锘??xml version="1.0" encoding="utf-8" standalone="yes"?> 鍏跺疄浠庢煇縐嶈搴﹁錛屽垝鍒嗚仛綾繪槸瀹屽叏涓嶇敤璧樿堪鐨勪竴縐嶈仛綾繪柟娉曪紝鍙兘涔熸槸鏈甯歌鐨勮仛綾葷畻娉曚簡銆傝憲鍚嶇殑k-means綆楁硶灝辨槸涓腑鍏稿瀷銆傝繖嬈$殑鍐呭涓昏鏄氳繃k-means鑱氱被綆楁硶鏉ユ諱綋浠嬬粛涓涓嬪垝鍒嗚仛綾匯?/span> 綆鍗曟潵璁詫紝k鍧囧艱仛綾葷┒绔熷仛浜嗕粈涔堜簨錛屾垜浠彲浠ヨ繖鏍鋒潵鐪嬶紝鏈?/span>N涓暟鎹偣鐨勯泦鍚?/span>D={x1,x2,…,xn}錛屾瘡涓?/span>xi浠h〃涓涓壒寰佸悜閲忥紝鐩爣鏄皢榪?/span>N涓偣鏍規嵁鏌愮鐩鎬技鍑嗗垯灝嗗叾鍒掑垎鍒?/span>K涓垎綾諱腑銆傝?/span>k鍧囧兼墍琛ㄨ揪鐨勯噸瑕佸湪浜庣浉浼煎噯鍒欑殑閫夊彇錛屽嵆涓嶆柇鐨勪嬌鐢ㄧ被綈囩殑鍧囧兼潵瀹屾垚榪欐牱鐨勫垝鍒嗐傚綋鐒朵篃鏈変功鎶婅繖縐嶇浉浼煎噯鍒欑О涔嬩負璇勫垎鍑芥暟銆傚熀浜庡垝鍒嗙殑鑱氱被綆楁硶瀵逛簬homogeneity鐨勫疄鐜版槸閫氳繃閫夊彇閫傚綋鐨勮瘎鍒嗗嚱鏁板茍浣挎瘡涓涓暟鎹偣鍒板畠鎵灞炵殑鑱氱被涓績鐨勮窛紱繪渶灝忓寲銆傝屽叧閿氨鏄浣曞畾涔夎繖縐嶈窛紱伙紝鍜屾墍璋撶殑鑱氱被涓績銆備婦涓緥瀛愭潵璁詫紝濡傛灉瀹氫箟鑱氱被闂磋窛紱諱負嬈у紡璺濈錛岄偅涔堝彲浠ヤ嬌鐢ㄥ崗鏂瑰樊鐨勬蹇墊潵瀹氫箟閫氱敤鐨勮瘎鍒嗗嚱鏁般傚垝鍒嗚仛綾葷殑鎬濇兂鏄渶鐩磋鍜屾槗鎳傜殑鍒嗙被鎬濇兂錛屽洜姝ゆ垜涔熶笉鍦ㄨ繖閲岄暱綃囦粙緇嶏紝榪樻槸浠ョ畻娉曠殑瀹炵幇鍜屼唬鐮佹潵鐩磋琛ㄧ幇鍒掑垎鑱氱被鐨勬ц兘銆?/span> 鎴戜滑浠?/span>k-means綆楁硶涓轟緥鏉ュ疄鐜板垝鍒嗚仛綾匯傝綆楁硶鐨勫鏉傚害涓?/span>O(KnI)錛屽叾涓?/span>I鏄凱浠f鏁般傝繖縐嶇畻娉曠殑涓涓彉浣撴槸渚濇鍒嗘瀽姣忎釜鏁版嵁鐐癸紝鑰屼笖涓鏃︽湁鏁版嵁鐐硅閲嶆柊鍒嗛厤灝辨洿鏂拌仛綾諱腑蹇冿紝鍙嶅鐨勫湪鏁版嵁鐐逛腑寰幆鐩村埌瑙d笉鍐嶅彉鍖栥?/span>k-means綆楁硶鐨勬悳绱㈣繃紼嬪眬闄愪簬鍏ㄩ儴鍙兘鐨勫垝鍒嗙┖闂寸殑涓涓緢灝忕殑閮ㄥ垎銆傚洜姝ゆ湁鍙兘鍥犱負綆楁硶鏀舵暃鍒拌瘎鍒嗗嚱鏁扮殑灞閮ㄨ岄潪鍏ㄥ眬鏈灝忚岄敊榪囨洿濂界殑瑙c傚綋鐒剁紦瑙f柟娉曞彲浠ラ氳繃閫夊彇闅忔満璧峰鐐規潵鏀硅繘鎼滅儲錛堟垜浠緥瀛愪腑鐨?/span>KMPP綆楁硶錛夛紝鎴栬呭埄鐢ㄦā鎷熼鐏瓑絳栫暐鏉ユ敼鍠勬悳绱㈡ц兘銆傚洜姝わ紝浠庤繖涓搴︽潵鐞嗚В錛岃仛綾誨垎鏋愬疄璐ㄤ笂鏄竴涓湪搴炲ぇ鐨勮В絀洪棿涓紭鍖栫壒瀹氳瘎鍒嗗嚱鏁扮殑鎼滅儲闂銆?/span> 涓嶅璇翠簡錛岀洿鎺ヤ笂浠g爜鍚э紒錛侊紒 k-means綆楁硶錛?/span> for k = 1, … , K 浠?/span> r(k) 涓轟粠D涓殢鏈洪夊彇鐨勪竴涓偣錛?/span> while 鍦ㄨ仛綾?/span>Ck涓湁鍙樺寲鍙戠敓 do 褰㈡垚鑱氱被錛?/span> For k = 1, … , K do Ck = { x ∈ D | d(rk,x) <= d(rj,x) 瀵規墍鏈?/span>j=1, … , K, j != k}錛?/span> End; 璁$畻鏂拌仛綾諱腑蹇冿細 For k = 1, … , K do Rk = Ck 鍐呯偣鐨勫潎鍊煎悜閲?/span> End; End; 鍏蜂綋瀹炵幇閮ㄥ垎鍥犱負鏈?/span>Apache Commons Math鐨勭幇鎴愪唬鐮侊紝縐夌潃Eric Raymond鐨?/span>TAOUP涓殑鏋佸ぇ鍒╃敤宸ュ叿鍘熷垯錛屾垜娌℃湁鍐?/span>k-means鐨勫疄鐜幫紝鑰屾槸鐩存帴鍒╃敤Apache Commons Math涓殑k-means plus plus浠g爜鏉ヤ綔涓轟緥瀛愩?/span> 鍏蜂綋濡備綍嫻嬭瘯榪欎竴綆楁硶錛岀粰鍑轟簡嫻嬭瘯浠g爜濡備笅錛?br />
鍒掑垎鑱氱被鏄仛綾誨垎鏋愪腑鏈甯哥敤鐨勪竴縐嶈仛綾葷畻娉曚簡錛屽浜庡叾鐮旂┒鐨勮鏂囦篃鏄濡傜墰姣涖傛劅鍏磋叮鐨勬湅鍙嬩滑瀹屽叏鍙互閫氳繃闃呰鍚勭鐩稿叧璁烘枃鏉ユ劅鍙楄繖涓綆楁硶鐨勭編濡欍傚綋鐒惰繕瑕佸啀嬈℃劅璋?/span>Apache Commons Math瀵逛簬璇稿甯哥敤鏁板璁$畻鐨勫疄鐜般傚浜庤仛綾誨垎鏋愮殑鎬葷粨瀛︿範鏆傛椂鍒版鍛婁竴孌佃惤錛屾渶榪戣蹇欑潃鍐欒鏂囷紝絳夎繃孌墊椂闂存湁絀哄彲浠ヨ冭檻緇х畫鑱氱被綆楁硶鐨勭爺絀跺涔犮?/span> [1]PatternRecognitionThird Edition, Sergios Theodoridis, Konstantinos Koutroumbas [2]妯″紡璇嗗埆絎笁鐗?/span>, Sergios Theodoridis, Konstantinos Koutroumbas钁?/span>, 鏉庢櫠鐨?/span>, 鐜嬬埍渚?/span>, 寮犲箍婧愮瓑璇?/span> [3]鏁版嵁鎸栨帢鍘熺悊, David Hand and et al, 寮犻摱濂庣瓑璇?/span> [4]http://commons.apache.org/math/2. 綆楁硶瀹炵幇
private static void testKMeansPP(){
2
3 //ori is sample as n instances with m features, here n=8,m=2
4
5 int ori[][] = {{2,5},{6,4},{5,3},{2,2},{1,4},{5,2},{3,3},{2,3}};
6
7 int n = 8;
8
