問題発見技法 6．クラスタ分析

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第 3 レベル <= /div>

第 4 レベル <= /div>

第 5 レベル

<日付/時刻>

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file:///C:/72BBA416/06htf_6.files/master51.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

マスタ = 2479;イトルの書式設定

マスタ = 2469;ブタイトルの書式ෑ= 3;定

<日付/時刻>

<フッタ= ー>

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<= /div>

<ヘッダー>

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<日付/時&#= 21051;>

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<フッター>

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<#>

------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

問題= ;発見技法

6．ク= ;ラスタ分析

= 情報学部　堀田敬介

2006年７月４日

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クラ= ;スタ分析

<= span style=3D'mso-fareast-hint:yes'> 3D"*"

= Conten= ts

<= span style=3D'mso-fareast-hint:yes'>1.クラスタ分析= 010;要

<= span style=3D'mso-fareast-hint:yes'>2.類似度の測定

<= span style=3D'mso-fareast-hint:yes'>3.クラスタ間の$= 817;さの決定

<= span style=3D'mso-fareast-hint:yes'>4.クラスタ分析= 398;実施〔SPSS&#= 65292;手計算〕

<= span style=3D'mso-fareast-hint:yes'>5.クラスター分= 512;実施上の注意点

<= span style=3D'mso-fareast-hint:yes'>6.演習：やって= 415;よう！

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1．ク= ;ラスタ分析概要

&#= 12463;ラスタ分析とは？

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<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; mso-fareast-hint:yes'>複数の対象（= 418;の，変数など）を，= ;

類似ò= 30;（similarity）を定義し，

均質な集団（cluster）に分類する

方法の総称

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&#= 12463;ラスタ分析の種類

&#= 38542;層的方法

•樹形= 259;（デンドログラム）= ;を作成

•= 目的によ&#= 12426;高さを決めてクラスタ&#= 12522;ング

1．ク= ;ラスタ分析概要

&#= 38750;階層的方法

•= 予めクラ&#= 12473;タ数を決め

（or決まっていてA= 289;，

クラスタリ&#= 12531;グを行う

<= ![if !ppt]>

類似度

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1．ク= ;ラスタ分析概要

例：

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4<= /div>

5<= /div>

6<= /div>

0<= /div>

どうやって= ;

類似度ʌ= 88;距離）を

測るのか=

例）CとEの類似度？

どうやって= ;

&= #12463;ラスタ間の近さ= を決めるのか

&= #20363;）クラスタ（G,B)とクラ= スタ(D)の近さ？

補足：類߬= 4;度は相関で測る場合&= #12418;ある

（距離：๡= 7;いほうが類似してい&= #12427;）

（相関：ོ= 0;いほうが類似してい&= #12427;）

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7gsKh8QUsIhMKn3HpfMJNQai1Kq107xqt8Qs9wu2ecPksmpsTqtB6LV73X7LyfG5fVu/66n5vX/Z 9yfYNTVoGBV4qJiTuOgo0/gouRI5aWlSeanZUrjpCZP5KRoq6klaqnmKaqm6Ktnq6ggbqzhLa2h7 K5ir68fbq/cLbCc8LFds7IacrLbMbOb8TNcpPUpdbXqNnaq9zdrt/QoeLjtOXouRrr7O3u7+HlEA ADs= ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0053.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

2．類= ;似度の測定

距離，間隔尺= 230;

= ユークリӠ= 3;ド距離

= ユークリӠ= 3;ド平方距離

= 重み付きӣ= 8;ークリッド距離

= マンハッӟ= 9;ン距離

= ミンコフӟ= 3;キー距離

= マハラノӡ= 9;ス汎距離

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:71%;mso-fareast-hint:yes'>相関，間隔尺= 230;

Pearsonの積率相໶= 6;係数

= ベクトルࠦ= 9;積

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:71%;mso-fareast-hint:yes'>相関，順序尺= 度

= Spearmanの順位&= #30456;関係数

= Kendallの順位&= #30456;関係数 <= /div>

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:71%;mso-fareast-hint:yes'>距離，名義尺&#= 24230; [0, 1]

= 類似比

= 一致係数

Russel-Rao係数

Rogers-Tanimoto係数

Hamann係数

= ファイ係ਤ= 8;

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:71%;mso-fareast-hint:yes'>変量間類߬= 4;度，名義尺&#= 24230;

= 平均平方੬= 1;一致係数

= グッドマӥ= 1;・クラスカルのλ

------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0053_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFgAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAV ABMAggAAAJaSjMnEvPz48/v27/rz6gECAwECAwNQOLTc3mGMQqu9NU7Mre5BAEpXqIXYl5mSWZJr OJhoBhe0NNP2huc7F0X1YwVruBvtxBsqgU2nr8hEJqc/3e6FpVqlnfBVPOqSk4K0es1mJwAAOw== ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

2．類= ;似度の測定

尺度について

比率尺度

名義尺度

順序尺度 =

間隔尺度

= ∩

単なる分Ɔ= 06;

　例)名前，性࠶= 9;

順序関係{= 64;ある

　例) 成績評価ӌ= 8;（A > B >= C > D）

差に意味{= 64;ある

　例) 温度　気଄= 1;20&= #8451;より30&= #8451;の方が10&= #8451;高い

比に意味{= 64;ある（絶対原点が存= 在)

