]> AND Private Git Repository - these_gilles.git/blob - DOCS/L'estimation du gradient d'une fonction de densité, avec des applications dans Motif Recognition_ Baidu bibliothèque_files/_wk_2b04e7729dfe2503f00bb56e8dfe3e05_0(2).json
Logo AND Algorithmique Numérique Distribuée

Private GIT Repository
modif finale lnivs + keywords
[these_gilles.git] / DOCS / L'estimation du gradient d'une fonction de densité, avec des applications dans Motif Recognition_ Baidu bibliothèque_files / _wk_2b04e7729dfe2503f00bb56e8dfe3e05_0(2).json
1 wenku_3({"font":{"11b6a7de6f1aff00bed51eac0010003":"Helvetica"},"style":[{"t":"style","c":[1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,0],"s":{"font-family":"Arial"}},{"t":"style","c":[1],"s":{"letter-spacing":"0.628"}},{"t":"style","c":[1,2],"s":{"font-size":"11.879"}},{"t":"style","c":[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,3],"s":{"color":"#000000"}},{"t":"style","c":[5,17,18,22,4],"s":{"font-size":"8.64"}},{"t":"style","c":[5],"s":{"letter-spacing":"0.539"}},{"t":"style","c":[6],"s":{"letter-spacing":"0.549"}},{"t":"style","c":[8,11,13,14,16,19,20,21,23,24,7],"s":{"font-size":"16.2"}},{"t":"style","c":[8],"s":{"letter-spacing":"1.174"}},{"t":"style","c":[10,12,25,9],"s":{"font-size":"14.76"}},{"t":"style","c":[10],"s":{"letter-spacing":"0.625"}},{"t":"style","c":[11],"s":{"letter-spacing":"0.853"}},{"t":"style","c":[12],"s":{"letter-spacing":"0.504"}},{"t":"style","c":[13],"s":{"letter-spacing":"0.883"}},{"t":"style","c":[14],"s":{"letter-spacing":"0.882"}},{"t":"style","c":[16,17,15],"s":{"letter-spacing":"0.407"}},{"t":"style","c":[16],"s":{"letter-spacing":"0.407"}},{"t":"style","c":[17],"s":{"letter-spacing":"0.407"}},{"t":"style","c":[18],"s":{"letter-spacing":"0.295"}},{"t":"style","c":[19],"s":{"letter-spacing":"1.043"}},{"t":"style","c":[20],"s":{"letter-spacing":"1.339"}},{"t":"style","c":[21],"s":{"letter-spacing":"1.079"}},{"t":"style","c":[22],"s":{"letter-spacing":"0.267"}},{"t":"style","c":[23],"s":{"letter-spacing":"0.961"}},{"t":"style","c":[24],"s":{"letter-spacing":"1.219"}},{"t":"style","c":[25],"s":{"letter-spacing":"0.366"}},{"t":"style","c":[26],"s":{"letter-spacing":"0.591"}},{"t":"style","c":[27],"s":{"letter-spacing":"0.403"}},{"t":"style","c":[28],"s":{"font-size":"19.44"}},{"t":"style","c":[29],"s":{"letter-spacing":"1.119"}}],"body":[{"c":{"ix":0,"iy":0,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":-0.059,"y0":36.3,"y1":-0.059,"y2":-0.059,"y3":36.3,"z":0},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_0.png"},"t":"pic"},{"c":{"ix":0,"iy":66,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":36.3,"y0":72.66,"y1":36.3,"y2":36.3,"y3":72.66,"z":1},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_1.png"},"t":"pic"},{"c":{"ix":0,"iy":132,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":72.659,"y0":109.019,"y1":72.659,"y2":72.659,"y3":109.019,"z":2},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_2.png"},"t":"pic"},{"c":{"ix":0,"iy":198,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":109.019,"y0":145.379,"y1":109.019,"y2":109.019,"y3":145.379,"z":3},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_3.png"},"t":"pic"},{"c":{"ix":0,"iy":264,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":145.38,"y0":181.74,"y1":145.38,"y2":145.38,"y3":181.74,"z":4},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_4.png"},"t":"pic"},{"c":{"ix":0,"iy":330,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":181.739,"y0":218.099,"y1":181.739,"y2":181.739,"y3":218.099,"z":5},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_5.png"},"t":"pic"},{"c":{"ix":0,"iy":396,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":218.1,"y0":254.46,"y1":218.1,"y2":218.1,"y3":254.46,"z":6},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_6.png"},"t":"pic"},{"c":{"ix":0,"iy":462,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":254.459,"y0":290.819,"y1":254.459,"y2":254.459,"y3":290.819,"z":7},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_7.png"},"t":"pic"},{"c":{"ix":0,"iy":528,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":290.82,"y0":327.18,"y1":290.82,"y2":290.82,"y3":327.18,"z":8},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_8.png"},"t":"pic"},{"c":{"ix":0,"iy":594,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":327.179,"y0":363.539,"y1":327.179,"y2":327.179,"y3":363.539,"z":9},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_9.png"},"t":"pic"},{"c":{"ix":0,"iy":660,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":363.54,"y0":399.9,"y1":363.54,"y2":363.54,"y3":399.9,"z":10},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_10.png"},"t":"pic"},{"c":{"ix":0,"iy":726,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":399.9,"y0":436.26,"y1":399.9,"y2":399.9,"y3":436.26,"z":11},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_11.png"},"t":"pic"},{"c":{"ix":0,"iy":792,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":436.26,"y0":472.62,"y1":436.26,"y2":436.26,"y3":472.62,"z":12},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_12.png"},"t":"pic"},{"c":{"ix":0,"iy":858,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":472.62,"y0":508.98,"y1":472.62,"y2":472.62,"y3":508.98,"z":13},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_13.png"},"t":"pic"},{"c":{"ix":0,"iy":924,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":508.98,"y0":545.34,"y1":508.98,"y2":508.98,"y3":545.34,"z":14},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_14.png"},"t":"pic"},{"c":{"ix":0,"iy":990,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":545.34,"y0":581.7,"y1":545.34,"y2":545.34,"y3":581.7,"z":15},