9 Collection<EuclideanIntegerPoint> col = new ArrayList<EuclideanIntegerPoint>();
10
11 for(int i=0;i<n;i++){
12
13 EuclideanIntegerPoint ec = new EuclideanIntegerPoint(ori[i]);
14
15 col.add(ec);
16
17 }
18
19 KMeansPlusPlusClusterer<EuclideanIntegerPoint> km = new KMeansPlusPlusClusterer<EuclideanIntegerPoint>(new Random(n));
20
21 List<Cluster<EuclideanIntegerPoint>> list = new ArrayList<Cluster<EuclideanIntegerPoint>>();
22
23 list = km.cluster(col, 3, 100);
24
25 output(list);
26
27 }
28
29private static void output(List<Cluster<EuclideanIntegerPoint>> list){
30
31 int ind = 1;
32
33 Iterator<Cluster<EuclideanIntegerPoint>> it = list.iterator();
34
35 while(it.hasNext()){
36
37 Cluster<EuclideanIntegerPoint> cl = it.next();
38
39 System.out.print("Cluster"+(ind++)+" :");
40
41 List<EuclideanIntegerPoint> li = cl.getPoints();
42
43 Iterator<EuclideanIntegerPoint> ii = li.iterator();
44
45 while(ii.hasNext()){
46
47 EuclideanIntegerPoint eip = ii.next();
48
49 System.out.print(eip+" ");
50
51 }
52
53 System.out.println();
54
55 }
56
57 }
58
59 /**
60
61 *@param args
62
63 */
64
65 public static void main(String[] args) {
66
67 //testHierachicalCluster();
68
69 testKMeansPP();
70
71 //testBSAS();
72
73 //testMBSAS();
74
75 }
76
77
3. 灝忕粨
4. 鍙傝冩枃鐚強鎺ㄨ崘闃呰
]]>
]]>
浜嬪疄涓婏紝灝?/span>n涓璞★紝鑱氱被鍒?/span>k涓仛綾諱腑榪欎歡浜嬫湰韜槸涓涓?/span>NP闅鵑棶棰樸傜啛鎮夌粍鍚堟暟瀛﹀簲璇ョ煡閬撹繖涓棶棰樼殑瑙d簨絎簩綾?/span>Stirling鏁幫細銆傝繖鏍烽棶棰樹篃灝卞嚭鐜頒簡錛屽鏋?/span>k鍊煎浐瀹氾紝閭d箞璁$畻榪樻槸鍙鐨勶紝濡傛灉k鍊間笉鍥哄畾錛屽氨瑕佸鎵鏈夌殑鍙兘k閮借繘琛岃綆楋紝閭h繍琛屾椂闂村彲鎯寵岀煡浜嗐傜劧鑰屽茍涓嶆槸鎵鏈夌殑鍙鑱氱被鏂規閮芥槸鍚堢悊鐨勶紝鎵璋撶殑鍚堢悊錛屾垜鐞嗚В灝辨槸璇存帴榪戜綘鐨勮仛綾葷洰鏍囩殑錛屼箣鎵浠ユ垜浠鍒嗙被錛屽繀鐒舵湁鍒濆鍔ㄦ満錛岄偅涔堝彲浠ユ牴鎹繖涓姩鏈哄埗瀹氬彲琛岀殑鑱氱被鏂規錛岃繖鏍鳳紝澶嶆潅搴︾殑闂灝卞洖閬夸簡銆?/span>
欏哄簭綆楁硶錛?/span>sequential algorithms錛夋槸涓縐嶉潪甯哥畝鍗曠殑鑱氱被綆楁硶錛屽ぇ澶氭暟閮借嚦灝戝皢鎵鏈夌壒寰佸悜閲忎嬌鐢ㄤ竴嬈℃垨鍑犳錛屾渶鍚庣殑緇撴灉渚濊禆浜庡悜閲忓弬涓庣畻娉曠殑欏哄簭銆傝繖縐嶈仛綾葷畻娉曚竴鑸槸涓嶉鍏堢煡閬撹仛綾繪暟閲?/span>k鐨勶紝浣嗘湁鍙兘緇欏嚭涓涓仛綾繪暟涓婄晫q銆傛湰鏂囧皢涓昏浠嬬粛鍩烘湰欏哄簭綆楁硶錛?/span>Basic Sequential Algorithmic Scheme,BSAS錛夊拰鍏跺嚑涓彉縐嶏紝騫剁粰鍑轟唬鐮佸疄鐜般?/span>
棣栧厛鐪?/span>BSAS錛岃繖涓畻娉曟柟妗堥渶瑕佺敤鎴峰畾涔夊弬鏁幫細涓嶇浉浼兼ч槇鍊?#952;鍜屽厑璁哥殑鏈澶ц仛綾繪暟q銆傜畻娉曠殑鍩烘湰鎬濇兂錛氱敱浜庤鑰冭檻姣忎釜鏂板悜閲忥紝鏍規嵁鍚戦噺鍒板凡鏈夎仛綾葷殑璺濈錛屽皢瀹冨垎閰嶅埌涓涓凡鏈夌殑鑱氱被涓紝鎴栬呬竴涓柊鐢熸垚鐨勮仛綾諱腑銆傜畻娉曠殑浼爜鎻忚堪濡備笅錛?/span>
1. m=1 /*{鑱氱被鏁伴噺}*/
2. Cm={x1}
3. For i=2 to N
4. 鎵?/span>Ck: d(xi,Ck)=min1£j£md(xi,Cj)
5. If (d(xi,Ck)>Θ) AND (m<q) then
6. m=m+1
7. Cm={xi}
8. Else
9. Ck=CkÈ{xi}
10. 濡傛灉闇瑕侊紝鏇存柊鍚戦噺琛ㄨ揪
11. End {if}
12. End {for}
