A鵜pj"pij c"3.1: Không gian Metric 嫉n "o瓜v"d瓜"4"vj pj"rj亥p"*M,d+."vtqpi"8„< ‚ M là m瓜t t壱p h嬰p (h英u h衣n hay vô h衣n) ‚ d: M ×M s"温 là hàm tính kho違ng cách gi英a 2 ph亥n t穎 b医t k c栄a M th臼a các 8k隠u ki羽n: o 穴岫捲 検岻 半 "ど 褐捲 検 樺 警 (3.1) o 穴岫捲 検岻 噺 穴岫検 捲岻 褐捲 検 樺 警 (3.2) o 穴岫捲 検岻 噺 ど 垣 捲 噺 検 (3.3)
o 穴岫捲 検岻 髪 穴岫検 権岻 半 穴岫捲 権岻褐捲 検 権 樺 警 (b医v"8鰯ng th泳c tam giác) (3.4) Vtqpi"vj詠e"v院."e„"t医v"pjk隠w"j o"v pj"mjq違pi"eƒej"mjƒe"pjcw"v́{"x q"8員e"v pj"e栄c" 8嘘k"v逢嬰pi"e亥p"mj違q"uƒv0"Vj»pi"vj逢運ng, v‒p"e栄c"j o"v pj"mjq違pi"eƒej"e pi là tên e栄c không gian Metric.
X "f映<
‚ Không gian Euclid 1 chi隠u, 2 chi隠u, 3 chi隠u,...
3.1.3. Kho違ng cách Hamming
Mjq違pi"eƒej"Jcookpi"f́pi"8吋"8q"u詠"mjƒe"dk羽v"ik英c"4"ejw厩k"dkv"pj鵜"rj¤p"*e„"vj吋"ƒr" f映pi"ejq"ejw厩k"eƒe" m#"u嘘"vco"rj¤p."vj壱r"rj¤p.000+0" Mjq違pi"eƒej" Jcookpi"8逢嬰e" 8鵜pj"pij c"pj逢"ucw<
A鵜pj"pij c"3.2:
穴張岫捲 検岻 噺 岶件 捲沈 塙 検沈岼 褐捲 検 樺 芸津 (3.5)
Vc"e„"vj吋"f宇"f pi"ej泳pi"okpj"8逢嬰e"mjq違pi"cách Hamming vj臼c"o«p"eƒe"v pj"ej医v" e栄c"o瓜v"mj»pi"ikcp"ogvtke
o 穴岫捲 検岻 半 ど 褐捲 検 樺 警 *fq"n逢嬰ng s嘘 c栄a t壱p h嬰p luôn là giá tr鵜 không âm)
o 穴岫捲 検岻 噺 穴岫検 捲岻 褐捲 検 樺 警 (ta th医y vai trò c栄c"z."{"vtqpi"8鵜pj"pij c" n "pj逢"pjcw+ o 穴岫捲 検岻 噺 ど 垣 褐件 捲件" 噺 検件" 垣 捲 噺 検 o 穴岫捲 検岻 髪 穴岫検 権岻 半 穴岫捲 権岻褐捲 検 権 樺 警 V噂i m丑i i ta có: 岫捲沈 噺 検沈岻 巻 岫検沈 噺 権沈岻 馨 捲沈 噺 権沈 捲沈 塙 権沈 馨 岫捲沈 塙 検沈岻 喚 岫検沈 塙 権沈岻 馨 岶件 捲沈 塙 権沈岼 稀 岶件 捲沈 塙 検沈岼笈岶件 検沈 塙 権沈岼
馨 岶件 捲沈 塙 権沈岼 判 岶件 捲沈 塙 検沈岼 髪 岶件 検沈 塙 権沈岼 馨 穴岫捲 検岻 髪 穴岫検 権岻 半 穴岫捲 権岻褐捲 検 権 樺 警 3.1.4. A鵜pj"pij c"o«"u穎a l厩i ‚ Cho m瓜t t壱p h英u h衣n A: g丑i là t壱p ký t詠 *vj逢運ng là t壱p các ký s嘘 nh鵜 phân A={0,1}) ‚ An8逢嬰c g丑i là không gian mã ‚ a 樺 An 8逢嬰c g丑i là m瓜t t瑛 ‚ C 稀 An8逢嬰c g丑i là m瓜t mã (ho員c t瑛8k吋n) ‚ c 樺 C 8逢嬰c g丑i là m瓜t t瑛 mã ‚ n là chi隠u dài c栄a mã
A鵜pj" pij c"3.3: Mjq違pi" eƒej" Jcookpi" e栄c" o瓜v" o«" 8逢嬰e" 8鵜pj" pij c" n " mjq違pi" eƒej"Jcookpi"v嘘k"vjk吋w"ik英c"4"v瑛"o«<
穴陳沈津岫系岻 "噺 "兼件券岶穴張岫捲 検岻 "捲 検" 樺 "系 捲" 塙 "検岼 (3.6) Mjq違pi"eƒej"Jcookpi"e„"#"pij c"swcp"vtqpi"vtqpi"xk羽e"rjƒv"jk羽p"n厩k"x "u穎c"n厩k" vtqpi"o»"j·pj"vtw{隠p"vj»pi"e栄c"Ujcpqp."o瓜v"o«"e„"mjq違pi"eƒeh Hamming v嘘k"vjk吋w dminu胤"e„"mj違"p<pi"rjƒv"jk羽p"v嘘k"8c"*dminÎ3+"n厩k"x "u英c"v嘘k"8c"**dminÎ3+14+"n厩k0"
Không gian mã An x " mjq違pi" eƒej" Jcookpi"dH v衣q" vj pj" mj»pi" ikcp" Ogvtke" Hamming 嫉=( An, dH)0"Ik違"u穎"vc"vtw{隠p"8k"o瓜v"v瑛"o«"c 樺 C."p院w"n厩k"z違{"tc"vt‒p"d dkv."d‒p"pj壱p"u胤"pj壱p"8逢嬰e"eÓx噂k"dH (c,cÓ+?d. P院w"d ø dminÎ1 thì cÓ鞄 C."d‒p"pj壱p"u胤" dk院v"8逢嬰e"e„"n厩k"z違{"tc"vt‒p"8逢運pi"vtw{隠p0
J·pj"3.10"O»"rjぎpi"mjＶ"p<pi"uぬc"nざk"eてc"oじv"o«
Ik違"u穎"C chia không gian mã An thành các v壱r"eqp."o厩k"v壱r"eqpdcq"i欝o"o瓜v"v瑛"o«" c x "eƒe"v瑛"cÓ"ucq"ejq"dH (c,cÓ+"ø"*dminÎ1)/2."vc"f宇"f pi"pj壱p"vj医{"eƒe"v壱r"eqp này không giao nhaụ Pj逢"x壱{"o厩k"v瑛"cÓ"u胤"vjw瓜e"x隠"pjk隠w"pj医v"o瓜v"v壱r"eqp0
Mjk"d‒p"pj壱p"pj壱p"8逢嬰e"cÓ."p院w"vc"ik違"u穎"n厩k"z違{"tc"vt‒p"pjk隠w"pj医v"n "*dminÎ1)/2 bit vj·"v瑛"o«"dcp"8亥w"d‒p"i穎k"i穎k"8k"n "v瑛"o«"fw{"pj医v"e栄c"v壱r"eqp"ej泳c"cÓ.
