Which tool to cluster schools by phase and size?

[p_monk]

I have about 470 schools and several data for each, including their phase (age group) and size.  Each school is geolocated.

I'd like to cluster the schools hierarchically - associating smaller schools for younger pupils with a single, larger school with older pupils.

The end result would be a number of clusters covering all of the schools.

If possible, it would be great to be able to limit travel time and/or spatial extent of a cluster to be able to adjust clusters that might grow very large because of the spatial distribution of smaller schools.

I'm not sure which tool to use for this - any advice or initial direction would be welcome.

I'm using the latest version of ArcGIS Pro for desktop

Edit: Added screenshot of data

[DanPatterson]

Do you have the spatial statistics extension?

An overview of the Mapping Clusters toolset—ArcGIS Pro | Documentation

or have you looked at other options

Aggregate features into clusters—ArcGIS Pro | Documentation

[p_monk]

I have all extensions.  I've also already searched the Docs for 'Cluster' - I'm after a bit more specific guidance so I know I'm spending the little time I have on this well.  🙂

[Robert_LeClair]

I wonder if Multivariate Clustering is a start to the process?  It finds clusters based upon feature attributes and finds clusters more alike than not alike.  To limit the geography, I wonder if you can do this if the feature class with the attributes are based upon School Attendance Zones or similar?

[p_monk]

Thanks for the suggestion, Robert.

In the UK there isn't available data on school attendance zones - each school would have a 'catchment' these days based on a straightline between the school entrance and the front door of the house in which a pupil lives.

I'm not sure Multivariate clustering is suitable, as it'll just cluster together schools but type/size.

It may well be that what I'm actually trying to do is group, not cluster. 

I could use buffers to create areas around secondary (high) schools then group primary (elementary) schools where they intersect.  There are always outliers to this approach, though, and I'm not sure how best to deal with these beyond manually associating them (and not sure how to do that, either!).

Perhaps a screenshot would help?  Secondary schools are orange, Primaries are purple.