鐢變笂闈㈢殑鎻忚堪鍙互鐪嬪嚭BSAS綆楁硶瀵瑰悜閲忛『搴忛潪甯鎬緷璧栵紝鏃犺鏄仛綾繪暟閲忚繕鏄仛綾繪湰韜紝涓嶅悓鐨勫悜閲忛『搴忎細瀵艱嚧瀹屽叏涓嶅悓鐨勮仛綾葷粨鏋溿傚彟涓涓獎鍝嶈仛綾葷畻娉曠粨鏋滅殑閲嶈鍥犵礌鏄槇鍊?#952;鐨勯夋嫨錛岃繖涓肩洿鎺ュ獎鍝嶆渶緇堣仛綾葷殑鏁伴噺錛屽鏋?#952;澶皬錛屽氨浼氱敓鎴愬緢澶氫笉蹇呰鐨勮仛綾伙紝鍥犱負寰堝鎯呭喌涓嬪悜閲忎笌鑱氱被鐨勫悎騫舵潯浠墮兘鍙楀埌θ鐨勯檺鍒訛紝鑰屽鏋?#952;澶ぇ錛屽垯鑱氱被鏁伴噺鍙堜細涓嶅銆?/span>BSAS姣旇緝閫傚悎鑷村瘑鑱氱被錛屽叾瀵規暟鎹泦榪涜涓嬈℃壂鎻忥紝姣忔榪唬涓綆楀綋鍓嶅悜閲忎笌鑱氱被闂寸殑璺濈錛屽洜涓烘渶鍚庣殑鑱氱被鏁?/span>m琚涓鴻繙灝忎簬N錛屾晠BSAS鐨勬椂闂村鏉傚害涓?/span>O(N)銆?/span>
鐢變簬BSAS綆楁硶渚濊禆浜?/span>q錛屽洜姝よ繖閲屼粙緇嶄竴縐嶈嚜鍔ㄤ及璁¤仛綾繪暟q鐨勭畝鍗曟柟娉曪紝璇ユ柟娉曚篃閫傜敤浜庡叾浠栫殑鑱氱被綆楁硶錛屼護BSAS(Θ)涓哄叿鏈夌粰瀹氫笉鐩鎬技闃堝?#952;鐨?/span>BSAS綆楁硶銆?/span>
1. For Θ=a to b step c
2. 綆楁硶BSAS(Θ)鎵цs嬈?/span>錛屾瘡涓嬈¢兘浣跨敤涓嶅悓鐨勯『搴忚〃紺烘暟鎹?/span>
3. 浼拌鑱氱被鏁幫紝mΘ浣滀負浠?/span>s嬈?/span>BSAS(Θ)綆楁硶寰楁潵鐨勬渶甯稿嚭鐜扮殑鑱氱被鏁般?/span>
4. Next Θ
鍏朵腑a鍜?/span>b鏄暟鎹泦鐨勬墍鏈夊悜閲忓鐨勬渶灝忓拰鏈澶т笉鐩鎬技綰у埆錛?/span>c鐨勯夋嫨鐩存帴鍙?/span>d(x,C)鐨勫獎鍝嶃?/span>
鎴戠殑鑱氱被紼嬪簭涓昏鎵╁睍鑷?/span>Apache Commons Math寮婧愭鏋訛紝涓嬮潰鏄叾緇撴瀯錛屾垜綆鍗曞姞鍏ヤ簡Clusterer綾諱綔涓烘娊璞℃ā鏉跨被錛屼嬌鐢ㄦā鏉挎柟娉曟ā寮忎慨鏀逛簡妗嗘灦錛屼負鍚庣畫鍔犲叆鐨勪緥濡?/span>BSAS綆楁硶鎻愪緵妯℃澘銆?br />
欏哄簭綆楁硶綆鍗曟槗瀹炵幇錛屽浜庡涔犺仛綾繪潵璇存槸鍏ラ棬鐨勬渶濂介夋嫨錛岃冭檻鍒扮瘒騫呯殑闄愬埗錛屼笉鑳藉皢浠g爜鍏ㄩ儴鍙戜笂鏉ワ紝濡傛灉鏈夐渶瑕佸彲浠ュ悜鎴戠儲瑕侊紝Apache Commons Math妗嗘灦鍙互鍒?/span>Apache鐨勭綉绔欎笂涓嬭澆銆傚彟澶栬繕鏈夊緢澶氫粙緇嶄笉澶熻緇嗭紝鎰熷叴瓚g殑鏈嬪弸鍙互緇х畫娣卞叆鐮旂┒BSAS鐨勬墿灞曘?/span>
[1]Pattern Recognition Third Edition, Sergios Theodoridis, Konstantinos Koutroumbas
[2]妯″紡璇嗗埆絎笁鐗?/span>, Sergios Theodoridis, Konstantinos Koutroumbas钁?/span>, 鏉庢櫠鐨?/span>, 鐜嬬埍渚?/span>, 寮犲箍婧愮瓑璇?/span>
“鏁板涓婏紝嫻嬪害(Measure)鏄竴涓嚱鏁幫紝瀹冨涓涓粰瀹氶泦鍚堢殑鏌愪簺瀛愰泦鎸囧畾涓涓暟錛岃繖涓暟鍙互姣斾綔澶у皬銆佷綋縐佹鐜囩瓑絳夈備紶緇熺殑縐垎鏄湪鍖洪棿涓婅繘琛岀殑錛屽悗鏉ヤ漢浠笇鏈涙妸縐垎鎺ㄥ箍鍒頒換鎰忕殑闆嗗悎涓婏紝灝卞彂灞曞嚭嫻嬪害鐨勬蹇碉紝瀹冨湪鏁板鍒嗘瀽鍜屾鐜囪鏈夐噸瑕佺殑鍦頒綅” 鈥斺?/span>wikipedia
鑱氱被涔嬪墠涓瀹氳瀹氫箟濂藉悜閲忎箣闂寸殑鐩鎬技紼嬪害鈥斺斿嵆榪戦偦嫻嬪害銆傚湪鑱氱被榪囩▼涓垜浠嬌鐢ㄧ殑嫻嬪害錛岃寖鍥磋鏇村箍娉涳紝棣栧厛瀹氫箟鍚戦噺涔嬮棿鐨勬祴搴︼紝鎺ョ潃灝辨槸闆嗗悎涓庡悜閲忥紝闆嗗悎涔嬮棿鐨勬祴搴︺?/span>
瀵逛簬X涓婄殑涓嶇浉浼兼祴搴?/strong>(Dissimilarity Measure, DM) d 鏄竴涓嚱鏁幫細 鍏朵腑R鏄疄鏁伴泦鍚堬紝濡傛灉d鏈変互涓嬬殑灞炴э細
錛?/span>1.1錛?/span>
錛?/span>1.2錛?/span>
錛?/span>1.3錛?/span>
濡傛灉鍙堟弧瓚?/span>
錛?/span>1.4錛?/span>
錛?/span>1.5錛?/span>
閭d箞d琚О涓哄害閲?/span>DM銆傚叾涓殑鍏紡錛?/span>1.5錛変篃鍙笁瑙掍笉絳夊紡銆傜◢紼嶈В閲婁竴涓嬶紙鍏跺疄澶ソ鐞嗚В浜嗭級錛屼笉鐩鎬技鎬ф祴搴﹀叾瀹炲氨鍍忔垜浠鐨勮窛紱諱竴鏍鳳紝涓や釜鍚戦噺浠h〃涓や釜瀵硅薄濂戒簡銆傚叕寮?/span>1.2瀹氫箟錛堝悜閲忥級瀵硅薄鑷繁鍜岃嚜宸辯殑璺濈鏄?/span>d0錛涘叕寮?/span>1.1璇存槑浜嗕換鎰忎袱涓璞′箣闂寸殑璺濈瑕佸皬浜庢鏃犵┓鍗村ぇ浜庤嚜宸卞拰鑷繁鐨勮窛紱伙紙浣犲拰鍒漢鐨勮窛紱誨ぇ浜庝綘鍜岃嚜宸辯殑璺濈錛岃繖涓嶅簾璇濆悧錛撅伎錛撅級錛涘叕寮?/span>1.3璇存槑璺濈鐨勪氦浜掓э紱鍏紡1.4涓嶈В閲婁簡錛屽叕寮?/span>1.5灝辨槸涓夎涓嶇瓑寮忥紙鍒濅腑姘村鉤錛夈?/span>
鍚岀悊鐩鎬技鎬ф祴搴?/strong>(Similarity Measure, SM)瀹氫箟涓?img style="width: 128px; height: 29px" height="29" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/1.0.JPG" width="128" border="0" />婊¤凍錛?/span>
錛?/span>1.6錛?/span>
錛?/span>1.7錛?/span>
錛?/span>1.8錛?/span>
濡傛灉鍙堟弧瓚?/span>
錛?/span>1.9錛?/span>
錛?/span>1.10錛?/span>
灝辨妸s鍙仛搴﹂噺SM銆傚叿浣撳悓DM錛屽悇鍏紡鐨勮〃杈句竴鐩簡鐒跺摝~~~