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_15.png"},"t":"pic"},{"c":{"ix":0,"iy":1056,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":581.7,"y0":618.06,"y1":581.7,"y2":581.7,"y3":618.06,"z":16},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_16.png"},"t":"pic"},{"c":{"ix":0,"iy":1122,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":618.06,"y0":654.42,"y1":618.06,"y2":618.06,"y3":654.42,"z":17},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_17.png"},"t":"pic"},{"c":{"ix":0,"iy":1188,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":654.42,"y0":690.78,"y1":654.42,"y2":654.42,"y3":690.78,"z":18},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_18.png"},"t":"pic"},{"c":{"ix":0,"iy":1254,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":690.78,"y0":727.14,"y1":690.78,"y2":690.78,"y3":727.14,"z":19},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_19.png"},"t":"pic"},{"c":{"ix":0,"iy":1320,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":727.14,"y0":763.5,"y1":727.14,"y2":727.14,"y3":763.5,"z":20},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_20.png"},"t":"pic"},{"c":{"ix":0,"iy":1386,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":763.5,"y0":799.86,"y1":763.5,"y2":763.5,"y3":799.86,"z":21},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_21.png"},"t":"pic"},{"c":{"ix":0,"iy":1452,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":799.86,"y0":836.22,"y1":799.86,"y2":799.86,"y3":836.22,"z":22},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_22.png"},"t":"pic"},{"c":{"ix":0,"iy":1518,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":836.219,"y0":872.579,"y1":836.219,"y2":836.219,"y3":872.579,"z":23},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_23.png"},"t":"pic"},{"c":{"ix":0,"iy":1584,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":872.58,"y0":908.94,"y1":872.58,"y2":872.58,"y3":908.94,"z":24},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_24.png"},"t":"pic"},{"c":{"ix":0,"iy":1650,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":908.939,"y0":945.3,"y1":908.939,"y2":908.939,"y3":945.3,"z":25},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_25.png"},"t":"pic"},{"c":{"ix":0,"iy":1716,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":945.3,"y0":981.66,"y1":945.3,"y2":945.3,"y3":981.66,"z":26},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_26.png"},"t":"pic"},{"c":{"ix":0,"iy":1782,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":981.66,"y0":1018.02,"y1":981.66,"y2":981.66,"y3":1018.02,"z":27},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_27.png"},"t":"pic"},{"c":{"ix":0,"iy":1848,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":1018.02,"y0":1054.38,"y1":1018.02,"y2":1018.02,"y3":1054.38,"z":28},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_28.png"},"t":"pic"},{"c":{"ix":0,"iy":1914,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":1054.38,"y0":1090.74,"y1":1054.38,"y2":1054.38,"y3":1090.74,"z":29},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_29.png"},"t":"pic"},{"c":{"ix":0,"iy":1980,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":1090.74,"y0":1127.1,"y1":1090.74,"y2":1090.74,"y3":1127.1,"z":30},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_30.png"},"t":"pic"},{"c":{"ix":0,"iy":2046,"iw":1572,"ih":61},"p":{"h":61,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":1127.1,"y0":1163.46,"y1":1127.1,"y2":1127.1,"y3":1163.46,"z":31},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_31.png"},"t":"pic"},{"c":{"ix":0,"iy":2112,"iw":1572,"ih":53},"p":{"h":53,"opacity":1,"rotate":0,"w":924.479,"x":0,"x0":0,"x1":0,"x2":924.479,"x3":924.479,"y":1163.46,"y0":1195.14,"y1":1163.46,"y2":1163.46,"y3":1195.14,"z":32},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_3_32.png"},"t":"pic"},{"c":"34 ","p":{"h":12.664,"w":13.749,"x":113.399,"y":53.815,"z":33},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.892},"t":"word","r":[1]},{"c":"IEEE ","p":{"h":9.21,"w":17.959,"x":566.64,"y":54.798,"z":34},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[5]},{"c":"TRANSACTIONS ","p":{"h":9.21,"w":57.591,"x":590.398,"y":54.798,"z":35},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.58"},"t":"word","r":[4]},{"c":"ON ","p":{"h":9.21,"w":12.245,"x":669.233,"y":54.798,"z":36},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.687"},"t":"word","r":[4]},{"c":"INFORMATION ","p":{"h":9.21,"w":51.558,"x":687.592,"y":54.798,"z":37},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"font-size":"8.64"},"t":"word","r":[4,6]},{"c":"THEORY, ","p":{"h":9.21,"w":33.431,"x":761.028,"y":54.798,"z":38},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.57"},"t":"word","r":[4]},{"c":"JANUARY ","p":{"h":9.21,"w":35.021,"x":808.185,"y":54.798,"z":39},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.605"},"t":"word","r":[4]},{"c":"1975 ","p":{"h":12.664,"w":25.312,"x":859.68,"y":52.015,"z":40},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.892},"t":"word","r":[1]},{"c":"The conditions to be satisfied are listed as follows ","p":{"h":17.269,"w":319.618,"x":113.039,"y":89.344,"z":41},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.778"},"t":"word","r":[7]},{"c":"0 ","p":{"h":17.269,"w":10.987,"x":114.479,"y":119.944,"z":42},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"N-tCO ","p":{"h":9.21,"w":22.331,"x":231.12,"y":171.438,"z":47},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.557"},"t":"word","r":[4]},{"c":"lim h(N) * ","p":{"h":17.269,"w":73.081,"x":257.4,"y":116.344,"z":43},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.799"},"t":"word","r":[7]},{"c":"0 ","p":{"h":17.269,"w":10.987,"x":342.361,"y":116.344,"z":44},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"N-C.3 ","p":{"h":9.21,"w":20.763,"x":254.52,"y":134.718,"z":45},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.51"},"t":"word","r":[4]},{"c":"(26) ","p":{"h":15.734,"w":25.841,"x":465.84,"y":120.101,"z":64},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"The same ","p":{"h":17.269,"w":66.596,"x":507.96,"y":87.904,"z":149},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.033"},"t":"word","r":[7]},{"c":"g","p":{"h":17.269,"w":7.134,"x":572.041,"y":87.904,"z":150},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"eneral ","p":{"h":17.269,"w":44.259,"x":580.117,"y":87.904,"z":151},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.941"},"t":"word","r":[7]},{"c":"f","p":{"h":17.269,"w":3.567,"x":621.361,"y":87.904,"z":152},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"orm will result if the kernel function is of ","p":{"h":17.269,"w":261.194,"x":625.754,"y":87.904,"z":153},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[11]},{"c":"the form ","p":{"h":17.269,"w":55.852,"x":507.96,"y":106.624,"z":154},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.827"},"t":"word","r":[7]},{"c":"k(X) ","p":{"h":15.734,"w":25.849,"x":642.599,"y":129.821,"z":155},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"= g(XTX). ","p":{"h":15.734,"w":62.201,"x":679.68,"y":129.821,"z":156},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.241"},"t":"word","r":[9]},{"c":"(32) ","p":{"h":17.269,"w":29.522,"x":860.039,"y":131.464,"z":157},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"XTX ","p":{"h":17.269,"w":29.826,"x":753.12,"y":183.664,"z":165},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[14]},{"c":"I; 1 ","p":{"h":17.269,"w":28.987,"x":793.8,"y":183.664,"z":166},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.128"},"t":"word","r":[7]},{"c":"xTx ","p":{"h":17.269,"w":25.498,"x":753.48,"y":202.024,"z":168},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.689"},"t":"word","r":[7]},{"c":"> 1 ","p":{"h":17.269,"w":29.347,"x":793.8,"y":202.024,"z":169},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"3.073"},"t":"word","r":[7]},{"c":"lim Nh2\u201d+2(N) = cc ","p":{"h":17.269,"w":142.779,"x":234,"y":152.344,"z":46},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.704"},"t":"word","r":[7]},{"c":"2) the characteristic function ","p":{"h":17.269,"w":186.57,"x":113.399,"y":188.704,"z":48},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.826"},"t":"word","r":[7]},{"c":"G(W) = ","p":{"h":17.269,"w":54.234,"x":184.32,"y":225.424,"z":49},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.74"},"t":"word","r":[7]},{"c":"[ ","p":{"h":17.269,"w":7.499,"x":248.76,"y":225.424,"z":50},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[16]},{"c":"exp (jWrX)V,k(X) ","p":{"h":17.269,"w":108.982,"x":269.64,"y":225.424,"z":51},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.677"},"t":"word","r":[7]},{"c":"JR\" ","p":{"h":9.21,"w":12.862,"x":244.799,"y":246.678,"z":53},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.431"},"t":"word","r":[4]},{"c":"(27) ","p":{"h":17.269,"w":29.522,"x":465.84,"y":155.224,"z":65},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"The most simple kernel with this form is ","p":{"h":17.269,"w":262.869,"x":522.358,"y":155.944,"z":158},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.003"},"t":"word","r":[7]},{"c":"k(X) ","p":{"h":9.21,"w":14.883,"x":574.2,"y":202.398,"z":159},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.362"},"t":"word","r":[4]},{"c":"= ","p":{"h":9.21,"w":5.836,"x":612.357,"y":202.398,"z":160},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[5]},{"c":"1 ","p":{"h":9.21,"w":5.662,"x":631.436,"y":212.118,"z":161},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[17]},{"c":"c(l ","p":{"h":9.21,"w":9.395,"x":637.916,"y":190.518,"z":162},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.269"},"t":"word","r":[4]},{"c":"o ","p":{"h":9.21,"w":5.662,"x":637.56,"y":202.398,"z":167},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[17]},{"c":"- ","p":{"h":9.21,"w":4.294,"x":663.114,"y":190.518,"z":163},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[18]},{"c":"XTX), ","p":{"h":9.21,"w":19.887,"x":680.393,"y":190.518,"z":164},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.436"},"t":"word","r":[4]},{"c":"3 ","p":{"h":17.269,"w":10.987,"x":645.839,"y":204.184,"z":171},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"(33) ","p":{"h":17.269,"w":29.522,"x":860.4,"y":195.544,"z":170},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"dX ","p":{"h":15.734,"w":18.056,"x":401.76,"y":226.661,"z":52},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.808"},"t":"word","r":[9]},{"c":"where ","p":{"h":17.269,"w":42.922,"x":507.598,"y":224.704,"z":172},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[19]},{"c":"(34) ","p":{"h":17.269,"w":29.522,"x":860.76,"y":258.904,"z":173},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"is the normalizing constant required to make the kernel ","p":{"h":17.269,"w":381.156,"x":507.958,"y":294.904,"z":174},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.301"},"t":"word","r":[7]},{"c":"function integrate to one and l?