Swƒ"vt·pj"ik違k"o«"8逢嬰e"8鵜pj"pij c"n "swƒ"vt·pj"mj»k"rj映e"n衣k"v瑛"o«"dcp"8亥w"d‒p"i穎k" i穎k"8k"v瑛"ejw厩k"dkv"o "d‒p"pj壱p"pj壱p"8逢嬰e"x噂k"ik違"8鵜pj n厩k"z違{"tc"vt‒p"pjk隠w"pj医v"n " (dminÎ1)/2 bit.
3.2. Rj逢挨pi"rjƒr"rj¤p"v ej"vj pj"rj亥p"ej pj"*REC+
Vtqpi"eƒe"vj詠e"pijk羽o"mjqc"j丑e"e pi"pj逢"eƒe"vj嘘pi"m‒."eƒe"dk院p"e嘘"swcp"uƒv"8逢嬰e" e„"vj吋"e„"u嘘"ejk隠w"mjƒn噂p."xk羽e"rj¤p"v ej"f英"nk羽w"vt‒p"v壱r"f英"nk羽w"p {"i員r"pjk隠w"mj„" mj<p0 Vw{"pjk‒p."ikƒ"vt鵜"vt‒p"eƒe"ejk隠w"e栄c"eƒe"dk院p"e嘘"p {"vj逢運pi"e„"o嘘k"v逢挨pi" swcp" x噂k" pjcw0 Rj¤p" v ej" vj pj" rj亥p" ej pj" *REC+" n " o瓜v" rj逢挨pi" rjƒr" vqƒp" j丑e" dk院p"8鰻k"o瓜v"v壱r"eƒe"dk院p"e嘘"8c"ejk隠w"ucpi"o瓜v"j羽"vt映e"v丑c"8瓜"vt詠e"ikcq"o噂k"ucq"ejq" ikƒ"vt鵜"vt‒p"eƒe"ejk隠w"n "mj»pi"v逢挨pi"swcp"vw{院p"v pj"x噂k"pjcw."u嘘"ejk隠w"vtqpi"mj»pi" ikcp"o噂k"e„"vj吋 pj臼"j挨p"u嘘"ejk隠w"vtqpi"mj»pi"ikcp"dcp"8亥w. Vtqpi"mj»pi"ikcp"o噂k"
p {" vc" e pi" e„" vj吋" ej丑p" d臼" 8k" o瓜v" x k" vj pj" rj亥p" *ejk隠w+" o " mj»pi" d鵜" o医v" swƒ" pjk隠w"vj»pi"vkp."cj雨"ik英"n衣k"eƒe"vj pj"rj亥p"ej pj."ik¿r"ejq"xk羽e"rj¤p"v ej"f英"nk羽w" 8逢嬰e"f宇"f pi"j挨p0
Rj亥p"p {"u胤"ik噂k"vjk羽w"eƒe"mjƒk"pk羽o"nk‒p"swcp"x "#"pij c"e栄c"rj逢挨pi"rjƒr"REC." mj»pi"8k"u¤w"x q"ejk"vk院v"jk羽p"vj詠e0
3.2.1. Ví d映
A吋"jk吋w"t "j挨p"x隠"#"pij c"e栄c"rj逢挨pi"rjƒr"REC."vc"zgo"zfiv"o瓜v"x "f映"ucw"8¤{. Vc"zfiv"o瓜v"dk院p"e嘘"4"ejk隠w"x噂k"v壱r"ikƒ"vt鵜"swcp"uƒv"8逢嬰e"pj逢"ucw<
x 2.5 0.5 2.2 1.9 3.1 2.3 2 1 1.5 1.1 y 2.4 0.7 2.9 2.2 3.0 2.7 1.6 1.1 1.6 0.9 J·pj"3.2 [13] ucw"dk吋w"fk宇p"v壱r"f英"nk羽w"vt‒p"vtqpi"mj»pi"ikcp"4"ejk隠w
J·pj"3.20"Dkあw"fkいp"fの"nkうw"swcp"uƒv"8⇔ぢe"vtqpi"mj»pi"ikcp"4"ejkｚw
Vc"f宇"f pi"vj医{"t pi"mjk"x v<pi"vj·"y e pi"e„"zw"j逢噂pi"v<pi"x "pi逢嬰e"n衣k."jc{"p„k" cách khác, x và y e„"o嘘k"swcp"j羽"v逢挨pi"swcp"x噂k"pjcw0
Ta ej丑p"i嘘e"v丑c"8瓜"o噂k"n "ikƒ"vt鵜"vtwpi"d·pj"e栄c"v壱r"f英"nk羽w."ucw"8„"zqc{"eƒe"vt映e"v丑c" 8瓜"pj逢"o»"v違"vtqpi"j·pj"x胤"ucw<
J·pj"3.30"Dkあw"fkいp"fの"nkうw"swcp"uƒv"8⇔ぢe"ucw"mjk"vおpj"vkｘp"iぐe"vがc"8じ
Ik違"u穎"vc"ej丑p"eƒe"8逢運pi"vj鰯pi"pfiv"8泳v"n o"j羽"vt映e"v丑c"8瓜"o噂k."v壱r"f英"nk羽w"8逢嬰e" dk吋w"fk宇p"pj逢"j·pj"ucw<
J·pj"3.40"Dkあw"fkいp"fの"nkうw"ucw"mjk"dkｘp"8ごk"vtばe"ikcq
Xk羽e"zƒe"8鵜pj"j羽"vt映e"v丑c"8瓜"o噂k"p {"u胤"8逢嬰e"vt·pj"d {"vtqpi"rj亥p"3.2.3."荏"8¤{"vc" ej雨"ik違"u穎"pj逢"vc"8«"zƒe"8鵜pj"8逢嬰e"j羽"vt映e"v丑c"8瓜"o噂k"p {"x "zgo"zfiv"#"pij c"e栄c" nó.