　例）身໲= 3;　180cm<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:89%;mso-fareast-hint:yes'>のAさんは息ड= 6;(100cm)の1.8倍背が高ӓ= 6;

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2．類= ;似度の測定

個&= #20307;間類似度

<= span style=3D'font-size:71%'> 3D"*"

ユークリッド距= 8626;

（<= /span>cf. l2-ノルム）

<= span style=3D'font-size:71%'> 3D"*"

マンハッタン距= 8626;

（<= /span>cf. l1-ノ&= #12523;ム）

<= span style=3D'font-size:71%'> 3D"*"

ミンコフスキー= 6317;離

（cf. lp-ノルム）

（<= /span>cf. l∞-ノルム）

マ&= #12495;ラノビス距離

（注：2変量の差ベク

　トルに対す= 427;ノルム）

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R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAACAgMz//wECAwIUBIJpJ+3B3IuyofoCthpDyi0JshQAOx== ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

2．類= ;似度の測定

個&= #20307;間類似度

ユ&= #12540;クリッド距離 <= /div>

（cf. l<= i>2-ノルム）

マ&= #12531;ハッタン距離 <= /div>

（cf. l1-ノルム）

ミ&= #12531;コフスキー距離 =

（cf. lp-ノルム）

（cf. l∞-ノ&= #12523;ム）

<= span style=3D'font-size:71%'> 3D"*"

マハラノビス距= 8626;

（注：2変量の差ベク

　トルに対す= 427;ノルム）

左側の対象= ;内での，A-B間距離と=

右側の対象= ;内でのA-B間距離が=

異なるʌ= 81;

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charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定

= 新たなクӤ= 1;スタ生成時の近さの&= #27770;定

= クラスタp，クラスӟ= 9;q が一つのӞ= 3;ラスタt になる場ࡧ= 2;，他のクラスタr との類似ॷ= 0;（距離）はどうなる&= #65311; <= /div>

= r

spq

spr

sqr

str

(spr : クラスタp, rの類= 0284;度[距離])

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quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定

<= span style=3D'mso-fareast-hint:yes'> 3D"*"

クラスタ間の$= 817;さ決定方法

（事前にクラスタă= 68;を決める必要はない= 方法群）

1.最= 701;距離法 (nearest neighbor method)

2.最&= 263;距離法 (furthest neighbor method) <= /span>

3.群= 179;均法 (group average method)

4.重= 515;法 (centroid method)

5.中= 830;値法 (median method)

6.ウ= 457;ード法 (Ward method)

------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定

1.&#= 26368;短距離法 (nearest neighbor method)

•= 〔ࡕ= 6;連結法 (single linkage method)〕

※類似ò= 30;は，対象間の類似度= の大小関係だけで決= 2414;る．

よって，類似= 230;（距離）は順序尺度ならばよい．

s= tr = = =3D min{spr, sqr}

<= /div>
r

p<= /div>

q<= /div>

s<= i>pr

s<= i>qr

<= /div>

t<= /div>

spr

あるクラスタ= 395;おいて，クラスタ内= ;の各対象が，そ= ;のクラスタ外の任意&#= 12398;対象よりも，そ= ;のクラスタ内の少なく{= 92;も1つの対象{= 92;より近接している．= ;

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charset="us-ascii" 問題発見技法 6．クラスタ分析

<= /div>

t<= /span>

r<= /span>

3．クラスタ= ;化の方法の決定

1.&#= 26368;短距離法 <= /div>

s= tr = = =3D min{spr, sqr}

= <= /div>
4 = ;

5 = ;

p<= /span>

q<= /span>

r<= /span>

4

= 3 = ;

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Content-Type: image/gif R0lGODlhvQBQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALA8ADQCn AD8AggAAAGdFF4AAgMyZ//rz6gECAwECAwECAwP/CLrc/jDKSau9LujNOf5gKI7ktxFoqqpe6b5w bGprbaearO/8SN/AW65HLBoBgaASODw6n6HfclprQq/YDHUrzHqzSa54Zf2aeeGxGndu69LreMBN L8Hj8rrehO+z94ASd355gYYNg4RrcyIthzuJfgKTY4wYJzhlj3aKKgIDoAKVF1I2mpsgkX2foWqW glSvqKmdnqADoqMTqqaysxW8q5SLsGK+v7u1yscKwUzIFs7Kuoh4zNAM0tNcvtpB19hI28vVfeDY 3uNTr+nf4RDt6u4L8V3v5fKKjPXP9/T5nfYtmZRLyblZ/ABWaaaEFa51/hgq9DPHmcOC8/wFI4hx 8iIZcQ1vdbSnMchFj12kcYQYkddJlAsTZrznshVMMjJnvts48mapWgc35Zz4M2BEkDeNDSVZMim3 paaOInW6DurCo1bVFdUndSrVb1lZdA07bSuhoKjIAvVqdOzNle7UEkCLEObLqGy5ds2rzuFDkmrp 1vXIqicKdmX3ZkM5jKlKgiwV800qS6VNg5L/ff2z2OStv/0yS/x6zOLl0KInK2RmETLm1Jp9FqMI G5/Hc1AFt5SLN5m52vBWk/oN/AHvuYJl6lZsljgfV8UpYKK4PPaW6rCbL9ngIh124BxinfIRK7qd DujHd2+u3jy09O3d10kAADs= ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0039_image098.gif Content-Transfer-Encoding: base64 Content-Type: image/gif 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3．クラスタ= ;化の方法の決定