(w) ","p":{"h":17.269,"w":230.358,"x":508.318,"y":312.904,"z":175},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[19]},{"c":"i","p":{"h":17.269,"w":2.774,"x":735.839,"y":312.904,"z":176},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"s the gamma function. ","p":{"h":17.269,"w":147.523,"x":738.945,"y":312.904,"z":177},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.977"},"t":"word","r":[7]},{"c":"This kernel function can easily be shown to satisfy all the ","p":{"h":17.269,"w":381.036,"x":507.958,"y":330.904,"z":178},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.051"},"t":"word","r":[7]},{"c":"conditions for asymptotic unbiasedness, ","p":{"h":17.269,"w":273.379,"x":508.318,"y":348.904,"z":179},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.16"},"t":"word","r":[7]},{"c":"c","p":{"h":17.269,"w":6.341,"x":778.68,"y":348.904,"z":180},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"onsistency, and ","p":{"h":17.269,"w":103.731,"x":785.715,"y":348.904,"z":181},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.841"},"t":"word","r":[7]},{"c":"uniform consistency of the gradient estimate and is, in a ","p":{"h":17.269,"w":381.429,"x":507.958,"y":366.904,"z":182},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.189"},"t":"word","r":[7]},{"c":"sense, quite similar to the asymptotic optimum product ","p":{"h":17.269,"w":378.915,"x":508.678,"y":384.904,"z":183},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.332"},"t":"word","r":[7]},{"c":"kernel discussed ","p":{"h":17.269,"w":110.688,"x":508.318,"y":403.264,"z":184},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.806"},"t":"word","r":[7]},{"c":"b","p":{"h":17.269,"w":7.134,"x":615.239,"y":403.264,"z":185},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"y Epanechnikov [lo]. ","p":{"h":17.269,"w":134.844,"x":623.228,"y":403.264,"z":186},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.919"},"t":"word","r":[7]},{"c":"Substituting (33) into (lo), we obtain as the gradient ","p":{"h":17.269,"w":366.707,"x":523.078,"y":420.904,"z":187},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.445"},"t":"word","r":[7]},{"c":"estimate ","p":{"h":17.269,"w":57.219,"x":508.318,"y":439.264,"z":188},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.766"},"t":"word","r":[7]},{"c":"oxpNtx) ","p":{"h":9.21,"w":26.46,"x":508.68,"y":476.358,"z":189},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.394"},"t":"word","r":[4]},{"c":"of V&(X) ","p":{"h":17.269,"w":58.154,"x":114.479,"y":263.944,"z":54},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.936"},"t":"word","r":[7]},{"c":"is absolutely integrable (i.e., ","p":{"h":17.269,"w":182.33,"x":182.52,"y":263.944,"z":55},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.686"},"t":"word","r":[7]},{"c":"s ","p":{"h":17.269,"w":10.261,"x":132.839,"y":313.264,"z":56},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.535"},"t":"word","r":[7]},{"c":"R\" ","p":{"h":9.21,"w":9.327,"x":140.76,"y":322.278,"z":60},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.513"},"t":"word","r":[4]},{"c":"IIWVII ","p":{"h":17.269,"w":41.465,"x":159.12,"y":303.544,"z":57},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.613"},"t":"word","r":[7]},{"c":"dW < ~0, ","p":{"h":17.269,"w":72.13,"x":213.84,"y":303.544,"z":58},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.364"},"t":"word","r":[7]},{"c":"where W = [or - ","p":{"h":17.269,"w":117.354,"x":308.16,"y":300.304,"z":59},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.927"},"t":"word","r":[7]},{"c":". . ","p":{"h":15.734,"w":14.286,"x":424.439,"y":297.581,"z":63},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.572"},"t":"word","r":[9]},{"c":"%lT) ","p":{"h":22.258,"w":41.083,"x":439.2,"y":299.524,"z":66},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.898},"s":{"font-size":"20.88","letter-spacing":"0.968"},"t":"word","r":[0]},{"c":"(28) ","p":{"h":15.734,"w":25.841,"x":466.2,"y":334.661,"z":67},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"V,p(X) is uniformly continuous. ","p":{"h":17.269,"w":210.368,"x":208.08,"y":357.184,"z":62},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.136"},"t":"word","r":[7]},{"c":"(29) ","p":{"h":17.269,"w":29.522,"x":466.56,"y":360.064,"z":68},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"3) ","p":{"h":17.269,"w":16.261,"x":115.56,"y":360.784,"z":61},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"The proof follows from the definition of Vx&X) ","p":{"h":17.269,"w":319.653,"x":128.878,"y":384.544,"z":69},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.402"},"t":"word","r":[7]},{"c":"and ","p":{"h":17.269,"w":27.606,"x":466.919,"y":384.544,"z":70},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"the properties of characteristic functions, the details of ","p":{"h":17.269,"w":378.627,"x":114.477,"y":402.544,"z":71},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.253"},"t":"word","r":[7]},{"c":"which are given in the Appendix. Again we see that the ","p":{"h":17.269,"w":379.956,"x":114.837,"y":420.544,"z":72},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[20]},{"c":"additional power of two in the condition (27) on h(N) ","p":{"h":17.269,"w":377.054,"x":114.837,"y":438.544,"z":73},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.618"},"t":"word","r":[7]},{"c":"is present. ","p":{"h":17.269,"w":70.475,"x":114.837,"y":456.904,"z":74},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.755"},"t":"word","r":[7]},{"c":"III. ","p":{"h":17.269,"w":19.424,"x":200.158,"y":483.544,"z":75},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[16]},{"c":"SPECIAL ","p":{"h":12.664,"w":45.333,"x":228.6,"y":487.255,"z":76},"ps":{"_opacity":1,"_scaleX":0.892},"s":{"letter-spacing":"0.694"},"t":"word","r":[2]},{"c":"KERNEL ","p":{"h":12.664,"w":42.978,"x":282.602,"y":487.255,"z":77},"ps":{"_opacity":1,"_scaleX":0.892},"s":{"letter-spacing":"0.764"},"t":"word","r":[2]},{"c":"FUNCTIONS ","p":{"h":12.664,"w":61.674,"x":336.604,"y":487.255,"z":78},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.892},"s":{"letter-spacing":"0.738"},"t":"word","r":[2]},{"c":"Having