This functionality is experimental and may be changed or removed completely in a future release.
The aggregations in this family operate on multiple fields and produce a matrix result based on the values extracted from the requested document fields. Unlike metric and bucket aggregations, this aggregation family does not yet support scripting.
The matrix_stats
aggregation is a numeric aggregation that computes the following statistics over a set of document fields:

Number of per field samples included in the calculation. 

The average value for each field. 

Per field Measurement for how spread out the samples are from the mean. 

Per field measurement quantifying the asymmetric distribution around the mean. 

Per field measurement quantifying the shape of the distribution. 

A matrix that quantitatively describes how changes in one field are associated with another. 

The covariance matrix scaled to a range of 1 to 1, inclusive. Describes the relationship between field distributions. 
The following example demonstrates the use of matrix stats to describe the relationship between income and poverty.
{ "aggs": { "matrixstats": { "matrix_stats": { "fields": ["poverty", "income"] } } } }
The aggregation type is matrix_stats
and the fields
setting defines the set of fields (as an array) for computing
the statistics. The above request returns the following response:
{ ... "aggregations": { "matrixstats": { "fields": [{ "name": "income", "count": 50, "mean": 51985.1, "variance": 7.383377037755103E7, "skewness": 0.5595114003506483, "kurtosis": 2.5692365287787124, "covariance": { "income": 7.383377037755103E7, "poverty": 21093.65836734694 }, "correlation": { "income": 1.0, "poverty": 0.8352655256272504 } }, { "name": "poverty", "count": 50, "mean": 12.732000000000001, "variance": 8.637730612244896, "skewness": 0.4516049811903419, "kurtosis": 2.8615929677997767, "covariance": { "income": 21093.65836734694, "poverty": 8.637730612244896 }, "correlation": { "income": 0.8352655256272504, "poverty": 1.0 } }] } } }
The matrix_stats
aggregation treats each document field as an independent sample. The mode
parameter controls what
array value the aggregation will use for array or multivalued fields. This parameter can take one of the following:

(default) Use the average of all values. 

Pick the lowest value. 

Pick the highest value. 

Use the sum of all values. 

Use the median of all values. 
The missing
parameter defines how documents that are missing a value should be treated.
By default they will be ignored but it is also possible to treat them as if they had a value.
This is done by adding a set of fieldname : value mappings to specify default values per field.