Vtqpi"j羽"vt映e"v丑c"8瓜"o噂k"p {."vc"vj医{<
‚ Giá tr鵜 cách thành ph亥n x và y không có m嘘k"v逢挨pi"swcp"x噂i nhau ‚ Giá tr鵜 trên tr映c x bi院n thiên nhi隠w"j挨p"ikƒ"vt鵜 trên tr映c ỵ
Rj逢挨pi"rjƒr"REC"8逢嬰e"f́pi"8吋"uw{"ik違o"u嘘"ejk隠w"e栄c"v壱r"f英"nk羽w."P院w"vc"nq衣k"d臼" vj pj"rj亥p"y."vc"e pi"mj»pi"o医v"swƒ"pjk隠w"vj»pi"vkp0"F英"nk羽w"ucw"mjk"nq衣k"d臼"vj pj" rj亥p"y."ucw"8„"dk院p"8鰻k"x隠"j羽"vt映e"v丑c"8瓜"dcp"8亥w"8逢嬰e"dk吋w"fk宇p"vtqpi J·pj"3.5. Ta
vj医{"f英"nk羽w"o噂k"mj»pi"swƒ"mjƒe"*mj»pi"o医v"swƒ"pjk隠w"vj»pi"vkp+"uq"x噂k"v壱r"f英"nk羽w" i嘘e"dcp"8亥w
J·pj"3.50"Fの"nkうw"8⇔ぢe"mj»k"rjつe"ucw"ejえ"ikの"nＴk"vj pj"rjＺp"ej pj
Pj逢"x壱{."ucw"swƒ"vt·pj"dk院p"8鰻k"vt詠e"ikcq"x "nq衣k"d臼"8k"o瓜v"u嘘"vj pj"rj亥p"e„"vt丑pi" u嘘"vj医r."ej雨"ik英"n衣k"pj英pi"vj pj"rj亥p"e„"vt丑pi"u嘘"ecq"*vj pj"rj亥p"ej pj+."vc"e„"8逢嬰e" o瓜v"v壱r"f英"nk羽w"o噂k"x噂k"u嘘"ejk隠w" v"j挨p"u嘘"ejk隠w"dcp"8亥w"o "mj»pi"o医v"swƒ"pjk隠w" vj»pi"vkp."ik¿r"ejq"xk羽e"rj¤p"v ej"f英"nk羽w"8逢嬰e"f宇"f pi"j挨p0
Rj亥p"ucw"u胤"vt·pj"d {"eƒe"d逢噂e"e映"vj吋"e栄c"rj逢挨pi"rjƒr"REC
3.2.2. Vector riêng và tr鵜 riêng
峙に ぬに な峩 抜 峙なぬ峩 噺 峙ななの 峩 (3.7)
峙に ぬに な峩 抜 峙ぬに峩 噺 峙なにぱ 峩 噺 ね 抜 峙ぬに峩 (3.8)
Vtqpi" x " f映" *509+" vc" vj医{" m院v" sw違" e栄c" rjfir" pj¤p" oc" vt壱p" mj»pi" rj違k" n " d瓜k" e栄c" xgevqt"dcp"8亥w0"Pi逢嬰e"n衣k."vtqpi"x "f映"*50:+"vc"vj医{"m院v"sw違"rjfir"pj¤p"n "d瓜k"e栄c" xgevqt"dcp"8亥w. Vector 峙ぬに峩 8逢嬰e"i丑k"n "o瓜v"xgevqt"tk‒pi"(eigen vector) e栄c"oc"vt壱p" x "6"n "vt鵜"tk‒pi"(eigen value) v逢挨pi"泳pi0
A鵜pj"pij c"3.4:
v là vector riêng c栄a ma trân A n院u và ch雨 n院u 畦 抜 懸 噺 潔 抜 懸 潔 樺 温 c n "ikƒ"vt鵜"tk‒pi"v逢挨pi"泳pi"x噂k"vector v
V pj"ej医v<
‚ Ch雨 có ma tr壱n vuông m噂i có vector riêng và không ph違i m丑i ma tr壱n vuông 8隠u có vector riêng.
‚ N院u m瓜t ma tr壱n vuông n×n có vector riêng thì nó có n vector riêng.
‚ N院u v là m瓜t vector riêng thì c×v (c樺温+"e pi"n "o瓜t vector riêng có cùng tr鵜 riêng v噂i c.
‚ Các vector riêng tr詠c giao v噂i nhaụ
Xk羽e"vjc{"8鰻k"8瓜"f k"*mj»pi"vjc{"8鰻k"j逢噂pi+"e栄c"o瓜v"xgevqt"mj»pi"n o"違pj"j逢荏pi" 8院p"v pj"ej医v"Ðxgevqt"tk‒piÑ"e栄c"p„."vtqpi"vqƒp"j丑ẹ"vc"vj逢運pi"n o"xk羽e"x噂k"xgevqt" riêng e„"8瓜"f k"n "3."i丑k"n "Ðxgevqt"tk‒pi"ejw育p"j„cÑjc{"Ðxgevqt"tk‒pi"8挨p"x鵜Ñ.
X "f映."xgevqt"tk‒pi"8挨p"x鵜"v逢挨pi"泳pi"x噂k峙ぬに峩 là 琴 欽 欽 欣ぬ斑ヂなぬ に ヂなぬ 斑 筋 禽 禽 禁 .
Xk羽e"v·o"xgevqt"tk‒pi"8嘘k"x噂k"eƒe"oc"vt¤p"e„"m pj"vj逢噂e"n噂p"*n噂p"j挨p"5×5+"8”k"j臼i nhi隠u tính toán ph泳c t衣p [13]. Lu壱p"x<p"p {"u胤 mj»pi"vt·pj"d {"rj逢挨pi"rjƒr"v·o" vector riêng. Trong th詠c t院 có r医t nhi隠w"vj逢"xk羽n có th吋 giúp ta làm vi羽c nàỵ
3.2.3. Rj逢挨pi"rjƒr"REC
Rj亥p"p {"u胤"vt·pj"d {"eƒe"d逢噂e"e栄c"rj逢挨pi"rjƒr"REC0
Ik違"u穎"vc"e„"v壱r"f英"nk羽w"n ejk隠w8逢嬰e"dk吋w"fk宇p"d荏k"*x1, x2,..., xn). D逢噂e"3<V pj"ikƒ"vt鵜"m "x丑pi"x "oc"vt壱p"jk羽rrj逢挨pi"uck
捲違 噺 岫捲違怠 捲違態 捲違津岻 (3.9) 潔剣懸 噺 頒 潔剣懸岫捲違怠 捲違怠岻 潔剣懸岫捲違怠 捲違態岻 潔剣懸岫捲違怠 捲違津岻 潔剣懸岫捲違態 捲違怠岻 潔剣懸岫捲違態 捲違態岻 潔剣懸岫捲違態 捲違津岻 教 教 狂 教 潔剣懸岫捲違津 捲違怠岻 潔剣懸岫捲違津 捲違態岻 潔剣懸岫捲違津 捲違津岻 番 (3.10)
Ikƒ"vt鵜"m "x丑pi"x "oc"vt壱p"jk羽r"rj逢挨pi"uck"v逢挨pi"泳pi"x噂k"f英"nk羽w"vtqpi"rj亥p"3.2.1 là:
捲違 噺 岫な ぱな な ひな岻
潔剣懸 噺 峙ど はなはのののののののののののの ど はなのねねねねねねねねねねねねど はなのねねねねねねねねねねねね ど ばなはのののののののののののば峩
D逢噂e"2: Tính các vector riêng 8挨p"x鵜"x "vt鵜"tk‒pi"v逢挨pi"泳pi e栄c"oc"vt壱p"cov."u逸r" z院r"eƒe"vt鵜"tk‒pi"x "xgevqt"tk‒pi"vjgq"vj泳"v詠"ik違o"f亥p"e栄c"vt鵜"tk‒pị"dk吋w"fk宇p"eƒe" xgevqt" tk‒pi" f逢噂k" f衣pi" e瓜v." ijfir" eƒe" xgevqt" tk‒pi" n衣k" vc" 8逢嬰e" oc" vt壱p" eƒe" xgevqt" riêng.