2.&#= 26368;長距離法 (furthest neighbor method)

•= 〔ध= 6;全連結法 (complete linkage method)〕

※類似ò= 30;は，対象間の類似度= の大小関係だけで決= 2414;る．

よって，類似= 230;（距離）は順序尺度ならばよい．

s= tr = = =3D max{spr, sqr}

<= /div>
r

p<= /div>

q<= /div>
s<= i>pr

s<= i>qr

<= /div>

t<= /div>

str

あるクラスタ= 395;おいて，クラスタ内= ;の全ての対&= #35937;が，そのクラ= ;スタ外の任意の対象との距= ;離よりも常に近&= #25509;している．= ;

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<= /div>

t<= /span>

r<= /span>

3．クラスタ= ;化の方法の決定

2.&#= 26368;長距離法

= <= /div>

4 = ;

5 = ;

p<= /span>

q<= /span>

r<= /span>

= 3 = ;

s= tr = = =3D max{spr, sqr}

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R0lGODlhPgASAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwA5 AAwAgAAAAP8AAAI3hI+py33hopwxQIqzs7dZDS7cl3AhNqbqY2rquyojMgPwTZ52vsM62CrVfkBJ kIiUdZLMR/NUAAA7 ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0041_image114.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIQA+AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAkAAgAU ADgAgAAAAIAAgAJahI9poZ0BnYNRPsrswVUDnmkh5SFZ543lspph+8LtFpe1PW/5t/P7LQJahMMe cWJM5lCrI/IHjS5/TkXVqpxdH1nYVifVhmVNsI3BHKIXVVAT402rvx96PVcAADs= ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定

3.群平均法 (group average method)

※類似ò= 30;は，対象間の類似度= の大小関係だけで決= 2414;る．

よって，類似= 230;（距離）は順序尺度ならばよい．

<= /div>
r

p<= /div>

q<= /div>

s<= i>pr

s<= i>qr

<= /div>

t<= /div>

str

（np = ： = クラスタ p に含まれ|= 27;対象数） <= /span>

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AB4AgwAAAAAAAAoICQsJCgwKCwsKCggHBwcGBgkICAcGBwkHCAECAwECAwECAwECAwECAwS4EMhJ Zbg1611v4CD4WWGZjQBqriR7ii6req76Wlh8zrpN8ToOsOQp3ia+YAtZ2ySTwZG0eZumlLhcSrvy FaVcbEkwGADIBDGlUD4P0moJwQA4zM1xwEBAQNzzEgIFfWSAAHQIBYWGCXsACoaHAgmPkYeWFZCW AwiYEwKdO0aepE5fp6ipqqusX6WvsLGys7SyNF1htShQHUy1Gk9Cv0e9TsM/UMnHxKjFy77OP8/R 0L68sKPEW7cuEQA7 ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

<= /div>

t<= /span>

r<= /span>

3．クラスタ= ;化の方法の決定

3.群平均法

= <= /div>

4 = ;

5 = ;

p<= /span>

q<= /span>

r<= /span>

3･4+2<= /span>･5

3+2= = ;

= 3 = ;

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3．クラスタ= ;化の方法の決定

4.重心法 (centroid method)

<= /div>
r

p<= /div>
q<= /div>
s<= i>pr

s<= i>qr

<= /div>
r

t<= /div>

str

（np = ： = クラスタ p に含まれ|= 27;対象数） <= /span>

<= /div>
p

q

t

※導出ű= 42;程（tex-file参照）より，'= 006;似度Strは

　}= 18;ークリッド距離の平方の時のみ妥当A= 294;

※ xはベクトル= ;

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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

<= /div>
t<= /span>

r<= /span>

3．クラスタ= ;化の方法の決定

4.重心法

= <= /div>
4 = ;

5 = ;

p<= /span>

q<= /span>

r<= /span>

= 3 = ;

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3．クラスタ= ;化の方法の決定

5.中央値法 (median method)

<= /div>
r

p<= /div>
q<= /div>
s<= i>pr

s<= i>qr

<= /div>
r

t<= /div>

str

（重心= 法の簡易版，重心で= 2399;なく中央値を取るᦁ= 4;

　よっ= て，重心法でnp :=3D1, nq := =3D1 に相当= する）

<= /div>
p

q

t

※導出ű= 42;程（重心法参照）よ= り，類似度Strは

　}= 18;ークリッド距離の平方の時のみ妥当A= 294;

※ xはベクトル= ;

1<= span style=3D'font-family:"MS PGothic";mso-ascii-font-family:Garamond;mso-farea= st-font-family: "MS PGothic";mso-fareast-hint:yes'>　：　1

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file:///C:/72BBA416/06htf_6.files/slide0044.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

<= /div>
t<= /span>

r<= /span>

3．クラスタ= ;化の方法の決定

5.中央値法

= <= /div>
4 = ;

5 = ;

p<= /span>

q<= /span>

r<= /span>

= 3 = ;

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------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定

6.ウォード法 (Ward method)

※導出ű= 42;程（tex-file参照）より，'= 006;似度Strは

　}= 18;ークリッド距離の平方の時のみ妥当A= 294;