浠庡畾涔夊拰瀛楅潰涓婃垜浠兘鍙互鐪嬪嚭浜岃呯殑涓嶅悓錛屽湪琛ㄨ揪鐩鎬技鎬ф椂涓よ呴兘鍙互錛屽彧涓嶈繃搴﹂噺鐨勮搴︿笉鍚岋紝瀵逛簬鍒ゅ埆鐩鎬技錛?/span>DM瓚婂ぇ璇存槑瓚婁笉鐩鎬技錛岃秺灝忓垯瓚婄浉浼鹼紝鑰?/span>SM鍗存濂界浉鍙嶏紝鍥犳鎴戜滑涔熷彲浠ヨ仈鎯籌紝DM涓?/span>SM鍙互鍒╃敤榪欑瀵圭珛鍏崇郴鏉ュ畾涔夈備婦渚嬫潵璇達紝濡傛灉d鏄竴涓?/span>DM錛岄偅涔?/span>s=1/d灝辨槸涓涓?/span>SM銆?/span>
涓婇潰鐨勫畾涔夊彧鏄竴涓畯瑙傜殑姒傛嫭錛岄偅涔堝叿浣撶殑鍚戦噺涔嬮棿鐨勬祴搴﹀浣曡綆楀憿錛熶笅闈㈠皢璇︾粏鐨勪粙緇嶃?/span>
棣栧厛瀵逛簬瀹炲悜閲忕殑涓嶇浉浼兼祴搴︼紝瀹為檯搴旂敤涓渶閫氱敤鐨勫氨鏄?strong>鍔犳潈lp搴﹂噺浜嗭細
錛?/span>2.1錛?/span>
鍏朵腑鐨?/span>xi鍜?/span>yi鍒嗗埆鏄悜閲?/span>x鍜?/span>y涓殑絎?/span>i涓鹼紝wi鏄i涓潈閲嶇郴鏁幫紝l鏄悜閲忕殑緇存暟錛堜互涓嬪叕寮忓畾涔夊悓錛夈傝屾垜浠瘮杈冩劅鍏磋叮鐨勫氨鏄綋p=1鏃訛紝璇ュ害閲忓氨鏄姞鏉?/span>Manhattan鑼冩暟錛岃屽綋p=2鏃跺氨鏄姞鏉冩鍑犻噷寰楄寖鏁幫紝褰?/span>p=∞鏃跺氨鏄?/span>max1£i£l wi|xi-yi|浜嗐傛牴鎹繖浜?/span>DM錛屾垜浠畾涔?/span>SM涓?/span>bmax - dp(x,y)銆?/span>
鍙﹀榪樻湁涓浜涘叾浠栫殑瀹氫箟鏂規硶錛屾瘮濡?/span>
錛?/span>2.2錛?/span>
錛?/span>2.3錛?/span>
鍏朵粬鎳掑緱鍒楀嚭浜嗭紝鍏堟煡闃呰祫鏂欙紝榪欓噷涓嶈榪頒簡銆?/span>
瀵逛簬瀹炲悜閲忕殑鐩鎬技鎬ф祴搴︼紝瀹為檯涓父鐢ㄧ殑鏈夛細
鍐呯Н錛?img height="48" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/2.4.JPG" width="208" border="0" /> 錛?/span>2.4錛?/span>
Tanimoto嫻嬪害錛?img height="57" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/2.5.JPG" width="261" border="0" /> 錛?/span>2.5錛?/span>
鍏朵粬錛?img height="50" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/2.6.JPG" width="229" border="0" /> 錛?/span>2.6錛?/span>
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瀵逛簬紱繪暎鍊肩殑鍚戦噺錛岄鍏堝繀欏昏鎼炴竻妤氫竴涓蹇碉紝榪欓噷鍦ㄣ婃ā寮忚瘑鍒嬬殑涓枃璇戜綔涓垜鎰熻緲昏瘧鐨勫茍涓嶅ソ鐞嗚В錛屾墍浠ヨ繖閲屽睍寮璇存槑涓涓嬶紝閭e氨鏄竴涓彨鍋氱浉渚濊〃(contingency table)鐨勬蹇點傚浜庝竴涓悜閲?/span>x錛屽叾鍏冪礌鍊煎睘浜庢湁闄愰泦F={0,1,…,k-1}錛屽叾涓?/span>k鏄鏁存暟銆備護A(x,y)=[aij], i, j=0,1,…,k-1鏄竴涓?/span>k闃舵柟闃碉紝鍏朵腑鍏冪礌aij浠h〃鍦?/span>x涓墍鏈?/span>i鍊兼墍鍦ㄧ殑浣嶇疆鍦?/span>y鐨勫悓鏍蜂綅緗湁j鍊肩殑涓暟銆傞檮鍘熸枃錛?/span>the number of places where x has the i-th symbol and y has the j-th symbol銆備婦渚嬫潵璇村惂錛?/span>k=3錛屼笖x=[0,1,2,1,2,1]錛?/span>y=[1,0,2,1,0,1]錛岄偅涔?/span>A(x,y) = [0 1 0, 1 2 0, 1 0 1]銆備互絎竴涓?/span>0(a00)涓轟緥璇存槑錛?/span>0鍦?/span>A涓殑浣嶇疆鍐沖畾i=0錛?/span>j=0錛屽湪x涓?/span>0鎵鍦ㄧ殑浣嶇疆鏄涓涓綅緗紝鑰?/span>y涓?/span>0鎵鍦ㄧ殑浣嶇疆涓虹浜屼釜鍜岀浜斾釜錛屼袱涓悜閲忎腑娌℃湁鐩稿悓浣嶇疆涓婄殑鐩稿悓0鍏冪礌錛屽洜姝?/span>A涓涓涓厓绱?/span>a00涓?/span>0錛岃?/span>A涓浜屼釜涓?/span>1(a01)錛屾墍浠?/span>i=0錛?/span>j=1錛屽湪x涓?/span>0鎵鍦ㄧ殑浣嶇疆鏄涓涓紝鑰?/span>y涓?/span>1鎵鍦ㄧ殑浣嶇疆涓虹涓銆佸洓銆佸叚涓紝鍥犳鏈変竴涓浉鍚岋紝鎵浠?/span>a01=1銆?/span>
鍏充簬璁$畻鐭╅樀A榪欓噷闄勫姞java浠g爜瀹炵幇錛屽彲鍙傝冿細
鏈変簡鐩鎬緷琛ㄧ殑瀹氫箟錛屽彲浠ュ畾涔夌鏁e悜閲忎箣闂寸殑涓嶇浉浼兼ф祴搴︿簡銆?/span>
姹夋槑璺濈錛?img height="58" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/2.7.JPG" width="150" border="0" /> 錛?/span>2.7錛?/span>
L1璺濈錛?img height="48" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/2.8.JPG" width="176" border="0" /> 錛?/span>2.8錛?/span>
鍚屾牱錛岀浉浼兼ф祴搴︽湁
Tanimoto嫻嬪害錛?img height="93" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/2.9.JPG" width="225" border="0" /> 錛?/span>2.9錛?/span>