結件訣結券懸欠健憲結嫌 噺 岫結懸欠健怠 結懸欠健態 結懸欠健津岻 (3.11)
Pj逢"8«"vt·pj"d {"vtqpi"rj亥p"3.2.2, các vector viêng n {"vt詠e"ikcq"x噂k"pjcw."pj逢pi" swcp"vt丑pi"j挨p."p„"ejq"vc"vj医{"eƒe"vj pj"rj亥p"e栄c"f英"nk羽w"vjw"vj壱r"8逢嬰e0 O厩k"o瓜v" xgevqt"tk‒pi"v逢挨pi"泳pi"x噂k"o瓜v"vj pj"rj亥p."xgevqt"tk‒pi"e„"vt鵜"tk‒pi"e pi"n噂p."vj pj" rj亥p"8„"e pi"ej泳"pjk隠w"vj»pi"vkp0
Oc"vt壱p"xgevqt"tk‒pi"v逢挨pi"泳pi"x噂k"f英"nk羽w"x "f映"vtqpi"rj亥p"3.2.1 pj逢"ucw:
結件訣結券懸欠健憲結嫌 噺 岫な にぱねどにばばな ど どねひどぱぬぬひぱひ岻
結件訣結券懸結潔建剣堅嫌 噺 峙伐ど はばばぱばぬぬひひ 伐ど ばぬのなばぱはのは伐ど ばぬのなばぱはのは ど はばばぱばぬぬひひ 峩
D逢噂e"5<Ej丑p"o瓜v"u嘘"vj pj"rj亥p"ej pj."u嘘"n逢嬰pi"vj pj"rj亥p"u胤 n "u嘘"ejk隠w"e栄c"f英" nk羽w"ucw"rj¤p"v ej"REC."v́{"vjw瓜e"x q"{‒w"e亥w"e栄c"泳pi"f映pị"vc"u胤"ej丑p"u嘘"n逢嬰pi" vj pj"rj亥p"rj́"j嬰r0"Eƒe"vj pj"rj亥p"ej pj"n "eƒe"vj pj"rj亥p"e„"vt鵜"tk‒pi"n噂p"pj医v0 Ik違"u穎"vtqpi"x "f映"vt‒p."vc"ej丑p"o瓜v"vj pj"rj亥p"ej pj
系 噺 峙伐ど はばばぱばぬぬひひ伐ど ばぬのなばぱはのは峩 D逢噂e"6<Dk院p"8鰻k"f英"nk羽w
V噂i m瓜t giá tr鵜swcp"uƒv"8逢嬰c 捲 噺 岷捲怠 捲津峅
Vc"dk院p"8鰻k"vj pj: 捲賦 噺 "系 抜 岫捲 伐 捲違岻 (3.13) Vc"e„"vj吋"vj詠e"jk羽p"rj¤p"v ej"f英"nk羽w"vt‒p"ikƒ"vt鵜"ucw"mjk"8«"dk院p"8鰻k"捲賦 jq員e"dk院p"8鰻k" x隠"j羽"vt映e"v丑c"8瓜"dcp"8亥w"pj逢"d逢噂e"7
D逢噂e"7<"Dk院p"8鰻k"f英"nk羽w"x隠"j羽"vt映e"v丑c"8瓜"dcp"8亥w
Vtqpi"8„"系貸怠 n "oc"vt壱p"pij鵜ej"8違q"e栄c"oc"vt壱p"C0"P院w"C = eigenvector thì C-1=CT *oc"vt壱p"ejw{吋p"x鵜"e栄c"C). Ta có:
捲葡 噺 岫系脹 抜 捲賦岻 髪 捲違 (3.15)
Vtqpi"x "f映"荏"rj亥p"3.2.1."ik違"u穎"vc"ej丑p"3"vj pj"rj亥p"ej pj."J·pj"3.5 o»"v違"f英"nk羽w" ucw"mjk"rj映e"j欝k.
Vc"vj医{"f英"nk羽w"ucw"mjk rj映e"j欝k"p茨o"ej pj"zƒe"vt‒p"o瓜v"8逢運pi"vj鰯pị"u嘘"ejk隠w"e栄c" f英"nk羽w"8«"uw{"ik違o"zw嘘pi"e”p"3"ejk隠w0
3.3. Vjw壱v"vqƒp"pj壱p"fk羽p"i逢挨pi"o員v"Gkigphcegu
Vjw壱v"vqƒp"Gkigphcegu"f詠c"vt‒p"rj逢挨pi"rjƒr"rj¤p"v ej"vj pj"rj亥p"ej pj"*REC+"pj逢" 8«"vt·pj"d {"vtqpi"rj亥p"3.2 8吋"dk院p"8鰻k"j·pj"違pj"i逢挨pi"o員v"vj pj"o瓜v"xgevqt"8員e" vt逢pi0"Xk羽e"pj壱p"fk羽p"i逢挨pi"o員v"8逢嬰e"vj詠e"jk羽p"f詠c"vt‒p"rjfir"uq"uƒpj"eƒe"xgevqt" 8員e"vt逢pi"p {0 J·pj"3.6 o»"v違"eƒe"ikck"8q衣p"e栄c"o瓜v"j羽"vj嘘pi"pj壱p"fk羽p"i逢挨pi"o員v" dùng Eigenfaces.
J·pj"3.6. Sw{"vt·pj"pjｆp"fkうp"i⇔￢pi"oｐv"f́pi"Gkigphcegu
Ik違"u穎<
‚ M厩i 違pj"i逢挨pi"o員v"e„"m ej"vj逢噂c W×H pixels, ta có th吋 xem m厩i b泳c 違nh pj逢"o瓜v"8k吋m d英 li羽u trong không gian W×H chi隠ụ
‚ Ta mu嘘n bi院p"8鰻i m厩i b泳c 違pj"i逢挨pi"o員v"vj pj"xgevqt"8員e"vt逢pi"e„"N chi隠u Vjw壱v"vqƒp"Gkigphcegu"i欝o"eƒe"d逢噂e"pj逢"ucw<
D逢噂e"3"Î Jw医p"nw{羽p<"V瑛"o瓜v"v壱r"eƒe"d泳e"違pj"i逢挨pi"o員v"o磯w."vc"vj詠e"jk羽p"eƒe" d逢噂e"3."4"x "5"e栄c"swƒ"vt·pj"rj¤p"v ej"REC"pj逢"o»"v違"vtqpi"rj亥p 3.2.30"M院v"sw違" d逢噂e"p {"vc"e„"8逢嬰e"oc"vt壱p"C i欝o"N xgevqt"tk‒pi"x噂k"eƒe"vt鵜"tk‒pi"v逢挨pi"泳pi"n噂p" pj医v"x "ikƒ"vt鵜"vtwpi"d·pj"捲違 e栄c"v壱r"f英"nk羽w"o磯w. (Các vector riêni"p {"mjk"dk院p"8鰻k"
PCA C, 捲違 PCA ve1,...v PCA v dmin < T Ej医r" pj壱p ej嘘kV瑛" JwＸp"nw{うp A<pi"m# Mkあo tra
x隠"f衣pi"違pj"W×H rkzgnu"u胤"e„"j·pj"f衣pi"v瑛c"v詠c"pj逢"o瓜v"i逢挨pi"o員v."8„"n "n#"fq"x·" ucq"ik違k"vjw壱v"e„"v‒p"n "Gkigphceg+
J·pj"3.70"X "fつ"xｚ"gkigphceg
D逢噂e"4"Î A<pi"m#< Swƒ"vt·pj"8<pi"m#"e栄c"pi逢運k"f́pi"8逢嬰e"vj詠e"jk羽p"d茨pi"eƒej" ej映r"o瓜v"u嘘"違pj"i逢挨pi"o員v"e„"m ej"vj逢噂e"W×H *p院w"違pj"e„"m ej"vj逢噂e"mjƒẹ"vc" rj違k"eq"ik«p"違pj"x隠"8¿pi"W×H pixels)0"Vj詠e"jk羽p"d逢噂e"6"e栄c"swƒ"vt·pj"rj¤p"v ej" REC"pj逢"o»"v違"vtqpi"rj亥p"3.2.3."vc"dk院p"8鰻k"o厩k"d泳e"違pj"i逢挨pi"o員v"pi逢運k"f́pi" vj pj"o瓜v"xgevqt"8員e"vt逢ng có N ejk隠w"vjgq"e»pi"vj泳e"*5035+"x "n逢w"n衣k"eƒe"xgevqt" 8員e"vt逢pi"p {0Vc"i丑k"eƒe"xgevqt"8員e"vt逢pi"p {"là ve1, ve2,...vek.