=

<= /div>
r

p<= /div>
q<= /div>
s<= i>pr

s<= i>qr

<= /div>
r

t<= /div>

str
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<= /div>
t<= /span>

r<= /span>

3．クラスタ= ;化の方法の決定

6.ウォード法

= <= /div>
4 = ;

5 = ;

p<= /span>

q<= /span>

r<= /span>

= 3 = ;

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------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定（２） <= /div>

<= span style=3D'mso-fareast-hint:yes'>クラスタ間の$= 817;さ決定方法（= ;非階層的方法）

K-means法

<= span style=3D'font-family:"Times New Roman";font-style:normal;mso-fareast-hint:= yes'>•事前にクラスタ数|= 34;Kとしてクラスタリ}= 31;グを行う．

------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定（２） <= /div>

<= span style=3D'font-family:"Times New Roman";mso-fareast-hint:yes'>K-means法

1<= /div>
1

2<= /div>
3<= /div>
4<= /div>
5<= /div>
6<= /div>
7<= /div>
2

3

4

5

6

0

A

B

C

D

E

F

G

Step0：Kを決める=

(ex. K:=3D3)
Step1：適当に種= ;を置く

Step2：何らかの距&= 626;に

　より，も= ;っとも近い種

　に含まれ= ;るよう境界

　線で分け= ;る．

(ex. Euclidean distance)

(cf. Voronoi diagrams)

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3．クラスタ= ;化の方法の決定（２） <= /div>

<= span style=3D'font-family:"Times New Roman";mso-fareast-hint:yes'>K-means法

1<= /div>
1

2<= /div>
3<= /div>
4<= /div>
5<= /div>
6<= /div>
7<= /div>
2

3

4

5

6

0

A

B

C

D

E

F

G

Step0：Kを決める=

(ex. K:=3D3)
Step1：適当に種= ;を置く

Step2：何らかの距&= 626;に

　より，も= ;っとも近い種

　に含まれ= ;るよう境界

　線で分け= ;る．

(ex. Euclidean distance)

(cf. Voronoi diagrams)

= Step3：各クラス= ;タごとに

　何らかの= ;距離により，

　重心を計= ;算し，新たな

　種とする= ;．

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quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

Step2：何らかの距&= 626;に

　より，も= ;っとも近い種

　に含まれ= ;るよう境界

　線で分け= ;る．

(ex. Euclidean distance)

(cf. Voronoi diagrams)

Step3：各クラス= ;タごとに

　何らかの= ;距離により，

　重心を計= ;算し，新たな

　種とする= ;．

3．クラスタ= ;化の方法の決定（２） <= /div>

<= span style=3D'font-family:"Times New Roman";mso-fareast-hint:yes'>K-means法

1<= /div>
1

2<= /div>
3<= /div>
4<= /div>
5<= /div>
6<= /div>
7<= /div>
2

3

4

5

6

0

A

B

C

D

E

F

G

Step0：Kを決める=

(ex. K:=3D3)
Step1：適当に種= ;を置く

Step2-4 をクラスタが

　更新され= ;なくなる

　まで繰り= ;返す

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quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定（２） <= /div>

<= span style=3D'font-family:"Times New Roman";mso-fareast-hint:yes'>K-means法

1<= /div>
1

2<= /div>
3<= /div>
4<= /div>
5<= /div>
6<= /div>
7<= /div>
2

3

4

5

6

0

A

B

C

D

E

F

G

Step0：Kを決める=

(ex. K:=3D3)
Step1：適当に種= ;を置く

Step2：何らかの距&= 626;に

　より，も= ;っとも近い種

　に含まれ= ;るよう境界

　線で分け= ;る．

(ex. Euclidean distance)

(cf. Voronoi diagrams)

Step3：各クラス= ;タごとに

　何らかの= ;距離により，

　重心を計= ;算し，新たな

　種とする= ;．

Step2-4 をクラスタが

　更新され= ;なくなる

　まで繰り= ;返す

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image/gif R0lGODlhCwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAK AAoAgQAAAIAAgJkzZgECAwIXhINhF+KiznuqTVcvtRppKF2RRy0MshQAOx== ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0052.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

3．クラスタ= ;化の方法の決定（２） <= /div>

<= span style=3D'font-family:"Times New Roman";mso-fareast-hint:yes'>K-means法

1<= /div>
1

2<= /div>
3<= /div>
4<= /div>
5<= /div>
6<= /div>
7<= /div>
2

3

4

5

6

0

A

B

C

D

E

F

G

Step0：Kを決める=

(ex. K:=3D3)
Step1：適当に種= ;を置く

Step2：何らかの距&= 626;に

　より，も= ;っとも近い種

　に含まれ= ;るよう境界

　線で分け= ;る．

(ex. Euclidean distance)

(cf. Voronoi diagrams)

Step3：各クラス= ;タごとに

　何らかの= ;距離により，

　重心を計= ;算し，新たな

　種とする= ;．

Step2-4 をクラスタが

　更新され= ;なくなる

　まで繰り= ;返す

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4．ク= ;ラスタ分析の実施〔SPSS〕

統計パッӞ= 5;ージ SPSS &= #12395;よるクラスタ分析 <= /div>
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4．ク= ;ラスタ分析の実施〔SPSS〕

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:88%;mso-fareast-hint:yes'>統計パッӞ= 5;ージ SPSS &= #12395;よるクラスタ分析

