I want to decide which are the most relevant attributes for clustering algorithms.

My dataset has attribute this way:

 DBSCAN(data[latitude, Longitude, att1, att2, att3, att4, att5] ) 
 DBSCAN(data[att1, att2, att3, att4, att5] ) 

What metrics should I use in this case ? Should I decide based on Homogeneity and Completeness ?

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DBSCAN does not operate on the raw attributes. It is distance based.

Therefore, evaluate your distance measure, and the relevancy of attributes for distance and similarity measurement. Then DBSCAN should be fine.

Directly comparing DBSCAN results with internal evaluation measures will likely not work. The internal evaluation measures seem to be designed for k-means and similar algorithms; and usually cannot deal reasonably with "noise" as produced by DBSCAN.

Given that you have attributes "latitude" and "longitude": do not use Euclidean distance on these. Earth is not flat, but (approximately) a spheroid. Treating latitude and longitude as coordinates in Euclidean space is bogus. Use geodetic distance, and combine this with a similarity measure on your other attributes in a carefully chosen way. Or use GeneralizedDBSCAN!

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