D逢噂e"5"Î Zƒe"vj詠e: J羽"vj嘘pi"ej映r"違pj"i逢挨pi"o員v"e栄c"pi逢運k"f́pị"dk院p"8鰻k"違pj" i逢挨pi"o員v"vj pj"xgevqt"8員e"vt逢pi"vjgq"e»pi"vj泳e"*5035+ v逢挨pi"v詠"pj逢"d逢噂e"8<pi" ký. Vc"i丑k"xgevqt"8員e"vt逢pi"p {"n "vv. Xgevqt"8員e"vt逢pi"n¿e"zƒe"vj詠e"8逢嬰e"uq"uƒpj" x噂k"eƒe"xgevqt"8員e"vt逢pi"n¿e"8<pi"m# d茨pi"eƒej"v pj"mjq違pi"eƒej"Gwenkf."mjq違pi" eƒej"Gwenkf"ik英c"4"xgevqt"8員e"vt逢pi"x và y 8逢嬰e"8鵜pj"pij c"pj逢"ucw0
押捲 伐 検押態 噺 蕃布岫捲沈 伐 検沈岻態 朝 沈退怠 否 怠 態 (3.16) Vc"v pj"mjq違pi"eƒej"Gwenkf"ik英c"xgevqt"8員e"vt逢pi"n¿e"zƒe"vj詠e"x噂k"eƒe"xgevqt"8員e" vt逢pi"n¿e"8<pi"m#< 穴陳沈津 噺 ŒÆº 沈退怠 賃岫押懸懸 伐 懸結沈押態岻 (3.17)
P院w"dmin < T *o瓜v"ikƒ"vt鵜"pi逢叡pi"ejq"vt逢噂e+"swƒ"vt·pj"zƒe"vj詠e"vj pj"e»pị"pi逢運k" f́pi"8逢嬰e"ej壱r"pj壱p="pi逢嬰e"n衣k."swƒ"vt·pj"zƒe"vj詠e"vj医v"d衣k."pi逢運k"f́pi"d鵜"v瑛"ej嘘k0
3.4. Eƒe" mjƒk" pk羽o" ÐOkp" Gpvtqr{Ñ." ÐUgewtg" UmgvejÑ." ÐHw¦¦{"GzvtcevqtÑ GzvtcevqtÑ
Rj亥p" p {" u胤" vt·pj" d {" eƒe" mjƒk" pk羽o" 8逢嬰e" ik噂k" vjk羽w" vtqpi" [0Fqfku"[4] 8逢嬰e" u穎" f映pi"vt詠e"vk院r"vtqpi"nw壱p"x<p0
3.4.1. Entropy t嘘i thi吋u
Vtqpi"n#"vjw{院v"vj»pi"vkp."ÐentropyÑ l "mjƒk"pk羽o"f́pi"8吋"8q"o泳e"8瓜"j厩p"nq衣p"e栄c" vj»pi"vkp"n医{"v瑛"o瓜v"u詠"mk羽p"pi磯w"pjk‒p0"P„k"eƒej"mjƒẹ"gpvtqr{"e pi"ej雨"tc"e„"dcq" pjk‒w"vj»pi"vkp"vtqpi"v p"jk羽w."x噂k"vj»pi"vkp"n "eƒe"rj亥p"mj»pi"j厩p"nq衣p"pi磯w"pjk‒p" e栄c"v p"jk羽w0Gpvtqr{"8逢嬰e"8鵜pj"pij c"d荏k"Encwfg"G0"Ujcppqp"pj逢"ucw<
茎岫隙岻 噺 布 喧岫件岻 Øæ̌態喧岫件岻
津 沈退怠
(3.18)
Vtqpi"8„"X là m瓜t phân b嘘 ng磯u nhiên, 喧岫件岻 n "zƒe"zw医v"dk院p"e嘘"X pj壱p" ikƒ"vt鵜"xi.
Vw{"pjk‒p"vtqpi"eƒe"泳pi"f映pi"d違q"o壱v."vc"swcp"v¤o"8院p"mj違"p<pi"m飲"v医p"e»pi"e„"vj吋" 8qƒp"8逢嬰e"o瓜v"vj pj"rj亥p"d "o壱v"p q"8„0"Vj»pi"vj逢運pị"m飲"v医p"e»pi"u胤"vj穎"pj英pi"
ikƒ"vt鵜"e„"zƒe"zw医v"z違{"tc"ecq"pj医v0"X "f映."vtqpi"o瓜v"j羽"vj嘘pi"d違q"o壱v"f́pi"o壱v" mj育w."m飲"v医p"e»pi"u胤"vj穎"o壱v"mj育w"p q"vj逢運pi"8逢嬰e"f́pi"pj医v0"Mjƒk"pk羽o"Ðentropy v嘘k"vjk吋wÑ (min entropy - m#"jk羽w"n "茎著) [4] 8逢嬰e"8鵜pj"pij c"pj茨o"8ƒpj"ikƒ"o泳e"8瓜" bí o壱v"e栄c"j羽"vj嘘pi"vtqpi"vt逢運pi"j嬰r"p {0 A鵜pj"pij c"3.5: 茎著岫激岻 噺 伐 Øæ̌ 岾Œ̇® 栂 鶏堅岫激 噺 拳岻峇 (3.19) 茎著 e pi"n噂p"vj·"mj違"p<pi"vj pj"e»pi"e栄c"m飲"v医p"e»pi"mjk"vj穎"x噂k"ikƒ"vt鵜"rj鰻"dk院p" pj医v"u胤"e pi"vj医r0
3.4.2. Entropy t嘘i thi吋u trung bình
Vtqpi"vj詠e"v院."mjk"v医p"e»pi"x q"o瓜v"j羽"vj嘘pi"p q"8„."m飲"v医p"e»pi"e„"vj吋"dk院v"vt逢噂e" o瓜v"u嘘"vj»pi"vkp0"Mjƒk"pk羽o"Ðgpvtqr{"v嘘k"vjk吋w"vtwpi"d·pjÑ"(average min entropy Î m#" jk羽w" n "茎風著岻"8ƒpj" ikƒ" 8瓜" d " o壱v" e栄c" j羽" vj嘘pi" mjk" m飲" v医p" e»pi" dk院v" vt逢噂e" o瓜v" vj»pi"vkp"p q"8„. A鵜pj"pij c"3.6: 茎風著岫畦 稽岻 玩 伐 Øæ̌ 岾 順 長華喋峙Œ̇® 銚華凋 鶏堅岫畦 噺 欠 稽 噺 決岻峩峇 噺 Øæ̌ 岾 順 長華喋範に貸張屯岫凋 喋退長岻飯峇 (3.20) 3.4.3. Kho違pi"eƒej"v pj Mjq違pi"eƒej"v pj"n "mjƒk"pk羽o"f́pi"8吋"8ƒpj"ikƒ"u詠"mjƒe"pjcw"e栄c"4"rj¤p"d嘘"pi磯w" nhiên. A鵜pj"pij c"3.7:
鯨経岫畦 稽岻 噺なに布 2ø岫畦 噺 懸岻 伐 2ø"岫稽 噺 懸岻 塚 (3.21) Vj»pi"vj逢運pị"vc"f́pi"mjq違pi"eƒej"v pj"8吋"uq"uƒpj"o瓜v"rj¤p"d嘘"pi磯w"pjk‒p"ejq" vt逢噂e"x噂k"rj¤p"d嘘"8隠w"pj茨o"8ƒpj"ikƒ"o泳e"8瓜"8隠w"e栄c"rj¤p"d嘘"pi磯w"pjk‒p"8«"ejq0 3.4.4. Hàm Trích xu医t