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;mso-fareast-hint:yes'>「クラスӟ= 9;化の方法」の選択

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4．ク= ;ラスタ分析の実施〔SPSS〕

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Of3rn/v1RqGh1qqiKQiBdxyeSSfzJpa5H/hZ3hz+9c/9+qP+FneHP71z/wB+qLMBvj7rYfST/wBl orB8UeM9H1k2v2aSUeVv3b4yOuP8KKpbEs//2c== ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

ある部屋に次の&#= 65304;人（①～⑧）が図７= ;－１の様に座った。&#= 13;

座り方は任意な&#= 12398;で、似たもの同士z= 89;親しい同士ほど接近= して

座るものと思わ&#= 12428;る。座った位置の|= 87;ータは表７－１であ= る。

このデータをも&#= 12392;にして８人を分類{= 75;デンドログラムをつくる&#= 12290;

①
②
③
④
⑤
⑥
⑦
⑧
図７&#= 65293;１

表７&#= 65293;１

よこ&#= 24231;標

{= 83;て座標

4．&= #12463;ラスター分析の実施 = 〔例題= 〕

０
〔佐&= #12293;木作成スライド（2003堀田研ゼミ）〕= ;

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①
②
③
④
⑤
⑥
⑦
⑧
図７&#= 65293;１

よこ&#= 24231;標

{= 83;て座標

８人&#= 30456;互間のユークリッ|= 89;平方距離を表７－１= から求める。

②

最短距離法で更新！！

表7-2

値が&#= 23567;さいほど類似性を表す

０
〔佐&= #12293;木作成スライド（2003堀田研ゼミ）〕= ;

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file:///C:/72BBA416/06htf_6.files/slide0024_image272.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLQA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAo ADYAgQAAAGdFF9aWQAECAwKmhI+JEeoPXRCixYsZpQx7NW2i9WWhOJKlhLabuhqaS3cxcNI6fM36 X+GBckCg8EAsFm2LpFKpcj6fHYb1Kl1ir5Ds79ibjm448Yvs3aHNnDUbHEnX3GZ4l12hi+0PuYvP 8qY3BQiCV5jg14K4cDhI9QgVuTRpVPl1qXajiMKI5LgJGsM5FipoWpc5h7qn+ue6CNspWzoqukJ6 xkpIq2t7OrolLBxRAAA7 ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

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図７&#= 65293;１

よこ&#= 24231;標

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]= 13;

①

③

②

①

①

表7-3

表7-7

表7-6

表7-5

表7-4

更新

更新

更新

更新

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〔佐&= #12293;木作成スライド（2003堀田研ゼミ）〕= ;

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Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

②
⑤
⑦
①
④
⑧
③
⑥
10

5
<= ![endif]>
非類似度（ユー&#= 12463;リッド平方距離）

9.0

6.0

デン&#= 12489;ロ|= 64;ラム（樹形図）

各クラスターの= ;非類似度は、

表7-2～7-7でマークした値であ= ;る。

樹の高さを変え&#= 12427;ことにより、

クラスターの数&#= 12418;異なる

使用&#= 30446;的により高さを変えて判断

（②、⑤、⑦）&#= 65288;①、④、⑧）（③、&= #9317;）

（②、⑤、⑦、&#= 9312;、④、⑧）（③、⑥&#= 65289;

０
〔佐&= #12293;木作成スライド（2003堀田研ゼミ）〕= ;

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R0lGODlh4QAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADf ABMAgQAAAGdFF///zAECAwJ4RI6py+0Po5y02ovzA0b4D4biSJbmiabqyrbuC5tBF9f2jef6fgf8 DwwKh0If8YhMKo/GpfMJjcqk1KqVec1qt7Am9wsOC7zisjlKPqvXwzT7De/F5/SYu47Ph+76fv3g F6gHKFg4h2CYuDbDoeH4CBkpOUn5yFEAADs= ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0026_image332.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhxgAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADE ABMAgQAAAGdFF///zAECAwJ2RI6py+0Po5y02ouTEbz7D4biSJbmiabqyrbe4cbyTNf2DcL4zvf+ T9IBh8Si0SQ8KpfMXbIJjUqRgan1in1it1yitgsO277isllFPqvXuSr7DX+54/R1uo7PzvN87r0P uBSwEVjYdACQmLHI2Oj4CBmJkAhQAAA7 ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 問題発見技法 6．クラスタ分析

5．ク= ;ラスター分析実施上&#= 12398;注意点

= クラスタӦ= 0;分析の長所

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;mso-fareast-hint:yes'>探索的手ૢ= 1;：データの構造を= 事前に知らなくてよ= 2356;

= あらゆ= る種類のデータに適= 9992;可能：数値・ӝ= 9;テゴリー

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;mso-fareast-hint:yes'>適用が簡単<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;color:#3333FF;display:none'>

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;color:#3333FF;display:none'>

= クラスタӦ= 0;分析の短所

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;mso-fareast-hint:yes'>類似度（ฯ= 7;離）測定法の選択が= 256;難の可能性

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;mso-fareast-hint:yes;color:red'>クラス= 479;化法の選択が困難= の可能性

= 非階層的৔= 3;法の場合，事前に決&= #23450;するクラス= 479;数の決定が困難の可能性

<= span style=3D'font-family:"MS PGothic";mso-fareast-font-family:"MS PGothic"; font-size:86%;mso-fareast-hint:yes'>結果の解釈が= 256;難の可能性 <= /div>