derived a general class of probability density ","p":{"h":17.269,"w":365.167,"x":129.96,"y":507.664,"z":79},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.335"},"t":"word","r":[7]},{"c":"= ","p":{"h":17.269,"w":11.393,"x":572.04,"y":510.184,"z":191},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[21]},{"c":"gradient estimates and shown it to have certain desirable ","p":{"h":17.269,"w":382.307,"x":114.839,"y":525.664,"z":80},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.063"},"t":"word","r":[7]},{"c":"properties, we will now investigate specific kernel functions ","p":{"h":17.269,"w":378.877,"x":114.479,"y":543.664,"z":81},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.767"},"t":"word","r":[7]},{"c":"where ","p":{"h":17.269,"w":42.922,"x":509.039,"y":551.584,"z":192},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[19]},{"c":"in order to better ","p":{"h":17.269,"w":109.298,"x":114.839,"y":562.024,"z":82},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.739"},"t":"word","r":[7]},{"c":"u","p":{"h":17.269,"w":7.134,"x":222.48,"y":562.024,"z":83},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"nderstand ","p":{"h":17.269,"w":68.756,"x":230.59,"y":562.024,"z":84},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.975"},"t":"word","r":[7]},{"c":"t","p":{"h":17.269,"w":3.567,"x":296.28,"y":562.024,"z":85},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"he underlying process ","p":{"h":17.269,"w":141.258,"x":300.767,"y":562.024,"z":86},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.669"},"t":"word","r":[7]},{"c":"i","p":{"h":17.269,"w":2.774,"x":437.761,"y":562.024,"z":87},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"nvolved ","p":{"h":17.269,"w":52.412,"x":441.289,"y":562.024,"z":88},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.753"},"t":"word","r":[7]},{"c":"n ","p":{"h":9.21,"w":5.662,"x":758.153,"y":577.518,"z":200},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[17]},{"c":"n\/2 ","p":{"h":9.21,"w":11.813,"x":771.472,"y":577.518,"z":201},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.399"},"t":"word","r":[4]},{"c":"in gradient estimation. Ultimately this results in a simple ","p":{"h":17.269,"w":379.805,"x":114.839,"y":579.664,"z":89},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.137"},"t":"word","r":[7]},{"c":"dy= ","p":{"h":9.21,"w":13.408,"x":689.037,"y":590.118,"z":204},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.404"},"t":"word","r":[4]},{"c":"hs\u2019c ","p":{"h":9.21,"w":14.488,"x":750.594,"y":590.118,"z":205},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"-0.259"},"t":"word","r":[4]},{"c":"Q(X) ","p":{"h":9.21,"w":16.932,"x":591.123,"y":592.638,"z":202},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.456"},"t":"word","r":[4]},{"c":"= ","p":{"h":9.21,"w":5.836,"x":632.881,"y":592.638,"z":203},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[5]},{"c":"(36) ","p":{"h":17.269,"w":29.522,"x":861.48,"y":589.024,"z":208},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"and very intuitive ","p":{"h":17.269,"w":123.071,"x":114.839,"y":597.664,"z":90},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.393"},"t":"word","r":[7]},{"c":"mean-shift estimate for the density ","p":{"h":17.269,"w":246.726,"x":248.76,"y":597.664,"z":91},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.441"},"t":"word","r":[7]},{"c":"s ","p":{"h":9.21,"w":5.29,"x":650.52,"y":605.238,"z":199},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[22]},{"c":"&m ","p":{"h":9.21,"w":11.956,"x":658.079,"y":608.838,"z":206},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.577"},"t":"word","r":[4]},{"c":"I-(n + 2\/2) ","p":{"h":17.269,"w":75.756,"x":732.599,"y":598.744,"z":207},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.596"},"t":"word","r":[7]},{"c":"gradient. A simple modification then extends this in a ","p":{"h":17.269,"w":359.829,"x":115.56,"y":615.664,"z":92},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.167"},"t":"word","r":[7]},{"c":"k- ","p":{"h":15.734,"w":13.526,"x":478.439,"y":616.901,"z":93},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.46"},"t":"word","r":[9]},{"c":"is the volume of the region ","p":{"h":17.269,"w":176.551,"x":509.038,"y":624.664,"z":209},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[23]},{"c":"nearest-neighbor approach to gradient estimation much ","p":{"h":17.269,"w":379.078,"x":114.84,"y":633.664,"z":94},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[24]},{"c":"in the same manner as Loftsgaarden and Quesenberry\u2019s ","p":{"h":17.269,"w":386.185,"x":114.84,"y":651.664,"z":95},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.204"},"t":"word","r":[7]},{"c":"S,(X) ","p":{"h":15.734,"w":31.375,"x":570.96,"y":652.901,"z":210},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.527"},"t":"word","r":[9]},{"c":"= {Y: ","p":{"h":15.734,"w":37.018,"x":613.08,"y":652.901,"z":211},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.036"},"t":"word","r":[9]},{"c":"(Y - ","p":{"h":15.734,"w":29.401,"x":659.881,"y":652.901,"z":212},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.015"},"t":"word","r":[9]},{"c":"X)T(Y ","p":{"h":15.734,"w":35.181,"x":699.122,"y":652.901,"z":213},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.601"},"t":"word","r":[9]},{"c":"- ","p":{"h":15.734,"w":7.44,"x":745.563,"y":652.901,"z":214},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[25]},{"c":"X) I ","p":{"h":15.734,"w":30.846,"x":763.204,"y":652.901,"z":215},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.574"},"t":"word","r":[9]},{"c":"h2} ","p":{"h":15.734,"w":21.502,"x":804.245,"y":652.901,"z":216},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.711"},"t":"word","r":[9]},{"c":"(37) ","p":{"h":17.269,"w":29.522,"x":861.839,"y":654.544,"z":217},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"[9] extension