a row is an outlier or not

Example Usage

With a table website_visits and a column of the number of website visits in units of 10,000 visits:

| id | visits_10k |
|----|------------|
| 1  | 1 |
| 2  | 3 |
| 3  | 5 |
| 4  | 1 |
| 5  | 32 |
| 6  | 3 |
| 7  | 57 |
| 8  | 2 |

SELECT
  id,
  CDB_StaticOutlier(visits_10k, 11.0) As outlier,
  visits_10k
FROM website_visits

| id | outlier | visits_10k |
|----|---------|------------|
| 1  | f | 1 |
| 2  | f | 3 |
| 3  | f | 5 |
| 4  | f | 1 |
| 5  | t | 32 |
| 6  | f | 3 |
| 7  | t | 57 |
| 8  | f | 2 |

CDB_PercentOutlier(column_values numeric[], outlier_fraction numeric, ids int[])

CDB_PercentOutlier calculates whether or not a value falls above a given threshold based on a percentage above the mean value of the input values.

Arguments

Name	Type	Description
column_values	numeric[]	An array of the values to calculate the outlier classification on
outlier_fraction	numeric	The threshold above which a column value divided by the mean of all values is considered an outlier
ids	int[]	An array of the unique row ids of the input data (usually cartodb_id)

Returns

Returns a table of the outlier classification with the following columns

Name	Type	Description
is_outlier	boolean	classification of whether a row is an outlier or not
rowid	int	original row id (e.g., input cartodb_id) of the row which has the outlier classification

Example Usage

This example find outliers which are more than 100% larger than the average (that is, more than 2.0 times larger).

WITH cte As (
  SELECT
    unnest(Array[1,2,3,4,5,6,7,8]) As id,
    unnest(Array[1,3,5,1,32,3,57,2]) As visits_10k
  )
SELECT
  (CDB_PercentOutlier(array_agg(visits_10k), 2.0, array_agg(id))).*
FROM cte;

Output

| outlier | rowid |
|---------+-------|
| f | 1 |
| f | 2 |
| f | 3 |
| f | 4 |
| t | 5 |
| f | 6 |
| t | 7 |
| f | 8 |

CDB_StdDevOutlier(column_values numeric[], num_deviations numeric, ids int[], is_symmetric boolean DEFAULT true)

CDB_StdDevOutlier calculates whether or not a value falls above or below a given threshold based on the number of standard deviations from the mean.

Arguments

Name	Type	Description
column_values	numeric[]	An array of the values to calculate the outlier classification on
num_deviations	numeric	The threshold in units of standard deviation
ids	int[]	An array of the unique row ids of the input data (usually cartodb_id)
is_symmetric (optional)	boolean	Consider outliers that are symmetric about the mean (default: true)

Returns

Returns a table of the outlier classification with the following columns

Name	Type	Description
is_outlier	boolean	classification of whether a row is an outlier or not
rowid	int	original row id (e.g., input cartodb_id) of the row which has the outlier classification

Example Usage

This example find outliers which are more than 100% larger than the average (that is, more than 2.0 times larger).

WITH cte As (
  SELECT
    unnest(Array[1,2,3,4,5,6,7,8]) As id,
    unnest(Array[1,3,5,1,32,3,57,2]) As visits_10k
  )
SELECT
  (CDB_StdDevOutlier(array_agg(visits_10k), 2.0, array_agg(id))).*
FROM cte;

Output

| outlier | rowid |
|---------+-------|
| f | 1 |
| f | 2 |
| f | 3 |
| f | 4 |
| f | 5 |
| f | 6 |
| t | 7 |
| f | 8 |