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6．やってみよう！

演習：類߬= 4;度をユークリッド平&= #26041;距離，クラスタ化= 434;最短距離= 法でクラӟ= 3;タ分析しよう！ <= /div>
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4<= /div>
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6<= /div>
0<= /div>
A

B

C

D

E

F

G

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参考= ;文献

<= span style=3D'font-size:69%;mso-fareast-hint:yes'>= 田中豊ほか『多変ŵ= 27;統計解析法』現代数= 学社

<= span style=3D'font-size:69%;mso-fareast-hint:yes'>= 河口至商『多変量Š= 99;析入門Ⅱ』森北出版<= /span>

= 浅利英吉ほか『パ|= 77;コンによるデータマ= イニング』日刊工業= 6032;聞社

<= span style=3D'font-size:69%;mso-fareast-hint:yes'>= 東大教養学部統計é= 98;教室編『統計学入門= 』東京大学出版会

<= span style=3D'font-size:69%'>M.J.A.= ベリーほӔ= 3;『データマイニング&= #25163;法』海文堂

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<= /div>
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<ヘッダー>

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<日付/時&#= 21051;>

マスタテキスト{= 98;書式設定

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第 5 レベル

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<フッター>

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<= /div>

<#>

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ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } var g_HLinkArray =3D new Array(); =20 function IMapAreaObj( areaObj, coords ) { this.areaObj =3D areaObj; this.coords =3D coords; } function InitHLinkArray() { var appVer =3D navigator.appVersion; var msie =3D appVer.indexOf ( "MSIE " ) var ver =3D 0; if ( msie >=3D 0 ) ver =3D parseInt ( appVer.substring( msie+5 ) ); linkNum =3D 0; for (i=3D0; i 4 ) ) g_HLinkArray[linkNum++] =3D new IMapAreaObj( areaObj, ParseCoords( ar= eaObj.coords ) ); } } function ScaleHyperlinks( factor ) { =20 for ( ii=3D0; ii< g_HLinkArray.length; ii++) { coordsStr=3D""; imaObj =3D g_HLinkArray[ii]; for ( jj=3D0; jj < imaObj.coords.length-1; jj++ ) coordsStr +=3D (imaObj.coords[jj]*factor) + ","; coordsStr +=3D (imaObj.coords[jj]*factor); imaObj.areaObj.coords =3D coordsStr; } } function ParseCoords( coordsStr ) { var numArray =3D new Array(); var i =3D curPos =3D commaPos =3D 0; while ( ( commaPos =3D coordsStr.indexOf(",", curPos) ) !=3D -1 ) {=20 numArray[i++] =3D parseInt( coordsStr.substr( curPos, commaPos ) ); curPos =3D commaPos + 1; } numArray[i] =3D parseInt( coordsStr.substr( curPos ) ); return numArray; } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"スライドショӦ= 0;の最後です。クリッ= クすると終了します= 2290;", SCREEN_MODE=3D"Frames", gIsEndShow=3D0, NUM_VIS_SLDS=3D39, SCRIPT_H= REF=3D"script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0009.htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("= slide0002.htm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("s= lide0053.htm",1,-1,1),new hrefList("slide0027.htm",1,-1,1),new hrefList("sl= ide0021.htm",1,-1,1),new hrefList("slide0038.htm",1,-1,1),new hrefList("sli= de0003.htm",1,-1,1),new hrefList("slide0028.htm",1,-1,1),new hrefList("slid= e0006.htm",1,-1,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide= 0030.htm",1,-1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0= 031.htm",1,-1,1),new hrefList("slide0042.htm",1,-1,1),new hrefList("slide00= 32.htm",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new hrefList("slide003= 3.htm",1,-1,1),new hrefList("slide0044.htm",1,-1,1),new hrefList("slide0034= .htm",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0046.= htm",1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("slide0049.h= tm",1,-1,1),new hrefList("slide0050.htm",1,-1,1),new hrefList("slide0051.ht= m",1,-1,1),new hrefList("slide0052.htm",1,-1,1),new hrefList("slide0035.htm= ",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0037.htm"= ,1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("slide0024.htm",= 1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0026.htm",1= ,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("slide0011.htm",1,= -1,1),new hrefList("slide0004.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('

' + ENDSHOW_MESG + '
') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. 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charset="us-ascii" 問題発見技法 6．クラスタ分析 ------=_NextPart_01C6964C.B6D5BEA0 Content-Location: file:///C:/72BBA416/06htf_6.files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

&#= 12494;ート

スライドショー

アウトライ&#= 12531;

1

問題= 発見技法

6．クラスタ分析

2

クラ= スタ分析

Contents

クラスタ分析概要
類似度の測定

クラスタ間の近さ= 2398;決定

クラスタ分析の実= 6045;〔SPSS，手計算〕

クラスター分析実= 6045;上の注意点

演習：やってみよ= 2358;！

3

1．ク= ;ラスタ分析概要

クラスタ分析とはA= 311;