of kernel density estimates. ","p":{"h":17.269,"w":267.576,"x":115.919,"y":669.664,"z":96},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[11]},{"c":"and ","p":{"h":17.269,"w":27.606,"x":509.397,"y":678.664,"z":218},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"k ","p":{"h":15.734,"w":9.177,"x":539.64,"y":679.901,"z":219},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.555"},"t":"word","r":[9]},{"c":"is the number of observations falling within S,,(X) ","p":{"h":17.269,"w":335.734,"x":554.4,"y":678.664,"z":220},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.15"},"t":"word","r":[7]},{"c":"and, therefore, the number in the sum. ","p":{"h":17.269,"w":250.755,"x":509.399,"y":696.664,"z":221},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[14]},{"c":"A. Mean-Shift ","p":{"h":15.734,"w":86.358,"x":115.56,"y":700.781,"z":97},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.181"},"t":"word","r":[9]},{"c":"Gradient Estimates ","p":{"h":15.734,"w":115.017,"x":213.482,"y":700.781,"z":98},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.902"},"t":"word","r":[9]},{"c":"Equation (35) ","p":{"h":17.269,"w":91.803,"x":524.52,"y":714.304,"z":222},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[23]},{"c":"p","p":{"h":17.269,"w":7.134,"x":614.52,"y":714.304,"z":223},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"rovides us with an excellent ","p":{"h":17.269,"w":178.732,"x":622.466,"y":714.304,"z":224},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.773"},"t":"word","r":[7]},{"c":"i","p":{"h":17.269,"w":2.774,"x":799.201,"y":714.304,"z":225},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"nterpretation ","p":{"h":17.269,"w":85.364,"x":802.753,"y":714.304,"z":226},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.777"},"t":"word","r":[7]},{"c":"The Gaussian ","p":{"h":17.269,"w":94.315,"x":129.96,"y":723.664,"z":99},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.073"},"t":"word","r":[7]},{"c":"k","p":{"h":17.269,"w":6.341,"x":222.84,"y":723.664,"z":100},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"ernel function is perhaps the best known ","p":{"h":17.269,"w":263.803,"x":229.978,"y":723.664,"z":101},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.863"},"t":"word","r":[7]},{"c":"of the gradient estimation process. The last term in (35) ","p":{"h":17.269,"w":381.604,"x":509.759,"y":732.664,"z":227},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.224"},"t":"word","r":[7]},{"c":"differentiable multivariate kernel function satisfying the ","p":{"h":17.269,"w":380.316,"x":115.559,"y":741.304,"z":102},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.25"},"t":"word","r":[7]},{"c":"is the sample mean shift ","p":{"h":17.269,"w":156.147,"x":509.759,"y":750.664,"z":228},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.734"},"t":"word","r":[7]},{"c":"conditions for asymptotic unbiasedness, ","p":{"h":17.269,"w":273.019,"x":115.919,"y":759.664,"z":103},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.151"},"t":"word","r":[7]},{"c":"c","p":{"h":17.269,"w":6.341,"x":385.561,"y":759.664,"z":104},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"onsistency, and ","p":{"h":17.269,"w":103.372,"x":392.596,"y":759.664,"z":105},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.817"},"t":"word","r":[7]},{"c":"uniform consistency of the density gradient estimate. The ","p":{"h":17.269,"w":379.614,"x":115.92,"y":777.664,"z":106},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.009"},"t":"word","r":[7]},{"c":"(38) ","p":{"h":17.269,"w":29.522,"x":861.839,"y":789.904,"z":237},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"MhtX) ","p":{"h":9.21,"w":20.725,"x":601.56,"y":796.758,"z":229},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.448"},"t":"word","r":[4]},{"c":"E ","p":{"h":9.21,"w":6.223,"x":651.596,"y":796.758,"z":230},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"font-size":"8.64"},"t":"word","r":[4,26]},{"c":"t ","p":{"h":9.21,"w":3.882,"x":668.515,"y":796.758,"z":231},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.383"},"t":"word","r":[4]},{"c":"x ","p":{"h":9.21,"w":5.29,"x":681.835,"y":796.758,"z":232},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[22]},{"c":"Eqh(x) ","p":{"h":9.21,"w":22.815,"x":694.794,"y":796.758,"z":233},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.377"},"t":"word","r":[4]},{"c":"txi ","p":{"h":9.21,"w":9.052,"x":732.592,"y":796.758,"z":234},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.298"},"t":"word","r":[4]},{"c":"- ","p":{"h":9.21,"w":4.294,"x":759.95,"y":796.758,"z":235},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[18]},{"c":"x> ","p":{"h":9.21,"w":9.435,"x":776.869,"y":796.758,"z":236},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"font-size":"8.64"},"t":"word","r":[4,27]},{"c":"Gaussian probability ","p":{"h":17.269,"w":136.571,"x":116.28,"y":795.664,"z":107},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.911"},"t":"word","r":[7]},{"c":"density kernel function with zero ","p":{"h":17.269,"w":234.144,"x":262.801,"y":795.664,"z":108},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.541"},"t":"word","r":[7]},{"c":"i ","p":{"h":17.269,"w":6.736,"x":689.398,"y":800.704,"z":238},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.127"},"t":"word","r":[7]},{"c":"mean and identity covariance matrix is ","p":{"h":17.269,"w":251.709,"x":115.92,"y":814.024,"z":109},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.899"},"t":"word","r":[7]},{"c":"of