Cho m瓜t hàm 継捲建 岶ど な岼津 蝦 岶ど な岼鎮 n "o瓜v"j o"vt ej"zw医v"ejw厩k"l dkv"v瑛"o瓜v"ejw厩k"n bit. Hàm Ext e„"u泳e"o衣pj"*n,m,l,姦+"mjk"x噂k"o丑k"rj¤p"d嘘"W trên 岶ど な岼津 có entropy v嘘k"vjk吋w"m vj·"ejw厩k"vt ej"zw医v"8逢嬰e"e„"ejk隠w"f k"l và
鯨経岫岫継捲建岫激 隙岻 隙岻 岫戟鎮 隙岻岻 判樺 (3.22)
Vtqpi"8„<"Ul n "rj¤p"d嘘"8隠w trên 岶ど な岼津, X n "rj¤p"d嘘"pi磯w"pjk‒p"vt‒p" 岶ど な岼追
Hàm trích xu医v"e„"8瓜 m衣nh (n,m,l,姦) có th吋 trích xu医v"8逢嬰c 健 噺 兼 伐 に Øæ̌怠樺髪 頚岫な岻 dkv"i亥p"pj逢"pi磯w"pjk‒p0 E„"pjk隠w"j o"vt ej"zw医v"vj臼c"o«p"8k隠w"mk羽p"p {."eƒe"j o" vt ej"zw医v"vj逢運pi"rj泳e"v衣r"fq"ej¿pi"v嘘k"逢w"vjgq"ejk隠w"j逢噂pi"ik違o"ejk隠w"f k"e栄c"X [4, pp. 8-9]. 雲"8¤{."ej¿pi"vc"mj»pi"swcp"vt丑pi"ejk隠w"f k"e栄c"Z0"J o"d<o"rj鰻"swƒv" (upkxgtukcn"jcuj"hwpevkqp+"n "o瓜v"j o"vt ej"zw医v"vj臼c"8k隠w"mk羽p<
健 噺 兼 伐 に 健剣訣樺怠髪 に (3.23)
J o"d<o"rj鰻"swƒv"n "o瓜v"j o"茎掴 岶ど な岼津 蝦 岶ど な岼鎮 vj臼c"8k隠w"mk羽p
褐欠 塙 決 樺 岶ど な岼津 鶏堅盤茎掴岫欠岻 噺 茎掴岫決岻匪 噺 に貸鎮 (3.24)
3.4.5. Secure Sketch
ÐUgewtg"UmgvejÑ"8逢嬰e"jk吋w"n "p挨k"e医v"ik英"o瓜v"vj»pi"vkp"d "o壱v."vw{"pjk‒p."d "o壱v" mj»pi"vj壱v"u詠"8逢嬰e"n逢w"ik英."vjc{"x q"8„"ÐUgewtg"UmgvejÑ"ewpi"e医r"o瓜v"e挨"ej院"8吋"
rj映e"j欝k"n衣k"vj»pi"vkp"d "o壱v"mjk pj壱p"8逢嬰e"vj»pi"vkp"zƒe"vj詠e"v瑛"o瓜v"pi逢運k"f́pi" j嬰r"n羽0J·pj"3.8 o»"v違"ej泳e"p<pi"e栄c"o瓜v"ÐUgewtg"UmgvejÑ
J·pj"3.8. Secure Sketch
O瓜v"ÐUgewtg"UmgvejÑ"n "o瓜v"ik違k"vjw壱v"8吋"d違q"x羽"x "rj映e"j欝k"o瓜v"vj»pi"vkp"d "o壱v" và ch医r"pj壱p"pjk宇w."vj逢運pi"n "o瓜v"8員e"vt逢pi"ukpj"vt逸e"j丑e"p q"8„."i欝o"4"swƒ"vt·pj<
‚ B違o v羽: tính 嫌 噺 鯨鯨岫拳岻, s s胤8逢嬰e"n逢w"n衣k"x "zgo"pj逢"n "f英 li羽u công khai, s 8吋 l瓜 r医t ít thông tin v隠 w, khi s b鵜 l瓜 thì tính bí m壱t c栄a h羽 th嘘ng v磯p"8逢嬰c 8違m b違ọ
‚ Ph映c h欝i: tính 拳 噺 迎結潔岫拳嫗 嫌岻, n院u yÓ g亥n gi嘘ng v噂i w dcp"8亥u (w và yÓ là các m磯u sinh tr逸c h丑e"8q"8逢嬰c trên cùng m瓜v"8嘘k"v逢嬰ng), thì d英 li羽u sinh ra c栄a hàm Rec s胤 gi嘘ng chính xác v噂i w dcp"8亥ụ
A鵜pj"pij c"3.8: O瓜v"ÐUgewtg"UmgvejÑ"e„"8瓜"o衣pj"岫嫉 兼 兼蕪 建岻 n "o瓜v"e員r"4"j o" pi磯w"pjk‒p"SS và Rec ‚ 鯨鯨 嫉 蝦 岫ど な岻茅 拳 蝦 嫌 噺 鯨鯨岫拳岻 (3.25) ‚ 迎結潔 嫉 抜 岫ど な岻茅蝦 嫉 岫拳嫗 嫌岻 蝦 迎結潔岫拳嫗 嫌岻 sao cho n院u 穴件嫌岫拳 拳嫗岻 判 建 thì 迎結潔盤拳嫗 鯨鯨岫拳岻匪 噺 拳 (3.26) ‚ Tính bí m壱t c栄a h羽 th嘘ng ph違k"8逢嬰c b違q"8違m. V噂i m丑i phân b嘘 W trên 嫉, v噂i entropy t嘘i thi吋u là m, n院u k飲 t医n công n院u bi院v"8逢嬰c s, thì kh違p<pi"8qƒp" 8逢嬰c giá tr鵜dcp"8亥u c栄a W t嘘k"8c"là に貸陳蕪. Hay nói cách khác
3.4.6. Fuzzy Extractor
V逢挨pi"v詠"pj逢"ÐUgewtg"UmgvejÑ."ÐFuzzy ExtractorÑe pi"e„"vj吋"8逢嬰e"jk吋w"n "p挨k"e医v" ik英"o瓜v"d "o壱v"d茨pi"o瓜v"o磯w"ukpj"vt逸e"j丑ẹ"d "o壱v"p {"e„"vj吋"n "mj„c"f́pi"ejq"xk羽e" o«"j„c"f英"nk羽w."x "ejq"rjfir"rj映e"j欝k"n衣k"d "o壱v"p {"p院w"pj壱p"8逢嬰e"o瓜v"o磯w sinh vt逸e"j丑e"i亥p"ik嘘pi"x噂k"o磯w"8員e"vt逢pi"ukpj"vt逸e"j丑e"8«"8逢嬰e"f́pi"8吋"d違q"x羽0 J·pj" 3.9 o»"v違"ej泳e"p<pi"e栄c"o瓜v"ÐFuzzy ExtractorÑ0"O瓜v"ÐHw¦¦{"GzvtcevqtÑ"pj壱p"x q" o瓜v"o磯wukpj"vt逸e"j丑ẹ"ukpj"tc"4"vj pj"rj亥p."o瓜v"d "o壱v."o瓜v"e»pi"mjck="ucw"8„"ejq" rjfir"rj映e"j欝k"vj pj"rj亥p"d "o壱v"v瑛vj pj"rj亥p"e»pi"mjck"x "o瓜v"o磯w ukpj"vt逸e"j丑e" i亥p"ik嘘pi"x噂k"o磯w"ukpj"vt逸e"j丑e"dcp"8亥w0
J·pj"3.9. Fuzzy Extractor