鍏朵腑鐨?/span>nx( ny)琛ㄧずx(y)涓潪闆跺厓绱犵殑涓暟銆?/span>
涔︽湰寰寰鏁欑粰鎴戜滑鐨勬槸鍩虹鑰屼笉鏄簲鐢紝榪欎簺鍩虹鐭ヨ瘑鍦ㄥ疄闄呭簲鐢ㄤ腑鎵嶄細寰楀埌鏇村鐨勬敼榪涘拰鍙樺寲銆備篃璁告垜浠笉浼氱畝鍗曠殑鍦ㄨ仛綾諱腑搴旂敤榪欎簺嫻嬪害姒傚康錛屼絾鏄鏉傜殑緇勫悎閮芥槸鏉ユ簮浜庡熀紜銆傚洜姝わ紝瀵規祴搴︾殑鍩虹姒傚康涓瀹氳鐗㈢墷鎶婃彙銆傚湪鍓嶄竴闃舵鍋氬浘鍍忓垎鍓叉椂錛岃仛綾葷畻娉曟墽琛岀殑鍓嶆彁涔嬩竴嫻嬪害錛屾垜灝卞仛榪囧涓疄楠岋紝L1鍜?/span>L2鑼冩暟錛?/span>Tanimoto嫻嬪害絳夈傚綋鐒朵笉鍚岀殑鍥懼儚鐗瑰緛鏈変笉鍚岀殑璁$畻璺濈鏂規硶錛屾諱箣瀹為檯鐨勭粡楠屽憡璇夋垜錛屽熀紜鎵庡疄鍚庯紝鍦ㄥ簲鐢ㄨ搗鏉ユ槸鐩稿綋鐨勯『鎵嬪晩~~~錛堟渶璧風爜涓嶄細琚鏉傚叕寮忓悡鍒幫級
鑰冭檻鍒板疄渚嬪悜閲忕殑鐗瑰緛綾誨瀷寰寰鏄鏉傛販鍚堢殑錛岃繖縐嶆儏鍐典笅錛屽浣曡綆楄繎閭繪祴搴﹀憿錛熶竴浜涘伔鎳掔殑鍋氭硶灝辨槸灝嗘墍鏈夊奸兘鐪嬩綔鏄疄鍊肩被鍨嬶紝鎶婃販鍚堝悜閲忓綋浣滃疄鍚戦噺鏉ュ鐞嗐備絾鏄幇瀹炰嬌鐢ㄤ腑錛岃繖鏍峰仛鐨勬晥鏋滃線寰宸己浜烘剰銆傝冭檻灝嗗疄鍊肩被鍨嬭漿鎹㈡垚紱繪暎綾誨瀷錛岃繖灝辨槸钁楀悕鐨勭鏁e寲浜嗭紝鐗瑰緛鐨勭鏁e寲鎿嶄綔鏃剁壒寰佹垨灞炴ц繃婊?/span>(filter)鐨勪竴涓噸瑕佺殑鏂歸潰銆傚綋鐒舵垜鏈鎺ㄨ崘鐨勮繕鏄熀浜庤嚜宸卞紑鍙戠殑搴旂敤鍦烘櫙錛岃璁$浉鍏崇殑榪戦偦嫻嬪害銆傝繖鏍峰彲鑳介氱敤鎬ф瘮杈冨樊錛屼絾鏄鏋滄槸闂椹卞姩鐨勮瘽錛屾垨鑰呯洰鏍囬┍鍔紝閭d箞榪欎釜浣滀負涓涓?/span>solution涔熶笉澶變紭鑹с傚綋鐒跺紩鍏ユā緋婃祴搴︾殑姒傚康涔熸槸涓縐嶈В鍐蟲柟娉曪紝榪欓噷灝變笉緇嗚浜嗭紝鍏蜂綋搴旂敤鍙互鍙傜湅鏈夊叧妯$硦鍜屼笉紜畾鎬х殑鏂囩珷銆傚彟澶栦竴鐐歸渶瑕佽鏄庡氨鏄疄渚嬪悜閲忎腑閮ㄥ垎鐗瑰緛涓㈠け鐨勬儏鍐碉紝瀵逛簬涓㈠け鏁版嵁錛屽鏋滄垜浠煡閬撴暟鎹殑鍒嗗竷錛岄偅涔堝悎鐞嗗亣璁炬槸涓涓浛浠f柟妗堬紝浣嗘槸濡傛灉涓轟簡鐪佷簨錛屽父鐢ㄧ殑鍋氭硶鏄洿鎺ヤ涪寮冭瀹炰緥鍚戦噺錛屾垨鑰呭ソ鐐圭殑鍋氭硶鏄彇鎵鏈夊疄渚嬬殑騫沖潎鏁版嵁浣滀負璇ョ淮搴︾殑鏇夸唬鏁版嵁銆?/span>
闅忕潃鑱氱被榪囩▼鐨勪笉鏂繘琛岋紝灞傛閫愭笎娣卞叆錛岃仛綾誨凡緇忎笉浠呬粎鏄垽鏂偣涓庣偣涔嬮棿鐨勭浉浼肩▼搴︿簡錛岀偣涓庨泦鍚堢殑鐩鎬技紼嬪害涔熼渶瑕佽綆椼傝屽浣曞畾涔夊悜閲?/span>x鍜岃仛綾?/span>C涔嬮棿鐨勮繎閭繪э紝浠庤屽垽鏂槸鍚﹀皢x褰掔被涓?/span>C銆備互涓嬩笁涓畾涔夌粡甯哥敤鍒般?/span>
鏈澶ц繎閭誨嚱鏁?/span>Max proximity function錛?/span> 錛?/span>4.1錛?/span>
鏈灝忚繎閭誨嚱鏁?/span>Min proximity function錛?img height="30" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/4.2.JPG" width="197" border="0" /> 錛?/span>4.2錛?/span>
騫沖潎榪戦偦鍑芥暟Average proximity function錛?img height="49" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/4.3.JPG" width="193" border="0" /> 錛?/span>4.3錛?/span>
鍏朵腑nc鏄泦鍚?/span>C鐨勫娍銆?/span>
鍙互鐪嬪埌錛岃繖鏍風殑瀹氫箟鍦ㄦ蹇電悊璁哄眰嬈′笂浠嶆棫灝嗙偣瑙嗕綔鐐癸紝灝嗚仛綾昏浣滈泦鍚堛傚彟涓縐嶆儏鍐靛垯鏄皢鑱氱被瑙嗕綔涓涓偣錛屽洜涓虹偣涓庣偣涔嬮棿鐨勮繎閭繪祴搴﹀凡緇忓彲浠ヨ綆楋紝閭d箞灝嗛泦鍚堣涓轟竴涓偣錛屽氨灝嗚繖涓棶棰樺綊綰﹀埌浜嗙偣涓庣偣涔嬮棿鐨勯棶棰樹簡銆傚鑱氱被榪涜琛ㄨ揪錛屼富瑕佹湁浠ヤ笅鍑犵琛ㄨ揪錛?/span>
1錛?span style="font: 7pt 'Times New Roman'"> 鐐硅〃杈撅細灝嗚仛綾昏浣滀竴涓偣錛屽彲浠ユ槸鍧囧肩偣(mean vector)錛屼篃鍙互鏄潎鍊間腑蹇?/span>(mean center)錛屼篃鍙互鏄腑鍊間腑蹇?/span>(median center)銆傚叧浜庤繖鍑犱釜姒傚康鍜屽叕寮忥紝浠諱綍鐨勭粺璁℃暀鏉愰噷閮芥湁娑夌寧錛屾垜灝變笉涓涓鏋氫婦浜嗐傦紙涓昏璐村叕寮忕湡鐨勫緢绱紝鎬蹇?/span>Tex錛?/span>
2錛?span style="font: 7pt 'Times New Roman'"> 瓚呭鉤闈㈣〃杈撅細綰挎ц仛綾諱腑甯哥敤銆備笉琛ㄣ傛湁鍏磋叮鑰呭幓鏌ヨ祫鏂欍?/span>
3錛?span style="font: 7pt 'Times New Roman'"> 瓚呯悆闈㈣〃杈撅細鐞冨艦鑱氱被涓父鐢ㄣ傚悓涓娿?/span>
涓鍒囩殑瀛︿範閮戒負搴旂敤錛屾牴鎹疄闄呭簲鐢ㄧ殑涓嶅悓錛屾垜浠湪瀹氫箟榪欑鐐逛笌闆嗗悎涔嬮棿嫻嬪害鏃跺欎篃鏈夊緢澶х殑鐏墊椿鎬с?/span>
鍚屾牱鐨勶紝瀵逛簬闆嗗悎涓庨泦鍚堢殑嫻嬪害錛屽彲浠ュ悓鐐逛笌闆嗗悎鐨勬祴搴︾被浼箋傚彧瑕佽浣忎竴鐐癸紝閭e氨鏄泦鍚堜笌闆嗗悎闂寸殑榪戦偦嫻嬪害鏄緩绔嬪湪鐐逛笌鐐逛箣闂寸殑嫻嬪害鐨勫熀紜涓婄殑銆傛墍浠ヨ繎閭繪祴搴︾殑鍩虹鍦ㄧ偣涓庣偣涔嬮棿銆傚綋鐒惰仛綾葷粨鏋滅殑浼樺寲鏄竴涓弽澶嶈瘯楠岀殑榪囩▼錛屽叾涓篃瑕佽冭檻棰嗗煙涓撳鐨勬剰瑙併?/span>
