Weighted　K-Means　(WKM)　algorithms　are　increasingly　important　with　the　increase　of　data　dimension.　WKM　faces　an　initialization　problem　that　is　more　complicated　than　K-Means＇　because　in　addition　to　picking　initial　cluster　centers,　it　should　also　provide　feature　weights.　Moreover,　the　one-dimensional　solution　to　WKM＇s　widely　used　objective　function　is　unacceptable　in　most　cases.　Yet,　the　initialization　of　WKM,　especially　the　initialization　of　feature　weight,　has　been　largely　ignored.　This　paper　studies　the　problem　by　analyzing　Feature　weight　self-adjustment　K-Means(FWSA　K-Means),　a　popular　WKM　proposed　to　avoid　the　one-dimensional　solution.　Experimental　results　suggest　that　the　algorithm　is　actually　easy　to　cluster　mainly　based　on　a　single　feature　information　when　it　is　not　well　initialized.　Moreover,　the　paper　argues　that　initial　feature　weights　and　cluster　centers　are　equally　important　in　determining　the　final　partition.　Therefore　it　suggests　using　feature　level　constraints　to　improve　the　initialization　and　proposes　a　semi-supervised　algorithm　Constrained　FWSA　K-Means　(CFWSA　K-Means).　The　algorithm　uses　constraints　in　evaluating　feature　weights　and　clusters　to　guide　their　evolution　at　the　stage　of　initialization.　Experimental　results　suggest　that　it　is　effective　and　robust　in　utilizing　constraints.　In　addition,　if　its　initialization　process　is　started　by　the　cluster　centers　provided　by　BRIk,　an　initialization　approach　for　K-Means,　the　performance　can　be　further　improved.