the observations in the small region S,(X) about X. ","p":{"h":17.269,"w":377.499,"x":510.837,"y":826.264,"z":239},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.476"},"t":"word","r":[7]},{"c":"k(X) ","p":{"h":15.734,"w":25.849,"x":202.68,"y":842.261,"z":110},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"= (27~)-\u201c\/~ ","p":{"h":15.734,"w":70.321,"x":239.76,"y":842.261,"z":111},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.955"},"t":"word","r":[9]},{"c":"exp (- +XTX). ","p":{"h":17.269,"w":93.548,"x":312.12,"y":841.024,"z":112},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.172"},"t":"word","r":[7]},{"c":"(30) ","p":{"h":17.269,"w":29.522,"x":468.72,"y":844.264,"z":113},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[13]},{"c":"Clearly, if the gradient or slope is zero, corresponding ","p":{"h":17.269,"w":382.212,"x":510.838,"y":844.264,"z":240},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.408"},"t":"word","r":[7]},{"c":"Taking the gradient of (30) and substituting it into (10) ","p":{"h":17.269,"w":382.324,"x":116.278,"y":868.024,"z":114},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.396"},"t":"word","r":[7]},{"c":"to a uniform density over the region S,,(X), the average ","p":{"h":17.269,"w":384.568,"x":510.838,"y":862.264,"z":241},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[20]},{"c":"for Vk(X), we obtain as the estimate of the density gradient ","p":{"h":17.269,"w":381.107,"x":116.278,"y":886.024,"z":115},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.857"},"t":"word","r":[7]},{"c":"mean shift would be zero due to the symmetry of the ","p":{"h":17.269,"w":379.956,"x":510.837,"y":880.264,"z":242},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.696"},"t":"word","r":[7]},{"c":"observations near X. However, with a nonzero density ","p":{"h":17.269,"w":379.927,"x":511.197,"y":898.264,"z":243},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.446"},"t":"word","r":[7]},{"c":"gradient pointing in the direction of most rapid increase ","p":{"h":17.269,"w":383.007,"x":511.557,"y":916.264,"z":244},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.28"},"t":"word","r":[7]},{"c":"?xPN(x) = N -\u2019 2 (xi ","p":{"h":20.723,"w":161.193,"x":155.519,"y":919.961,"z":116},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"font-size":"19.44"},"t":"word","r":[28,29]},{"c":"_ X)(2n)-\u201c\/2h-(\u201c+2) ","p":{"h":20.723,"w":144.494,"x":322.557,"y":915.641,"z":117},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"0.612"},"t":"word","r":[28]},{"c":"i=l ","p":{"h":9.21,"w":9.331,"x":270.72,"y":940.758,"z":118},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.342"},"t":"word","r":[4]},{"c":"of the probability density function, on the average ","p":{"h":17.269,"w":344.968,"x":511.198,"y":934.264,"z":245},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.309"},"t":"word","r":[7]},{"c":"m","p":{"h":17.269,"w":10.305,"x":854.28,"y":934.264,"z":246},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"ore ","p":{"h":17.269,"w":24.532,"x":865.602,"y":934.264,"z":247},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.017"},"t":"word","r":[7]},{"c":"observations should fall along its direction than elsewhere ","p":{"h":17.269,"w":385.186,"x":511.558,"y":952.264,"z":248},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.984"},"t":"word","r":[7]},{"c":"* exp [-(X ","p":{"h":17.269,"w":64.134,"x":238.68,"y":967.744,"z":119},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.892"},"t":"word","r":[7]},{"c":"- ","p":{"h":17.269,"w":8.273,"x":322.92,"y":967.744,"z":120},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"font-size":"16.2"},"t":"word","r":[7,26]},{"c":"Xi)T (y)] ","p":{"h":17.269,"w":56.903,"x":340.92,"y":967.744,"z":121},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.958"},"t":"word","r":[7]},{"c":"* ","p":{"h":17.269,"w":8.64,"x":452.521,"y":967.744,"z":122},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.871"},"t":"word","r":[7]},{"c":"(31) ","p":{"h":15.734,"w":25.841,"x":469.079,"y":968.981,"z":123},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"in S,(X). Correspondingly, the average ","p":{"h":17.269,"w":262.168,"x":511.198,"y":970.264,"z":249},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.141"},"t":"word","r":[7]},{"c":"m","p":{"h":17.269,"w":10.305,"x":770.759,"y":970.264,"z":250},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"ean shift should ","p":{"h":17.269,"w":109.057,"x":782.227,"y":970.264,"z":251},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.096"},"t":"word","r":[7]},{"c":"point in that direction and have a length proportional to ","p":{"h":17.269,"w":378.267,"x":510.838,"y":988.264,"z":252},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.249"},"t":"word","r":[7]},{"c":"An intuitive interpretation of (31) is that it is essentially ","p":{"h":17.269,"w":367.895,"x":131.039,"y":1006.264,"z":124},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.024"},"t":"word","r":[7]},{"c":"the magnitude of the gradient. ","p":{"h":17.269,"w":197.577,"x":511.197,"y":1006.264,"z":253},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.893"},"t":"word","r":[7]},{"c":"a weighted measure of the mean shift of the observations ","p":{"h":17.269,"w":382.753,"x":116.999,"y":1024.264,"z":125},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[21]},{"c":"about the point X. The shift Xi - X of each ","p":{"h":17.269,"w":292.781,"x":116.999,"y":1042.264,"z":126},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.434"},"t":"word","r":[7]},{"c":"p","p":{"h":17.269,"w":7.134,"x":408.241,"y":1042.264,"z":127},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"oint