瀵逛簬榪戦偦嫻嬪害鐨勫涔狅紝涔嶄竴鐪嬪儚鏄函鏁板鐭ヨ瘑鐨勫涔狅紝鍏跺疄鍒欐槸瀵規垜浠紑濮嬭仛綾葷畻娉曠爺絀朵箣鍓嶇殑涓涓く瀹炲熀紜鐨勫涔犺繃紼嬨?/span>
[1]Pattern Recognition Third Edition, Sergios Theodoridis, Konstantinos Koutroumbas
[2] http://zh.wikipedia.org/wiki/%E6%B5%8B%E5%BA%A6%E8%AE%BA
[3]妯″紡璇嗗埆絎笁鐗?/span>, Sergios Theodoridis, Konstantinos Koutroumbas钁?/span>, 鏉庢櫠鐨?/span>, 鐜嬬埍渚?/span>, 寮犲箍婧愮瓑璇?/span>
浼犺錛?#8220;鑱氱被鏄漢綾繪渶鍘熷鐨勭簿紲炴椿鍔紝鐢ㄤ簬澶勭悊浠栦滑姣忓ぉ鎺ユ敹鍒扮殑澶ч噺淇℃伅”銆備負鏂逛究騫垮ぇ鍚屽瀛︿範浣跨敤錛屽皢鎴戝涔犺仛綾繪椂鐨勭瑪璁版暣鐞嗗彂甯冨叡浜?/span>
“鑱氱被鏄妸鐩鎬技鐨勫璞¢氳繃闈欐佸垎綾葷殑鏂規硶鍒嗘垚涓嶅悓鐨勭粍鍒垨鑰呮洿澶氱殑瀛愰泦錛?/span>subset錛?/span>,榪欐牱璁╁湪鍚屼竴涓瓙闆嗕腑鐨勬垚鍛樺璞¢兘鏈夌浉浼肩殑涓浜涘睘鎬с?#8221; 鈥斺?/span>wikipedia
“鑱氱被鍒嗘瀽鎸囧皢鐗╃悊鎴栨娊璞″璞$殑闆嗗悎鍒嗙粍鎴愪負鐢辯被浼肩殑瀵硅薄緇勬垚鐨勫涓被鐨勫垎鏋愯繃紼嬨傚畠鏄竴縐嶉噸瑕佺殑浜虹被琛屼負銆傝仛綾繪槸灝嗘暟鎹垎綾誨埌涓嶅悓鐨勭被鎴栬呯皣榪欐牱鐨勪竴涓繃紼嬶紝鎵浠ュ悓涓涓皣涓殑瀵硅薄鏈夊緢澶х殑鐩鎬技鎬э紝鑰屼笉鍚岀皣闂寸殑瀵硅薄鏈夊緢澶х殑鐩稿紓鎬с?/span>” 鈥斺旂櫨搴︾櫨縐?/span>
璇寸櫧浜嗭紝鑱氱被錛?/span>clustering錛夋槸瀹屽叏鍙互鎸夊瓧闈㈡剰鎬濇潵鐞嗚В鐨勨斺斿皢鐩稿悓銆佺浉浼箋佺浉榪戙佺浉鍏崇殑瀵硅薄瀹炰緥鑱氭垚涓綾葷殑榪囩▼銆傜畝鍗曠悊瑙o紝濡傛灉涓涓暟鎹泦鍚堝寘鍚?/span>N涓疄渚嬶紝鏍規嵁鏌愮鍑嗗垯鍙互灝嗚繖N涓疄渚嬪垝鍒嗕負m涓被鍒紝姣忎釜綾誨埆涓殑瀹炰緥閮芥槸鐩稿叧鐨勶紝鑰屼笉鍚岀被鍒箣闂存槸鍖哄埆鐨勪篃灝辨槸涓嶇浉鍏崇殑錛岃繖涓繃紼嬪氨鍙仛綾諱簡銆?/span>
褰㈠紡鍖栦竴鐐癸紝浠?img style="width: 162px; height: 22px" height="22" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/abc.JPG" width="162" border="0" />錛屽叾涓殑x閮芥槸鍚戦噺錛屼竴涓?/span>X鐨?/span>m鑱氱被R灝?/span>X鍒嗗壊涓?/span>m涓泦鍚?/span>C1, C2,…,Cm錛屼嬌鍏舵弧瓚充笅闈笁涓潯浠訛細
錛?/span>1錛?img height="22" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/abcd.JPG" width="162" border="0" />
錛?/span>2錛?img height="37" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/abcde.JPG" width="70" border="0" />
錛?/span>3錛?img height="28" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/ff.JPG" width="275" border="0" />
婊¤凍涓婅堪鏉′歡鐨勫悓鏃訛紝鍦ㄨ仛綾?/span>Ci涓殑鍚戦噺褰兼鐩鎬技錛岃屼笌鍏朵粬綾諱腑鐨勫悜閲忎笉鐩鎬技銆?/span>
浣嗘槸榪欑瀹氫箟涔熷彧鏄畾涔変簡紜畾鎬х殑鑱氱被錛屼篃鍙仛紜仛綾?/span>(hard clustering)錛屾瘡涓疄渚?/span>x閮界‘瀹氱殑灞炰簬鏌愪釜鑱氱被銆傝屼笉紜畾鎬ц仛綾伙紝涔熼渶瑕佸畾涔夛紝榪欏氨寮曞嚭浜嗘ā緋婅仛綾?/span>(fuzzy clustering)鐨勬蹇典簡銆傛ā緋婅仛綾諱腑錛屾瘡涓疄渚嬪悜閲?/span>x浠ヤ竴瀹氱殑闅跺睘搴﹀睘浜庢煇涓仛綾匯傚悓涓婇潰鐨勮緗紝X鐨勬ā緋婅仛綾繪槸灝?/span>X鍒嗘垚m涓被錛岀敱m涓嚱鏁?/span>uj琛ㄧず錛屽叾涓弧瓚籌細
錛?/span>1錛?img height="28" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/fff.JPG" width="214" border="0" />
錛?/span>2錛?img height="44" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/de.JPG" width="214" border="0" />
錛?/span>3錛?img height="44" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/def.JPG" width="240" border="0" />
鍏朵腑榪欎釜闅跺睘搴﹀嚱鏁?img height="23" alt="" src="http://m.tkk7.com/images/blogjava_net/changedi/ew.JPG" width="45" border="0" />瓚婃帴榪?/span>1錛岃鏄?/span>xi瓚婂彲鑳藉睘浜?/span>Ci錛屽弽涔嬪鏋滆秺鎺ヨ繎0錛屽垯璇存槑瓚婁笉鍙兘灞炰簬Ci銆?/span>