複数の対象（もの= 5292;変数など）を，

類似度（similarity）を定= ;義し，

均質な集団（cluster）&#= 12395;分類する

方法の総称

4

1．ク= ;ラスタ分析概要

非階層的方法

予めクラスタ数を&#= 27770;め

（or決まっていて）= ;，

クラスタリングを&= #34892;う

5

1．ク= ;ラスタ分析概要

例：

6

2．類= ;似度の測定

距離，間隔尺度

ユークリッド距離
ユークリッド平方= 6317;離

重み付きユークリ= 2483;ド距離

マンハッタン距離
ミンコフスキー距= 8626;

マハラノビス汎距= 8626;

相関，間隔尺度

Pearsonの積率相関係数

ベクトル内積

相関，順序尺度

Spearmanの順位相関係数
Kendallの順位相関係数

距離，名義尺度 [0, 1]

類似比

一致係数

Russel-Rao係数

Rogers-Tanimoto係数

Hamann係数

ファイ係数

変量間類似度，名 = 681;尺度

平均平方根一致係= 5968;

グッドマン・クラ= 2473;カルのλ

7

2．類= ;似度の測定

尺度について

8

2．類= ;似度の測定

個体間類似度

ユークリッド距離
（cf. l₂-ノルム）

マンハッタン距離
（cf. l₁-ノルム）

ミンコフスキー距= 8626;

（cf. l_p-ノルム）

（cf. l_∞-ノルム）<= /li>
マハラノビス距離

9

2．類= ;似度の測定

個体間類似度

ユークリッド距離
（cf. l₂-ノルム）

マンハッタン距離
（cf. l₁-ノルム）

ミンコフスキー距= 8626;

（cf. l_p-ノルム）

（cf. l_∞-ノルム）<= /li>
マハラノビス距離

10

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

新たなクラスタ生= 104;時の近さの決定

クラスタp，クラス&#= 12479;q が一つのクラスタt &= #12395;なる場合，他のク= 521;スタr との類似度（距離= 5289;はどうなる？

11

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

クラスタ間の近さ= 770;定方法

^{（事前にクラ&#=
12473;タ数を決める必要{=
99;ない方法群）}

最短距離法 (nearest neighbor method)<= /li>
最長距離法 (furthest neighbor method)=

群平均法 (group average method)

重心法 (centroid method)

中央値法 (median method)

ウォード法 (Ward method)

12

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

最短距離法 (nearest neighbor method)
〔単連結法 (single linkage method)= 2309;

13

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

最短距離法

14

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

最長距離法 (furthest neighbor method)<= /li>
〔完全連結法 (complete linkage method)〕

15

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

最長距離法

16

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

群平均法 (group average method)

17

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

群平均法

18

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

重心法 (centroid method)

19

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

重心法

20

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

中央値法 (median method)

21

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

中央値法

22

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

ウォード法 (Ward method)

23

3．Ӟ= 3;ラスタ化の方法の決&= #23450;

