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### Clustering & Classify sparse large features

My problem initial features are x , y ,theta that normalized in range[0,255].

For each object number of features is variable.

Clustering is applied so each cluster has number of features & each object belongs to multiple clusters. In the predict stage ,compute clusters for each object from initial features(new features).

Each object belongs to a maximum of 10 clusters.

Total number of clusters is 4000.

If we consider new features constant for each object we have 4000 dimension that it very large for classify.Only 10 features may be useful and my features is sparse.

My question :

Is there any way that we can classify these sparse features with best performance & which classifier is useful for it? Note:I use locality sensitive hashing for classify new features with 4000 dimension that is very slow.