褰撴垜浠煡閬撹仛綾繪槸浠涔堟椂錛屾垜浠笅涓姝ユ兂鐭ラ亾鐨勫簲璇ユ槸鎬庝箞榪涜鑱氱被銆傝繖涓鐐癸紝鏁欐潗涓婂仛浜嗚緇嗕粙緇嶏紝琛ュ厖涓鐐硅嚜宸辯悊瑙o細
1錛夌壒寰侀夋嫨(feature selection)錛氬氨鍍忓叾浠栧垎綾諱換鍔′竴鏍鳳紝鐗瑰緛寰寰鏄竴鍒囨椿鍔ㄧ殑鍩虹錛屽浣曢夊彇鐗瑰緛鏉ュ敖鍙兘鐨勮〃杈鵑渶瑕佸垎綾葷殑淇℃伅鏄竴涓噸瑕侀棶棰樸傝〃杈炬у己鐨勭壒寰佸皢寰堝獎鍝嶈仛綾繪晥鏋溿傝繖鐐瑰湪浠ュ悗鐨勫疄楠屼腑鎴戜細灞曠ず銆?/span>
2錛夎繎閭繪祴搴?/span>(proximity measure)錛氬綋閫夊畾浜嗗疄渚嬪悜閲忕殑鐗瑰緛琛ㄨ揪鍚庯紝濡備綍鍒ゆ柇涓や釜瀹炰緥鍚戦噺鐩鎬技鍛紵榪欎釜闂鏄潪甯稿叧閿殑涓涓棶棰橈紝鍦ㄨ仛綾昏繃紼嬩腑涔熸湁鐫鍐沖畾鎬х殑鎰忎箟錛屽洜涓鴻仛綾繪湰璐ㄥ湪鍖哄垎鐩鎬技涓庝笉鐩鎬技錛岃岃繎閭繪祴搴﹀氨鏄榪欑鐩鎬技鎬х殑涓縐嶅畾涔夈?/span>
3錛夎仛綾誨噯鍒?/span>(clustering criterion)錛氬畾涔変簡鐩鎬技鎬ц繕涓嶅錛岀粨鍚堣繎閭繪祴搴︼紝濡備綍鍒ゆ柇鐩鎬技鎵嶆槸鍏抽敭銆傜洿瑙傜悊瑙h仛綾誨噯鍒欒繖涓蹇靛氨鏄綍鏃惰仛綾伙紝浣曟椂涓嶈仛綾葷殑鑱氱被鏉′歡銆傚綋鎴戜滑浣跨敤鑱氱被綆楁硶榪涜璁$畻鏃訛紝濡備綍鑱氱被鏄畻娉曞叧蹇冪殑錛岃岃仛涓庡惁闇瑕佷竴涓爣鍑嗭紝鑱氱被鍑嗗垯灝辨槸榪欎釜鏍囧噯銆傦紙璇濊鏍囧噯榪欎笢瑗夸竴鎷垮嚭鏉ワ紝澶熷悡浜轟簡鍚?/span>^_^錛?/span>
4錛夎仛綾葷畻娉?/span>(clustering algorithm)錛氳繖涓笢瑗夸笉鐢ㄧ粏璇翠簡鍚э紝鏁翠釜瀛︿範鐨勯噸涓箣閲嶏紝鏍稿績鐨勪笢瑗胯繖閲屼笉璁詫紝浠ュ悗浼氱粏璇達紝綆鍗曞紑涓ご鈥斺斿埄鐢ㄨ繎閭繪祴搴﹀拰鑱氱被鍑嗗垯寮濮嬭仛綾葷殑榪囩▼銆?/span>
5錛夌粨鏋滈獙璇?/span>(validation of the results)錛氬叾瀹炲浜?/span>PR鐨勪綔鑰呮彁鍑鴻繖涓繃紼嬩篃鏀懼埌鑱氱被浠誨姟嫻佺▼涓紝鎴戣寰楁湁鐐瑰啑浣欙紝鍥犱負瀵逛簬楠岃瘉綆楁硶鐨勬紜ц繖浜嬪簲璇ユ斁鍒扮畻娉曞眰闈㈠惂錛屽彲浠ユ妸4錛夊拰5錛夌粨鍚堣嚦涓灞傘傚洜涓虹畻娉曟紜拰鏈夌┓鐨勯獙璇佹湰韜氨鏄畻娉曠殑鐗規у槢銆傦紙璋佽璁′簡涓涓畻娉曚笉寰楄瘉鏄庡晩錛?/span>
6錛?/span>(interpretation of the results)錛氫腑鏂囩増鐨?/span>PR涓婄炕璇戜負緇撴灉鍒ゅ畾錛岃屾垜鎰熻瀛楅潰鎰忔濆氨鏄粨鏋滆В閲娿傦紙鑱氱被鏈緇堜細灝嗘暟鎹泦鍒嗘垚鑻ュ共涓被錛屽仛浜嬪墠瑕佹湁鍘熷垯錛屽仛浜嬪悗瑕佹湁瑙i噴錛岃繖涓氨鏄В閲婁簡銆傝嚜鍦嗗叾璇村彲鑳芥槸姣旇緝濂界殑浜?/span>^_^錛?/span>
鏁翠釜鑱氱被浠誨姟璇︾粏鐨勪笢瑗夸細鍦ㄤ互鍚庤緇嗕粙緇嶏紝榪欓噷鍏堢粏璇翠竴涓嬭仛綾誨噯鍒欙紙铏界劧鎴戞劅瑙夊湪涓婇潰鎴戣鐨勫凡緇忓緇嗕簡錛夈備婦渚嬪惂錛屾瘮濡傦紝鏈夎繖鏍蜂竴涓暟鎹泦X錛屽寘鍚簡鍥涘悕鍚屽鐨勫熀鏈俊鎭拰鏁板鎴愮嘩銆?/span>
濮撳悕 |
騫寸駭 |
鐝駭 |
鏁板鎴愮嘩 |
寮犱笁 |
1 |
2 |
99 |
鏉庡洓 |
2 |
2 |
95 |
寮犻 |
3 |
1 |
59 |
璧典簯 |
2 |
1 |
90 |
鑱氱被鍑嗗垯灝辨槸涓涓垎綾繪爣鍑嗭紝瀵逛簬紺轟緥涓繖鏍蜂竴涓暟鎹泦鍚堬紝濡備綍鑱氱被鍛€傚綋鐒惰仛綾葷殑鍙兘鎯呭喌鏈夊緢澶氥傛瘮濡傦紝濡傛灉鎴戜滑鎸夌収騫寸駭鏄惁涓哄ぇ浜?/span>1鏉ュ垎綾伙紝閭d箞鏁版嵁闆?/span>X鍒嗕負涓ょ被錛?/span>{寮犱笁}錛?/span>{鏉庡洓錛屽紶椋烇紝璧典簯}錛涘鏋滄寜鐓х彮綰т笉鍚屾潵鍒嗭紝鍒嗕負涓ょ被錛?/span>{寮犱笁錛屾潕鍥?/span>}錛?/span>{寮犻錛岃檔浜?/span>}錛涘鏋滄寜鐓ф垚緇╂槸鍚﹀強鏍兼潵鍒嗭紙鍋囪鍙婃牸涓?/span>60鍒嗭級錛屽垎涓ょ被錛?/span>{寮犱笁錛屾潕鍥涳紝璧典簯}錛?/span>{寮犻}銆傚綋鐒惰仛綾誨噯鍒欑殑璁捐寰寰鏄鏉傜殑錛屽氨鐪嬩綘鎯蟲庝箞鍒掑垎浜嗐傛寜鐓у鍒嗙被鎬濇兂鐨勫嚑浣曠悊瑙o紝鏁版嵁闆嗙浉褰撲簬鏍鋒湰絀洪棿錛屾暟鎹疄渚嬬殑鐗瑰緛鏁幫紙鏈緥鍏辨湁4涓壒寰?/span>[濮撳悕錛屽勾綰э紝鐝駭錛屾暟瀛︽垚緇?/span>]錛夌浉褰撲簬絀洪棿緇村害錛岃屽疄渚嬪悜閲忓搴斿埌絀洪棿涓殑涓涓偣銆傞偅涔堣仛綾誨噯鍒欏氨搴旇鏄偅浜涚濂囩殑瓚呭鉤闈紙瀵瑰簲鏈夋暟瀛﹀嚱鏁拌〃杈懼紡錛屾垜涓漢璁や負榪欎簺鍑芥暟灝辯瓑鍚屼簬鑱氱被鍑嗗垯錛夛紝榪欎簺瓚呭鉤闈㈠皢鏁版嵁“瀹岀編鐨?#8221;鍒嗙寮浜嗐?/span>
鑱氱被鏃剁敤鍒扮殑鐗瑰緛濡備綍鍖哄垎鍛紝鏈変粈涔堢被鍨嬭姹傦紵鑱氱被鐨勭壒寰佹寜鐓у煙鍒掑垎錛屽彲浠ュ垎涓鴻繛緇殑鐗瑰緛鍜岀鏁g壒寰併傚叾涓繛緇壒寰佸搴旂殑瀹氫箟鍩熸槸鏁版嵁絀洪棿R鐨勮繛緇瓙絀洪棿錛岃岀鏁g壒寰佸搴旂殑鏄鏁e瓙闆嗭紝鍙﹀濡傛灉紱繪暎鐗瑰緛鍙寘鍚袱涓壒寰佸鹼紝閭d箞榪欎釜紱繪暎鐗瑰緛鍙堝彨浜屽肩壒寰併?/span>
