Dear Omar,

Your question needs more details such as what these data represents (is it an image? is it a digital elevation model?...etc). What  constraints do you want to add? is there a specific clustering algorithm in mind?

Normally, if this data represents an image, the clustering is based on the value of Z where Z in this case is the grey level value. Moreover, the position of the pixels (X,Y) are maintained, but each pixel is assigned to a specific cluster based on some conditions and constraints.

Best regards

Dear Me. Awad, 

x, y represents coordinates of highways center lines and Z represents the cost to repair each highway. The target is to group the roads that are closed to each other to be repaired in same 

Hi Omar,

If you're relying on Z in your task, then it's reasonable to convert the cluster problem into a classification one. Another option is to use Z to cluster the data (an evaluation approach).

HTH.

Samer

Dear Omar,

In this case as I said use any clustering algorithm such as K-Means, FCM, SOMs to cluster these data based on the Z values. When you get the cluster centers you can use threshold for assigning highways centers to each cluster. e.g. highways centers costs ( 2.5, 3, 1.5, 4.2...etc) cluster centers according to Z values (2.7, 2.8 , 1.7...) then you can set the threshold to be less than or equal to 0.2 as an example which represents  the difference between the centers of highways and the cluster centers .

Best wishes

Dear Omar,

If you have enough coordination data of those roads, you can try Spatial Clustering using Geographic Information System (GIS).

Best,