from X ","p":{"h":17.269,"w":78.787,"x":416.187,"y":1042.264,"z":128},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.388"},"t":"word","r":[7]},{"c":"B. Mean-Shift ","p":{"h":15.734,"w":84.918,"x":511.2,"y":1037.381,"z":254},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.07"},"t":"word","r":[9]},{"c":"Normalized ","p":{"h":15.734,"w":66.604,"x":607.322,"y":1037.381,"z":255},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.666"},"t":"word","r":[9]},{"c":"Gradient Estimates ","p":{"h":15.734,"w":115.377,"x":683.643,"y":1037.381,"z":256},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.922"},"t":"word","r":[9]},{"c":"Examining the proportionality constant in (35), we see ","p":{"h":17.269,"w":369.131,"x":525.96,"y":1059.904,"z":257},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[24]},{"c":"is calculated ","p":{"h":17.269,"w":81.535,"x":116.639,"y":1060.264,"z":129},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.63"},"t":"word","r":[7]},{"c":"a","p":{"h":17.269,"w":7.134,"x":196.56,"y":1060.264,"z":130},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"nd multiplied by the weighting factor ","p":{"h":17.269,"w":231.434,"x":204.869,"y":1060.264,"z":131},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.762"},"t":"word","r":[7]},{"c":"h-(\u201c+2) . ","p":{"h":15.734,"w":57.487,"x":437.4,"y":1061.501,"z":132},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.186"},"t":"word","r":[9]},{"c":"w- ","p":{"h":15.734,"w":16.212,"x":117.352,"y":1082.381,"z":133},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.713"},"t":"word","r":[9]},{"c":"\u20181\u2019 exp (-(X ","p":{"h":17.269,"w":74.781,"x":151.56,"y":1078.264,"z":134},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"-0.362"},"t":"word","r":[7]},{"c":"- Xi)T(X - ","p":{"h":17.269,"w":74.513,"x":240.12,"y":1078.264,"z":135},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.023"},"t":"word","r":[7]},{"c":"Xi)\/2h2). ","p":{"h":15.734,"w":51.068,"x":323.64,"y":1079.501,"z":136},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.568"},"t":"word","r":[9]},{"c":"The sample mean ","p":{"h":17.269,"w":116.092,"x":381.96,"y":1078.264,"z":137},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.888"},"t":"word","r":[7]},{"c":"that it contains a term identical to the probability density ","p":{"h":17.269,"w":380.287,"x":511.2,"y":1077.904,"z":258},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"font-size":"16.2"},"t":"word","r":[7,29]},{"c":"of these ","p":{"h":17.269,"w":54.609,"x":116.998,"y":1096.624,"z":138},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.812"},"t":"word","r":[7]},{"c":"w","p":{"h":17.269,"w":9.116,"x":167.398,"y":1096.624,"z":139},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"eighted ","p":{"h":17.269,"w":51.526,"x":177.454,"y":1096.624,"z":140},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.939"},"t":"word","r":[7]},{"c":"s","p":{"h":17.269,"w":6.341,"x":226.439,"y":1096.624,"z":141},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"hifts is then ","p":{"h":17.269,"w":73.88,"x":233.312,"y":1096.624,"z":142},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.501"},"t":"word","r":[7]},{"c":"t","p":{"h":17.269,"w":3.567,"x":305.639,"y":1096.624,"z":143},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"aken as ","p":{"h":17.269,"w":52.277,"x":310.1,"y":1096.624,"z":144},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.719"},"t":"word","r":[7]},{"c":"t","p":{"h":17.269,"w":3.567,"x":359.64,"y":1096.624,"z":145},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"he gradient ","p":{"h":17.269,"w":74.579,"x":364.126,"y":1096.624,"z":146},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.724"},"t":"word","r":[7]},{"c":"e","p":{"h":17.269,"w":7.134,"x":437.04,"y":1096.624,"z":147},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[7]},{"c":"stimate. ","p":{"h":17.269,"w":53.377,"x":444.901,"y":1096.624,"z":148},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.726"},"t":"word","r":[7]},{"c":"estimate using a uniform kernel function over the region ","p":{"h":17.269,"w":380.312,"x":510.84,"y":1095.904,"z":259},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.197"},"t":"word","r":[7]},{"c":"= ","p":{"h":17.269,"w":11.393,"x":572.04,"y":469.864,"z":190},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[21]},{"c":"(Nh\u201d+2)-12c ","p":{"h":15.734,"w":71.655,"x":589.319,"y":467.861,"z":193},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.426"},"t":"word","r":[9]},{"c":"C ","p":{"h":15.734,"w":11.577,"x":691.922,"y":467.861,"z":194},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.06"},"t":"word","r":[9]},{"c":"(Xi ","p":{"h":15.734,"w":18.108,"x":726.122,"y":467.861,"z":195},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[9,27]},{"c":"- ","p":{"h":15.734,"w":7.44,"x":753.483,"y":467.861,"z":196},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[25]},{"c":"X) ","p":{"h":15.734,"w":15.364,"x":770.763,"y":467.861,"z":197},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.549"},"t":"word","r":[6,9]},{"c":"xi Es&v ","p":{"h":15.734,"w":44.493,"x":675.001,"y":481.181,"z":198},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.599"},"t":"word","r":[9]},{"c":"Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 29, 2009 at 00:59 from IEEE Xplore.  Restrictions apply. ","p":{"h":9.594,"w":671.742,"x":48.12,"y":1174.884,"z":260},"ps":{"_enter":1},"s":{"font-family":"11b6a7de6f1aff00bed51eac0010003","font-size":"9"},"t":"word","r":[3]}],"page":{"ph":1195.5,"pw":925.5,"iw":1572,"ih":2165,"v":6,"t":"7","pptlike":false,"cx":0,"cy":0,"cw":924.479,"ch":1195.14}})