鏍規嵁鐗瑰緛鍙栧肩殑鐩稿鎰忎箟鍙堝彲浠ュ皢鐗瑰緛鍒嗕負浠ヤ笅鍥涚錛氭爣閲忕殑(Nominal)錛岄『搴忕殑(Ordinal)錛屽尯闂村昂搴︾殑(Interval-scaled)浠ュ強姣旂巼灝哄害鐨?/span>(Ratio-scaled)銆傚叾涓紝鏍囬噺鐗瑰緛鐢ㄤ簬緙栫爜涓綾葷壒寰佺殑鍙兘鐘舵侊紝姣斿浜虹殑鎬у埆錛岀紪鐮佷負鐢峰拰濂籌紱澶╂皵鐘跺喌緙栫爜涓洪槾銆佹櫞鍜岄洦絳夈傞『搴忕壒寰佸悓鏍囬噺鐗瑰緛綾諱技錛屽悓鏍鋒槸涓緋誨垪鐘舵佺殑緙栫爜錛屽彧鏄榪欎簺緙栫爜紼嶅姞綰︽潫錛屽嵆緙栫爜欏哄簭鏄湁鎰忎箟鐨勶紝姣斿瀵逛竴閬撹彍錛屽畠鐨勭壒寰佹湁{寰堥毦鍚冿紝闅懼悆錛屼竴鑸紝濂藉悆錛岀編鍛?/span>}鍑犱釜鍊兼潵瀹氫箟鐘舵侊紝浣嗘槸榪欎簺鐘舵佹槸鏈夐『搴忔剰涔夌殑銆傝繖綾葷壒寰佹垜璁や負灝辨槸鏍囬噺鐗瑰緛鐨勪竴涓壒瀹氬瓙闆嗭紝鎴栬呮槸涓涓姞綰︽潫鐨勬爣閲忕壒寰併傚尯闂村昂搴︾壒寰佽〃紺鴻鐗瑰緛鏁板間箣闂寸殑鍖洪棿鏈夋剰涔夎屾暟鍊肩殑姣旂巼鏃犳剰涔夛紝緇忓吀渚嬪瓙灝辨槸娓╁害錛?/span>A鍦扮殑娓╁害錛?/span>20鈩冿級姣?/span>B鍦幫紙15鈩冿級楂?/span>5搴︼紝榪欓噷鐨勫尯闂村樊鍊兼槸鏈夋剰涔夌殑錛屼絾浣犱笉鑳借A鍦版瘮B鍦扮儹1/3錛岃繖鏄棤鎰忎箟鐨勩傛瘮鐜囩壒寰佷笌姝ょ浉鍙嶏紝鍏舵瘮鐜囨槸鏈夋剰涔夌殑錛岀粡鍏鎬緥瀛愭槸閲嶉噺錛?/span>C閲?/span>100g錛?/span>D閲?/span>50g錛岄偅涔?/span>C姣?/span>D閲?/span>2鍊嶏紝榪欐槸鏈夋剰涔夌殑銆傦紙褰撶劧璇?/span>C姣?/span>D閲?/span>50g涔熸槸鍙互鐨勶紝鍥犳鍙互璁や負鍖洪棿灝哄害鏄瘮鐜囧昂搴︾殑涓涓湡瀛愰泦錛夈?/span>
鍦ㄥ父瑙佸簲鐢ㄤ腑錛屽寘鎷垜浠鉤鏃ュ叧蹇冪殑緙栫▼瀹炵幇涓紝涓鑸彧瀹氫箟nominal鐗瑰緛鍜?/span>numeric鐗瑰緛錛屽叾涓?/span>nominal鍙互鐢?/span>string鏉ヨ〃紺猴紝鑰?/span>numeric鍙互鐢?/span>number鏉ヨ〃紺恒傦紙weka涓殑attribute鐨勭壒寰佺被鍨嬪氨鏄繖涔堝畾涔夌殑錛?/span>
璇翠簡榪欎箞澶氬熀鏈蹇碉紝鏈瀹為檯鐨勮瘽棰樿帿榪囦簬搴旂敤浜嗐傚氨鍍忎負鑱氱被鍋氬箍鍛婁竴鏍鳳紝鍒板簳鎴戜滑鍙互鍦ㄥ摢閲屽簲鐢ㄥ畠鍛€傚氨鍍忓紩璦閲屾垜鎻愬埌鐨勪紶璇翠竴鏍鳳紝鍒嗙被浣滀負浜虹被璇嗗埆瀵硅薄鐨勪竴涓熀鏈椿鍔ㄥぇ姒備笌浜虹被鐨勬剰璇嗗叡鍚屽瓨鍦ㄧ潃錛屼篃鍙互璇翠漢綾繪櫤鑳借璇嗙殑鏈川媧誨姩涔嬩竴灝辨槸鍒嗙被銆傝岀爺絀惰呭鍒嗙被鐨勭爺絀跺張灝嗗垎綾誨垝鍒嗕負鏈夌洃鐫d笌鏃犵洃鐫o紝鍏朵腑鑱氱被灝辨槸鏃犵洃鐫e垎綾葷殑鏈甯哥敤鏂規硶涔熸槸緇濆浠h〃鎬ф柟娉曘傝鎯充竴涓嬶紝瀵逛簬涓緇勬暟鎹紝鎴栬呬竴鍫嗕俊鎭紝璁$畻鏈哄彲浠ヨ嚜鍔ㄥ湴灝嗗叾鍒嗕負鑻ュ共綾伙紝閭h繖瀵逛簬杈呭姪浜虹被鏅鴻兘鏉ヨ緇濆鏄繀瑕佺殑涔熸槸鏈夋剰涔夌殑銆傛墍浠ヨ仛綾葷殑涓涓牳蹇冨簲鐢ㄥ氨鏄暟鎹寲鎺樹笌妯″紡璇嗗埆銆傚彟澶栧悇涓瀛﹂鍩熷彧瑕佹秹鍙婂埌鍒嗙被鐨勪換鍔★紝澶у鏃犱笉鑱旀兂鍒拌仛綾?/span>~~~錛堣瘽璇存垜絎竴嬈℃寮忓湴瑙i櫎鑱氱被錛岃繕鏄湪23鏁欏妤煎惉涓涓矊浼兼槸鑷姩鍖栫殑鏁欐巿璁茬殑淇℃伅鍖栬紼嬶級銆傝屽鑰呮瘮杈冩潈濞佺殑鍒嗙被灝嗚仛綾葷殑搴旂敤鍒嗕負鍥涗釜鍩烘湰鐨勬柟鍚戯細1錛夋暟鎹幓鍐楋紝鍗沖皢嫻烽噺鏁版嵁涓殑鍐椾綑淇℃伅鍘婚櫎銆?/span>2錛夊亣璇寸敓鎴愶紝涓轟簡鎺ㄥ鍑烘暟鎹殑鏌愪簺鎬ц川錛屾垜浠彲浠ュ鏁版嵁榪涜鑱氱被鍒嗘瀽銆?/span>3錛夊亣璇存楠岋紝鍏跺疄灝辨槸閫氳繃鑱氱被鍒嗘瀽鏉ラ獙璇佹煇涓喅絳栫殑椋庨櫓紼嬪害銆?/span>4錛夊熀浜庡垎緇勭殑棰勬祴錛屽悓鎵鏈夐嫻嬩換鍔′竴鏍鳳紝灝嗗凡鏈夌殑鏁版嵁閮借仛綾誨垎綾誨悗錛屾柊鐨勬湭鏉ユ暟鎹彲浠ョ敤鍚屾牱鐨勮鍒欒繘琛岃瘑鍒嫻嬪叾鎵灞炲垎綾匯?/span>
鑱氱被鐨勫簲鐢ㄩ潪甯稿箍娉涳紝濡傛灉鎸夌鐩灇涓撅紝鎴戞槸鎳掑緱緗楀垪浜嗐傚彧瑕佺煡閬撲簡鍏跺師鐞嗗拰鐩爣錛屽叾搴旂敤棰嗗煙涔熷氨鑷劧鐞嗚В浜嗐?/span>
鑱氱被鐨勫熀鏈蹇靛氨鏄繖涔堜簺浜嗭紝鍏充簬鑱氱被鐨勫涔犲拰鐮旂┒宸茬粡鍘嗙粡鍑犲崄騫達紝鍙互搴嗗垢鐨勪竴鐐規槸榪欓噷鐨勫涔犳垜浠彲浠ョ珯鍦ㄥ緢澶氬法浜虹殑鑲╄唨涓婏紝鑰屽浣曞幓鏀硅繘鍒涙柊鎵╁睍搴旂敤錛岄偅灝辨槸鎴戜滑鏈潵鐨勭洰鐨勶紝“宸ユ鍠勫叾浜嬶紝蹇呭厛鍒╁叾鍣?#8221;錛岃繖閲岃仛綾誨氨鏄垜浠殑“鍣?#8221;浜嗐?/span>
[1]Pattern Recognition Third Edition, Sergios Theodoridis, Konstantinos Koutroumbas
[2] http://baike.baidu.com/view/903740.htm?fr=ala0_1_1
[3] http://zh.wikipedia.org/zh-cn/%E6%95%B0%E6%8D%AE%E8%81%9A%E7%B1%BB
[4]鏁版嵁鎸栨帢姒傚康涓庢妧鏈?/span>(Data mining concepts and techniques) Jiawei Han, Micheline Kamber钁?/span>鑼冩槑, 瀛熷皬宄拌瘧
[5]妯″紡璇嗗埆絎笁鐗?/span>, Sergios Theodoridis, Konstantinos Koutroumbas钁?/span>, 鏉庢櫠鐨?/span>, 鐜嬬埍渚?/span>, 寮犲箍婧愮瓑璇?/span>
[6]鏁版嵁鎸栨帢瀵艱(Introduction to data mining) Pang-Ning Tan, Michael Steinbach, Vipin Kumar钁?/span>鑼冩槑, 鑼冨畯寤?/span>絳夎瘧
[7]鏁版嵁鎸栨帢瀹炵敤鏈哄櫒瀛︿範鎶鏈?/span> (Data mining practical machine learning tools and techniques) Ian H.Witten, Eibe Frank钁?/span>钁g惓絳夎瘧
鏂囩珷杞澆璇鋒爣鏄巭~~