A鵜pj"pij c"3.9: O瓜v"ÐHw¦¦{"GzvtcevqtÑ"e„ 8瓜 m衣nh 岫嫉 兼 健 建 香岻n "o瓜v"e員r"4"j o" pi磯w"pjk‒p"Gen và Rep vj臼c"8k隠w"mk羽p<
‚ 罫結券 嫉 蝦 岶ど な岼鎮抜 岶ど な岼茅
拳 蝦 岫迎 鶏岻 噺 罫結券岫拳岻 (3.28)
R là thành ph亥n bí m壱t, có th吋 8逢嬰c dùng làm khóa cho các gi違i thu壱t mã hóa, P là thành ph亥n công khaị
‚ 迎結喧 嫉 抜 岶ど な岼茅 蝦 岶ど な岼鎮
岫拳嫗 鶏岻 蝦 迎 噺 迎結喧岫拳嫗 鶏岻
Hàm Rep ph違i b違q" 8違m tính ch鵜u nhi宇w." pij c" n " p院u 穴件嫌岫拳 拳嫗岻 判 建 và
‚ Tính bí m壱t c栄a h羽 th嘘ng ph違k"8逢嬰c b違q"8違m. V噂i m丑i phân b嘘 W trên 嫉, v噂i entropy t嘘i thi吋u là m, chu厩i R có phân b嘘 g亥p"8隠u cho dù k飲 t医n công có bi院v"8逢嬰c P, pij c"n
鯨経盤岫迎 鶏岻 岫戟鎮 鶏岻匪 判 香 (3.30)
J·pj"3.10 o»"v違"o瓜v"泳pi"f映pi"e栄c"ÐHw¦¦{"GzvtcevqtÑ"vtqpi"xk羽e"o«"j„c"f英"nk羽w" f́pi"8員e"vt逢pi"ukpj"vt逸e"j丑e0"O磯w"ukpj"vt逸e"j丑e"e栄c"pi逢運k"f́pi"8逢嬰e"f́pi"8吋"ukpj" ra khóa o«"j„c"f英"nk羽w0"F英"nk羽w"8«"8逢嬰e"o«"j„c"p {"ej雨"e„"vj吋"8逢嬰e"ik違k"o«"mjk"e„" u詠"jk羽p"fk羽p"e栄c"pi逢運k"f́pi"j嬰r"n羽0
J·pj"3.100"でpi"fつpi"eてc"Hw¦¦{"Gzvtcevqt
Vc" e„" vj吋" z¤{" f詠pi" o瓜v" ÐHw¦¦{" GzvtcevqtÑ" v瑛" o瓜v" ÐUgewtg" UmgvejÑ" x " o瓜v" j o" vt ej"zw医v"*pj逢"o»"v違"vtqpi"rj亥p"3.4.4), J·pj"3.11 o»"v違"eƒej"z¤{"f詠pi"p {0
J·pj"3.110"Z¤{"fばpi"Hw¦¦{"Gzvtcevqt"vな"Ugewtg"Umgvej"x "j o"vt ej"zwＸv
Hàm Gen: A亥w"vk‒p"vc"ƒr"f映pi"j o"SS e栄c"ÐUgewtg"UmgvejÑ"vt‒p"o磯w"f英"nk羽w"ukpj" vt逸e"j丑e"vjw"vj壱r"8逢嬰e"w 8吋"ukpj"tc"s. Scw"8„."vc ƒr"f映pi"j o"vt ej"zw医v"Ext trên w x "o瓜v"ejw厩k"pi磯w"pjk‒p"x 8吋"ukpj"tc"vj pj"rj亥p"d "o壱v"R."vj pj"rj亥p"e»pi"mjck"dcq" i欝o"x và s.
Hàm Rep: Vc"ƒr"f映pi"j o"Rec c栄c"ÐUgewtg"UmgevjÑ"vt‒p"o磯u d英 li羽u sinh tr逸c h丑c thu th壱r"8逢嬰c wÓ"x "s 8吋 sinh ra w0"Ucw"8„."vc"ƒr"f映ng hàm trích xu医t Ext trên w và x 8吋 sinh ra R. Hàm này b違q"8違m n院u 穴件嫌岫拳 拳岻 判 建 thì R ukpj"tc"ej pj"zƒe"d茨pi"R dcp"8亥w0
X噂k" eƒej" z¤{" f詠pi" vt‒p." p院w" ÐUgewtg" UmgvejÑ" e„" 8瓜" o衣pj"岫嫉 兼 兼蕪 建岻 và hàm trích xu医t Ext e„"8瓜 m衣nh 岫券 兼蕪 健 香岻 vj·"ÐHw¦¦{"GzvtcevqtÑ xây d詠pi"8逢嬰e"e„"8瓜 m衣nh 岫嫉 兼 健 建 香岻
Fq"vc"e„"vj吋"z¤{"f詠pi"ÐHw¦¦{"GzvtcevqtÑ"f詠c"vt‒p"ÐUgewtg"UmgvejÑ"p‒p"p瓜k"fwpi" nw壱p" x<p" u胤" v壱r" vtwpi" x q" ÐUgewtg" UmgvejÑ." 8隠" zw医v" rj逢挨pi" rjƒr" 8吋" z¤{" f詠pi" ÐUgewtg"UmgvejÑ"f詠c"vt‒p"o瓜v"8員e"vt逢pi"ukpj"vt逸e"j丑e"e映"vj吋0
Ej逢挨pi"60 Rj逢挨pi"rjƒr"Ugewtg"Umgvej"ejq"f英" nk羽w"違pj"i逢挨pi"o員v
4.1. Ik噂k"vjk羽w
Pj逢"8«"vt·pj"d {"vtqpi"rj亥p"3.2 và 3.3."vc"e„"vj吋"ƒr"f映pi"rj逢挨pi"rjƒr"rj¤p"v ej" vj pj" rj亥p" ej pj" x " vjw壱v" vqƒp" Gkigphcegu" 8吋" vt ej zw医v" xgevqt" 8員e" vt逢pi" v瑛" 違pj" i逢挨pi"o員v"e栄c"pi逢運k"f́pi0"Rj亥p"p {"u胤"vt·pj"d {"rj逢挨pi"rjƒr"z¤{"f詠pi"ÐUgewtg" UmgvejÑ"ƒr"f映pi"ejq"xgevqt"8員e"vt逢pi"p {0
4.2. Piw{‒p"n#"z¤{"f詠pi"ÐUgewtg"UmgvejÑ
O映e"8 ej"ej pj"e栄c ÐUgewtg"UmgvejÑ"n "rj映c h欝i l衣i m磯u d英 li羽u sinh tr逸c h丑c ban 8亥u w t瑛 m瓜t m磯u d英 li羽u sinh tr逸c h丑c g亥n gi嘘ng nó yÓ khi 穴件嫌岫拳 拳 岻 判 建0"Vc"vj医{" o«"u穎c"n厩k"*rj亥p"3.1+"8ƒr"泳pi"8逢嬰e"{‒w"e亥w"p {0"Fq"8„."[0Fqfku"[4] 8«"ik噂k"vjk羽w" rj逢挨pi"rjƒr"z¤{"f詠pi"ÐUgewtg"UmgvejÑ"f詠c"vt‒p"o«"u穎c"n厩k."rj逢挨pi"rjƒr"e„"v‒p"n " ÐEqfg"Qhhugv"EqpuvtwevkqpÑ, J·pj"4.1 o»"v違"rj逢挨pi"rjƒr"p {.
