Sparse　clustering,　which　aims　at　finding　a　proper　partition　of　extremely　high　dimensional　data　set　with　fewest　relevant　features,　has　been　attracted　more　and　more　attention.　Most　researches　model　the　problem　through　minimizing　weighted　feature　contributions　subject　to　a　l(1)　constraint.　However,　the　l(0)　constraint　is　the　essential　constraint　for　sparse　modeling　while　the　l(1)　constraint　is　only　a　convex　relaxation　of　it.　In　this　article,　we　bridge　the　gap　between　the　l(0)　constraint　and　the　l(1)　constraint　through　development　of　two　new　sparse　clustering　models,　which　are　the　sparse　k-means　with　the　l(q)　(0　＜　q　＜　1)　constraint　and　the　sparse　k-means　with　the　l(0)　constraint.　By　proving　the　certain　forms　of　the　optimal　solution　of　particular　l(q)　(0　＜=　q　＜1)　non-convex　optimizations,　two　efficient　iterative　algorithms　are　proposed.　We　conclude　with　experiments　on　both　synthetic　data　and　the　Allen　Developing　Mouse　Brain　Atlas　data　that　the　l(q)　(0　＜=　q　＜1)　models　exhibit　the　advantages　compared　with　the　standard　k-means　and　sparse　k-means　with　the　l(1)　constraint.