ウォード法

24

3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）

クラスタ間の近さ= 770;定方法（非階層的方= ;法）

K-means法

事前にクラスタ数&#= 12434;Kとしてクラスタリ= 531;グを行う．

25

3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）

K-means法

26

3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）

K-means法

27

3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）

K-means法

28

3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）

K-means法

29

3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）

K-means法

30

4．Ӟ= 3;ラスタ分析の実施〔S= PSS〕

統計パッケージ SPSS ӗ= 5;よるクラスタ分析

31

4．Ӟ= 3;ラスタ分析の実施〔S= PSS〕

統計パッケージ SPSS ӗ= 5;よるクラスタ分析

「クラスタ化の方= 7861;」の選択

32

4．Ӟ= 3;ラスタ分析の実施〔S= PSS〕

統計パッケージ SPSS ӗ= 5;よるクラスタ分析

「クラスタ間距離= 8204;定法」の選択

33

34

35

36

37

5．Ӟ= 3;ラスター分析実施上&= #12398;注意点

クラスター分析の&= 263;所

探索的手法：デー= 2479;の構造を事前に知Ӛ= 5;なくてよい

あらゆる種類のデ= 2540;タに適用可能：数ࠃ= 6;・カテゴリー

適用が簡単

クラスター分析の= 701;所

類似度（距離）測= 3450;法の選択が困難のࡤ= 7;能性

クラスタ化法の選= 5246;が困難の可能性

非階層的手法の場= 1512;，事前に決定するӞ= 3;ラスタ数の決定が困&= #38627;の可能性

結果の解釈が困難= 2398;可能性

38

6．Ӛ= 0;ってみよう！

演習：類似度をユ= 540;クリッド平方距離，= ;クラスタ化を最短距&#= 38626;法でクラスタ分析{= 75;よう！

39

参考= ;文献

田中豊ほか『多変%= 327;統計解析法』現代数= ;学社

河口至商『多変量#= 299;析入門Ⅱ』森北出版=

浅利英吉ほか『パ= 477;コンによるデータマ= ;イニング』日刊工業&#= 26032;聞社

東大教養学部統計= 398;教室編『統計学入門= ;』東京大学出版会

M.J.A.ベリーほか『デӦ= 0;タマイニング手法』&= #28023;文堂

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1	問題= 発見技法 6．クラスタ分析
2	クラ= スタ分析 Contents クラスタ分析概要類似度の測定クラスタ間の近さ= 2398;決定クラスタ分析の実= 6045;〔SPSS，手計算〕クラスター分析実= 6045;上の注意点演習：やってみよ= 2358;！
3	1．ク= ;ラスタ分析概要クラスタ分析とはA= 311; 複数の対象（もの= 5292;変数など）を，類似度（similarity）を定= ;義し，均質な集団（cluster）&#= 12395;分類する方法の総称
4	1．ク= ;ラスタ分析概要非階層的方法予めクラスタ数を&#= 27770;め（or決まっていて）= ;，クラスタリングを&= #34892;う
5	1．ク= ;ラスタ分析概要例：
6	2．類= ;似度の測定距離，間隔尺度ユークリッド距離ユークリッド平方= 6317;離重み付きユークリ= 2483;ド距離マンハッタン距離ミンコフスキー距= 8626; マハラノビス汎距= 8626; 相関，間隔尺度 Pearsonの積率相関係数ベクトル内積相関，順序尺度 Spearmanの順位相関係数 Kendallの順位相関係数距離，名義尺度 [0, 1] 類似比一致係数 Russel-Rao係数 Rogers-Tanimoto係数 Hamann係数ファイ係数変量間類似度，名 = 681;尺度平均平方根一致係= 5968; グッドマン・クラ= 2473;カルのλ
7	2．類= ;似度の測定尺度について
8	2．類= ;似度の測定個体間類似度ユークリッド距離（cf. l₂-ノルム）マンハッタン距離（cf. l₁-ノルム）ミンコフスキー距= 8626; （cf. l_p-ノルム）（cf. l_∞-ノルム）<= /li> マハラノビス距離
9	2．類= ;似度の測定個体間類似度ユークリッド距離（cf. l₂-ノルム）マンハッタン距離（cf. l₁-ノルム）ミンコフスキー距= 8626; （cf. l_p-ノルム）（cf. l_∞-ノルム）<= /li> マハラノビス距離
10	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 新たなクラスタ生= 104;時の近さの決定クラスタp，クラス&#= 12479;q が一つのクラスタt &= #12395;なる場合，他のク= 521;スタr との類似度（距離= 5289;はどうなる？
11	3．Ӟ= 3;ラスタ化の方法の決&= #23450; クラスタ間の近さ= 770;定方法 ^{（事前にクラ&#= 12473;タ数を決める必要{= 99;ない方法群）} 最短距離法 (nearest neighbor method)<= /li> 最長距離法 (furthest neighbor method)= 群平均法 (group average method) 重心法 (centroid method) 中央値法 (median method) ウォード法 (Ward method)
12	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 最短距離法 (nearest neighbor method) 〔単連結法 (single linkage method)= 2309;
13	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 最短距離法
14	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 最長距離法 (furthest neighbor method)<= /li> 〔完全連結法 (complete linkage method)〕
15	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 最長距離法
16	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 群平均法 (group average method)
17	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 群平均法
18	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 重心法 (centroid method)
19	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 重心法
20	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 中央値法 (median method)
21	3．Ӟ= 3;ラスタ化の方法の決&= #23450; 中央値法
22	3．Ӟ= 3;ラスタ化の方法の決&= #23450; ウォード法 (Ward method)
23	3．Ӟ= 3;ラスタ化の方法の決&= #23450; ウォード法
24	3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２）クラスタ間の近さ= 770;定方法（非階層的方= ;法） K-means法事前にクラスタ数&#= 12434;Kとしてクラスタリ= 531;グを行う．
25	3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２） K-means法
26	3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２） K-means法
27	3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２） K-means法
28	3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２） K-means法
29	3．Ӟ= 3;ラスタ化の方法の決&= #23450;（２） K-means法
30	4．Ӟ= 3;ラスタ分析の実施〔S= PSS〕統計パッケージ SPSS ӗ= 5;よるクラスタ分析
31	4．Ӟ= 3;ラスタ分析の実施〔S= PSS〕統計パッケージ SPSS ӗ= 5;よるクラスタ分析「クラスタ化の方= 7861;」の選択
32	4．Ӟ= 3;ラスタ分析の実施〔S= PSS〕統計パッケージ SPSS ӗ= 5;よるクラスタ分析「クラスタ間距離= 8204;定法」の選択
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37	5．Ӟ= 3;ラスター分析実施上&= #12398;注意点クラスター分析の&= 263;所探索的手法：デー= 2479;の構造を事前に知Ӛ= 5;なくてよいあらゆる種類のデ= 2540;タに適用可能：数ࠃ= 6;・カテゴリー適用が簡単クラスター分析の= 701;所類似度（距離）測= 3450;法の選択が困難のࡤ= 7;能性クラスタ化法の選= 5246;が困難の可能性非階層的手法の場= 1512;，事前に決定するӞ= 3;ラスタ数の決定が困&= #38627;の可能性結果の解釈が困難= 2398;可能性
38	6．Ӛ= 0;ってみよう！演習：類似度をユ= 540;クリッド平方距離，= ;クラスタ化を最短距&#= 38626;法でクラスタ分析{= 75;よう！
39	参考= ;文献田中豊ほか『多変%= 327;統計解析法』現代数= ;学社河口至商『多変量#= 299;析入門Ⅱ』森北出版= 浅利英吉ほか『パ= 477;コンによるデータマ= ;イニング』日刊工業&#= 26032;聞社東大教養学部統計= 398;教室編『統計学入門= ;』東京大学出版会 M.J.A.ベリーほか『デӦ= 0;タマイニング手法』&= #28023;文堂