J·pj"4.1. Code Offset construction for Secure Sketch
Lý thuy院t mã s穎a l厩i nói r茨ng ta có th吋 ph映c h欝i m瓜t t瑛 mã t瑛 m瓜t t瑛 b医t k cách t瑛 mã không quá 建 噺 岫穴陳沈津伐 な岻 に0"P院w"vc"z¤{"f詠pi"8逢嬰e"o瓜v"o«"u穎c"n厩k ej泳c"w, ta e„"vj吋"rj映e"j欝k"w v瑛"yÓ0"V瑛"o瓜v"o«"u穎c"n厩k"8«"8逢嬰e"z¤{"f詠pi"u印p."vc"f鵜ej"8k"o瓜v" vector s sao chq"o«"o噂k"8逢嬰e"v衣q"tc"ej泳c"w.
‚ Hàm SS:
o Ch丑n ng磯u nhiên 潔 樺 系 (C là m瓜v"o«"8逢嬰c xây d詠ng s印n) o K院t qu違: 嫌 噺 拳 伐 潔 ‚ Hàm Rec: o Nh壱n vào 拳 o 潔旺 噺 拳 伐 嫌 o Gi違i mã 潔, k院t qu違 nh壱p"8逢嬰c 潔 o K院t qu違: 拳 噺 潔 髪 嫌
Rj逢挨pi" rjƒr" p {" 8逢嬰c áp d映ng cho Hamming Metric, tuy nhiên nguyên lý xây d詠ng c栄a nó có th吋8逢嬰c áp d映ng cho các Metric khác0"Rj逢挨pi"rjƒr"o "nw壱p"x<p"8隠 xu医t áp d映pi"piw{‒p"n#"p {"8吋 xây d詠pi"ÐUgewtg"UmgvejÑ"ejq"Taxicab Metric. Ph亥n còn l衣i c栄c"ej逢挨pi"p {"u胤 trình bày chi ti院v"rj逢挨pi"rjƒr"p {0
4.3. Vczkecd"Ogvtke
Kho違ng cách Taxicab gi英c"4"8k吋m trong không gian n chi隠u có th吋 8逢嬰c hi吋u là sw«pi"8逢運pi"8k"pi逸n nh医t gi英c"4"8k吋o"8„"x噂k"8k隠u ki羽n là ch雨 có th吋8k"vjgq"8逢運ng g医p khúc bao g欝o"eƒe"8q衣n th鰯ng song song tr映c t丑c"8瓜. Hay nói cách khác, kho違ng cách Taxicab là t鰻ng sai bi羽t c栄a các thành ph亥n gi英c"4"8k吋o0"A鵜pj"pij c"j·pj"vj泳c cho kho違pi"eƒej"Vczkecd"pj逢"ucw<
A鵜pj"pij c"4.1: Kho違ng cách Taxicab
穴脹岫捲 検岻 噺 布 捲沈伐 検沈
津 沈退怠
(4.1)
Ta ch泳ng minh kho違ng cách Taxicab th臼c"eƒe"8k隠u ki羽n c栄a không gian metric.
o 穴脹岫捲 検岻 半 ど 褐捲 検 樺 警:
褐捲 検 樺 警 捲沈 伐 検沈 半 ど 馨 布 捲沈 伐 検沈
津 沈退怠
o 穴脹岫捲 検岻 噺 穴脹岫検 捲岻 褐捲 検 樺 警: 褐捲 検 樺 警 捲沈 伐 検沈 噺 検沈伐 捲沈 馨 布 捲沈 伐 検沈 津 沈退怠 噺 布 検沈伐 捲沈 津 沈退怠 馨 穴脹岫捲 検岻 噺 穴脹岫検 捲岻 褐捲 検 樺 警 o 穴脹岫捲 検岻 噺 ど 垣 捲 噺 検: 穴脹岫捲 検岻 噺 ど 垣 褐件 捲沈伐 検沈 噺 ど 垣 褐件 捲沈 噺 検沈 垣 捲 噺 検 o 穴脹岫捲 検岻 髪 穴脹岫検 権岻 半 穴脹岫捲 権岻褐捲 検 権 樺 警: V噂i m丑i i=1..n ta có: 捲沈検沈伐 捲沈権沈伐 検沈態髪 検沈権沈 半 捲沈検沈伐 捲沈権沈 伐 検沈態髪 検沈権沈 馨 に 捲沈検沈伐 捲沈権沈伐 検沈態髪 検沈権沈 半 に岫捲沈検沈 伐 捲沈権沈伐 検沈態髪 検沈権沈岻 馨 伐に捲沈検沈 髪 に検沈態伐 に検沈権沈髪 に 捲沈検沈伐 捲沈権沈伐 検沈態髪 検沈権沈 半 伐に捲沈権沈 馨 捲沈態伐 に捲沈検沈髪 検沈態髪 検沈態 伐 に検沈権沈髪 権沈態髪 に 捲沈検沈伐 捲沈権沈伐 検沈態髪 検沈権沈 半 捲沈態伐 に捲沈権沈 髪 権沈態 馨 岫捲沈 伐 検沈岻態髪 岫検沈 伐 権沈岻態髪 に 岫捲沈伐 検沈岻岫検沈伐 権沈岻 半 岫捲沈 伐 権沈岻態 馨 岫 捲沈伐 検沈 髪 検沈伐 権沈 岻態 半 捲沈伐 権沈 態 馨 捲沈 伐 検沈 髪 検沈伐 権沈 半 捲沈 伐 権沈 馨 布 捲沈 伐 検沈 津 沈退怠 髪 布 検沈伐 権沈 津 沈退怠 半 布 捲沈伐 権沈 津 沈退怠 馨 穴脹岫捲 検岻 髪 穴脹岫検 権岻 半 穴脹岫捲 権岻褐捲 検 権 樺 警
Gi違i thu壱t Eigenfaces truy隠n th嘘ng so sánh 2 vector 8員e"vt逢pi"f詠a trên kho違ng cách Euclid."p‒p"vt逢噂c tiên, ta ph違k"8ƒpj"ikƒ"zgo"xk羽c thay th院 kho違ng cách Euclid b茨ng kho違pi"eƒej"Vczkecd"e„"n o"vjc{"8鰻i t益 l羽 l厩i c栄a h羽 th嘘ng hay không. Ta xây d詠ng m瓜t h羽 th嘘ng xác th詠c d詠c" vt‒p" rjfir" uq" uƒpj" vj»pi" vj逢運ng (kj»pi" e„" ÐUgewtg" UmgvejÑ+" 8吋 so sánh t益 l羽 l厩i khi áp d映ng kho違ng cách Euclid và kho違ng cách Taxicab.
J·pj"4.2 th嘘ng kê t益 l羽 l厩i c栄a h羽 th嘘ng xác th詠c dùng kho違ng cách Euclid v噂i các giá tr鵜 pi逢叡ng khác nhau t瑛 k院t qu違 th詠c nghi羽m."xgevqt"8員e"vt逢pi"8逢嬰c trích xu医t
có 24 chi隠ụ K院t qu違 th詠c nghi羽o"8逢嬰c th詠c hi羽n trên e挨"u荏 d英 li羽u 違pj"i逢挨pi"o員t Essex94.
J·pj"4.20"Vぴ"nう"nざk"mjk"f́pi"mjqＶpi"eƒej"Gwenkf
J·pj"4.3 th嘘ng kê t益 l羽 l厩i c栄a h羽 th嘘ng xác th詠c dùng kho違ng cách Taxicab v噂i các giá tr鵜 pi逢叡pi"mjƒe"pjcw."xgevqt"8員e"vt逢pi"8逢嬰c trích xu医t có 24 chi隠w."e挨"u荏 d英