trt t ss s - PowerPoint PPT Presentation

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr❡♣r♦❝❡ss✐♥❣ ⇒ ❙✐♠✐❧❛r✐t② ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s✿ ❊✉❝❧✐❞❡❛♥ ❞✐st❛♥❝❡ • ❈❤♦♦s✐♥❣ ❛❝t✐✈❡ ✈❛r✐❛❜❧❡s ❑ � ❞ ✷ ( ✐ , ✐ ′ ) ( ① ✐❦ − ① ✐ ′ ❦ ) ✷ = ❦ = ✶ • ❱❛r✐❛❜❧❡s ❛r❡ ❛❧✇❛②s ❝❡♥tr❡❞ ❑ � ❞ ✷ ( ✐ , ✐ ′ ) ① ❦ )) ✷ = (( ① ✐❦ − ¯ ① ❦ ) − ( ① ✐ ′ ❦ − ¯ ❦ = ✶ • ❙t❛♥❞❛r❞✐③✐♥❣ ✈❛r✐❛❜❧❡s ♦r ♥♦t❄ ❑ ✶ � ❞ ✷ ( ✐ , ✐ ′ ) = ( ① ✐❦ − ① ✐ ′ ❦ ) ✷ s ✷ ❦ ❦ = ✶ ✶✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ■♥❞✐✈✐❞✉❛❧s ❝❧♦✉❞ • ❙t✉❞② t❤❡ str✉❝t✉r❡✱ ✐✳❡✳ t❤❡ s❤❛♣❡ ♦❢ t❤❡ ❝❧♦✉❞ ♦❢ ✐♥❞✐✈✐❞✉❛❧s • ■♥❞✐✈✐❞✉❛❧s ❛r❡ ✐♥ R ❑ ✶✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❋✐t t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❝❧♦✉❞ ❋✐♥❞ t❤❡ s✉❜s♣❛❝❡ ✇❤✐❝❤ ❜❡tt❡r s✉♠s ✉♣ t❤❡ ❞❛t❛ ❋✐❣✉r❡✿ ❈❛♠❡❧ ✈s ❞r♦♠❡❞❛r②❄ ⇒ ❈❧♦s❡st r❡♣r❡s❡♥t❛t✐♦♥ ❜② ♣r♦❥❡❝t✐♦♥ ⇒ ❇❡st r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❞✐✈❡rs✐t②✱ ✈❛r✐❛❜✐❧✐t② ✶✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❋✐t t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❝❧♦✉❞ � �� ✉ ✶ ( ✉ ′ ✶ ✉ ✶ ) − ✶ ✉ ′ P ✉ ✶ ( ① ✐ . ) = ✶ ① ✐ . min = < ① ✐ . , ✉ ✶ > ✉ ✶ max ❋ ✐ ✶ = < ① ✐ . , ✉ ✶ > � � � � � • ▼✐♥✐♠✐③❡ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ❛♥❞ t❤❡✐r ♣r♦❥❡❝t✐♦♥s • ▼❛①✐♠✐③❡ t❤❡ ✈❛r✐❛♥❝❡ ♦❢ t❤❡ ♣r♦❥❡❝t❡❞ ❞❛t❛ ✉ ✶ ∈ R ❑ ( ✈❛r ( ❳✉ ✶ )) ✇✐t❤ ✉ ′ ✉ ✶ = ❛r❣ ♠❛① ✉ ✶ ∈ R ❑ ( ✈❛r ( ❋ . ✶ )) = ❛r❣ ♠❛① ✶ ✉ ✶ = ✶ ⇒ ✉ ✶ ✜rst ❡✐❣❡♥✈❡❝t♦r ♦❢ t❤❡ ❝♦rr❡❧❛t✐♦♥ ♠❛tr✐① ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❧❛r❣❡st ❡✐❣❡♥✈❛❧✉❡ λ ✶ ✿ ❙✉ ✶ = λ ✶ ✉ ✶ ❱❛r ( ❋ . ✶ ) = ✈❛r ( ❳✉ ✶ ) = ✶ / ■ ✉ ′ ✶ ❳ ′ ❳✉ ✶ = ✉ ′ ✶ ❙✉ ✶ = λ ✶ ✉ ′ ✶ ✉ ✶ = λ ✶ ✶✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❋✐t t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❝❧♦✉❞ ❆❞❞✐t✐♦♥❛❧ ❛①❡s ❛r❡ s❡q✉❡♥t✐❛❧❧② ❞❡✜♥❡❞✿ ❡❛❝❤ ♥❡✇ ❞✐r❡❝t✐♦♥ ♠❛①✐♠✐③❡s t❤❡ ♣r♦❥❡❝t❡❞ ✈❛r✐❛♥❝❡ ❛♠♦♥❣ ❛❧❧ ♦rt❤♦❣♦♥❛❧ ❞✐r❡❝t✐♦♥s ⇒ ◗ ❡✐❣❡♥✈❡❝t♦rs ✉ ✶ ✱✳✳✳✱ ✉ ◗ ❛ss♦❝✐❛t❡❞ t♦ λ ✶ ✱✳✳✳✱ λ ◗ ❘❡♣r❡s❡♥t❛t✐♦♥ q✉❛❧✐t②✿ ❞✐♠❡♥s✐♦♥❛❧✐t② r❡❞✉❝t✐♦♥ ⇒ ❧♦♦s✐♥❣ ✐♥❢♦r♠❛t✐♦♥ • ❚♦t❛❧ ✈❛r✐❛♥❝❡ ♦❢ t❤❡ ✐♥✐t✐❛❧ ✐♥❞✐✈✐❞✉❛❧s ❝❧♦✉❞ ✭t♦t❛❧ ✐♥❡rt✐❛✮✿ ❑ ✶ � ■ � ① ✐ . − ❣ � ✷ = tr ( ❙ ) = λ ❦ (= ❑ ) ❦ = ✶ • ❱❛r✐❛♥❝❡ ♦❢ t❤❡ ♣r♦❥❡❝t❡❞ ✐♥❞✐✈✐❞✉❛❧s ❝❧♦✉❞ ✭◗✲❞✐♠❡♥s✐♦♥❛❧ r❡♣r❡s❡♥t❛t✐♦♥✮✿ ✈❛r ( ❋ ✶ ) + ✈❛r ( ❋ ✷ ) + ... + ✈❛r ( ❋ ◗ ) � ◗ ❦ = ✶ λ ❦ ⇒ P❡r❝❡♥t❛❣❡ ♦❢ ✈❛r✐❛♥❝❡ ❡①♣❧❛✐♥❡❞✿ � ❑ ❦ = ✶ λ ❦ ✶✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❊①❛♠♣❧❡✿ ✇✐♥❡ ❞❛t❛ • ❙❡♥s♦r② ❞❡s❝r✐♣t♦rs ❛r❡ ✉s❡❞ ❛s ❛❝t✐✈❡ ✈❛r✐❛❜❧❡s✿ ♦♥❧② t❤❡s❡ ✈❛r✐❛❜❧❡s ❛r❡ ✉s❡❞ t♦ ❝♦♥str✉❝t t❤❡ ❛①❡s • ❱❛r✐❛❜❧❡s ❛r❡ ✭❝❡♥tr❡❞ ❛♥❞✮ st❛♥❞❛r❞✐③❡❞ Aroma.persistency Overall.preference Aroma.intensity Visual.intensity Odor.preferene Astringency Sweetness Bitterness O.passion O.fruity O.citrus Acidity Label … S Michaud 4.3 2.4 5.7 … 3.5 5.9 4.1 1.4 7.1 6.7 5.0 6.0 5.0 Sauvignon S Renaudie 4.4 3.1 5.3 … 3.3 6.8 3.8 2.3 7.2 6.6 3.4 5.4 5.5 Sauvignon S Trotignon 5.1 4.0 5.3 … 3.0 6.1 4.1 2.4 6.1 6.1 3.0 5.0 5.5 Sauvignon S Buisse Domaine 4.3 2.4 3.6 … 3.9 5.6 2.5 3.0 4.9 5.1 4.1 5.3 4.6 Sauvignon S Buisse Cristal 5.6 3.1 3.5 … 3.4 6.6 5.0 3.1 6.1 5.1 3.6 6.1 5.0 Sauvignon V Aub Silex 3.9 0.7 3.3 … 7.9 4.4 3.0 2.4 5.9 5.6 4.0 5.0 5.5 Vouvray V Aub Marigny 2.1 0.7 1.0 … 3.5 6.4 5.0 4.0 6.3 6.7 6.0 5.1 4.1 Vouvray V Font Domaine 5.1 0.5 2.5 … 3.0 5.7 4.0 2.5 6.7 6.3 6.4 4.4 5.1 Vouvray V Font Brûlés 5.1 0.8 3.8 … 3.9 5.4 4.0 3.1 7.0 6.1 7.4 4.4 6.4 Vouvray V Font Coteaux 4.1 0.9 2.7 … 3.8 5.1 4.3 4.3 7.3 6.6 6.3 6.0 5.7 Vouvray ✶✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❊①❛♠♣❧❡✿ ❣r❛♣❤ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s V Aub Marigny V Font Coteaux S Renaudie 2 S Michaud S Trotignon V Font Brûlés 0 V Font Domaine Dim 2 (25.14%) S Buisse Cristal -2 S Buisse Domaine -4 V Aub Silex -6 -6 -4 -2 0 2 4 Dim 1 (43.48%) ⇒ ◆❡❡❞ ✈❛r✐❛❜❧❡s t♦ ✐♥t❡r♣r❡t t❤❡ ❞✐♠❡♥s✐♦♥s ♦❢ ✈❛r✐❛❜✐❧✐t② ✶✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ■♥❞✐✈✐❞✉❛❧s ❝♦♦r❞✐♥❛t❡s ❝♦♥s✐❞❡r❡❞ ❛s ✈❛r✐❛❜❧❡s u 2 u 2 � � � � � � � � � � � � � � � � � � � � � � � � � � � � V Aub Marigny V Aub Marigny S Renaudie S Renaudie V Font Coteaux V Font Coteaux S Michaud S Michaud S Trotignon S Trotignon V Font Brûlés V Font Brûlés � � � � � � � � � u 1 u 1 � �� � � � � � � V Font Domaine V Font Domaine � S Buisse Cristal S Buisse Cristal S Buisse Domaine S Buisse Domaine V Aub Silex V Aub Silex � � � � � � � � � � � ✶✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ■♥t❡r♣r❡t❛t✐♦♥ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❣r❛♣❤ ✇✐t❤ t❤❡ ✈❛r✐❛❜❧❡s • ❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ✈❛r✐❛❜❧❡ ① . ❦ ❛♥❞ ❋ . ✶ ✭❛♥❞ ❋ . ✷ ✮ 1 � �� � � � � � � � �� � O.Vanilla -1 1 0 � � � � � � � �� � -1 ⇒ ❈♦rr❡❧❛t✐♦♥ ❝✐r❝❧❡ ✶✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ■♥t❡r♣r❡t❛t✐♦♥ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❣r❛♣❤ ✇✐t❤ t❤❡ ✈❛r✐❛❜❧❡s Odor.Intensity.before.shaking 1.0 Odor.Intensity.after.shaking Expression Attack.intensity Aroma.persistency Bitterness Aroma.intensity Acidity O.wooded O.vanilla 0.5 O.alcohol Astringency Freshness Visual.intensity O.passion Grade Dim 2 (25.14%) O.citrus Surface.feeling 0.0 O.flower O.mushroom Smoothness O.plante O.candied.fruit Oxidation O.fruity Typicity -0.5 Sweetness -1.0 -1.0 -0.5 0.0 0.5 1.0 1.5 Dim 1 (43.48%) ✶✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❈❧♦✉❞ ♦❢ ✈❛r✐❛❜❧❡s O � �� � �� 1 ❙✐♥❝❡ ✈❛r✐❛❜❧❡s ❛r❡ ❝❡♥tr❡❞✿ � ■ ❝♦s ( θ ❦❧ ) = < ① . ❦ , ① . ❧ > ✐ = ✶ ① ✐❦ ① ✐❧ � ① . ❦ � � ① . ❧ � = = r ( ① . ❦ , ① . ❧ ) � ( � ■ ✐❦ )( � ■ ✐ = ✶ ① ✷ ✐ = ✶ ① ✷ ✐❧ ) ✷✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❋✐t t❤❡ ✈❛r✐❛❜❧❡s ❝❧♦✉❞ ❋✐♥❞ ✈ ✶ ✭✐♥ R ■ ✱ ✇✐t❤ ✈ ′ ✶ ✈ ✶ = ✶✮ ✇❤✐❝❤ ❜❡st ✜ts t❤❡ ❝❧♦✉❞ x �� ✈ ✶ ( ✈ ′ ✶ ✈ ✶ ) − ✶ ✈ ′ P ✈ ✶ ( ① . ❦ ) = ✶ ① . ❦ ● ❦ ✶ = ✶ / ■ < ✈ ✶ , ① . ❦ > θ ✶ / ■ < ✈ ✶ , ① . ❦ > ● ❦ ✶ = G � � v � � ✈ ✶ � � ① . ❦ � ❑ ❑ � � ● ✷ r ( ✈ ✶ , ① . ❦ ) ✷ ❛r❣ ♠❛① ❦ ✶ = ❛r❣ ♠❛① ✈ ✶ ∈ R ■ ✈ ✶ ∈ R ■ ✐ = ❦ ✐ = ❦ ⇒ ✈ ✶ ✐s t❤❡ ❜❡st s②♥t❤❡t✐❝ ✈❛r✐❛❜❧❡ ⇒ ✈ ✶ , ..., ✈ ◗ ❛r❡ t❤❡ ❡✐❣❡♥✈❡❝t♦rs ♦❢ ❲ = ❳❳ ′ t❤❡ ✐♥♥❡r ♣r♦❞✉❝t ♠❛tr✐① ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❧❛r❣❡st ❡✐❣❡♥✈❛❧✉❡s✿ ❲✈ q = λ q ✈ q ✷✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❋✐t t❤❡ ✈❛r✐❛❜❧❡s ❝❧♦✉❞ Odor.Intensity.before.shaking 1.0 Odor.Intensity.after.shaking Expression Attack.intensity Aroma.persistency Bitterness Acidity Aroma.intensity O.wooded O.vanilla 0.5 O.alcohol Astringency Freshness Visual.intensity O.passion Grade Dim 2 (25.14%) O.citrus Surface.feeling 0.0 O.flower O.mushroom Smoothness O.plante O.candied.fruit Oxidation O.fruity Typicity -0.5 Sweetness -1.0 -1.0 -0.5 0.0 0.5 1.0 1.5 Dim 1 (43.48%) ⇒ ❙❛♠❡ r❡♣r❡s❡♥t❛t✐♦♥✦ ❲❤❛t ❛ ✇♦♥❞❡r❢✉❧ r❡s✉❧t✦ ✷✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr♦❥❡❝t✐♦♥s✳✳✳ r ( ❆ , ❇ ) = ❝♦s ( θ ❆ , ❇ ) ❝♦s ( θ ❆ , ❇ ) ≈ ❝♦s ( θ ❍ ❆ , ❍ ❇ ) ✐❢ ✈❛r✐❛❜❧❡s ❛r❡ ✇❡❧❧ ♣r♦❥❡❝t❡❞ A H A H B H A D H D H B H D H E H C H E E H C B C ❖♥❧② ✇❡❧❧ ♣r♦❥❡❝t❡❞ ✈❛r✐❛❜❧❡s ❝❛♥ ❜❡ ✐♥t❡r♣r❡t❡❞✦ ✷✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▲✐♥❦ ❜❡t✇❡❡♥ t❤❡ t✇♦ r❡♣r❡s❡♥t❛t✐♦♥s✿ tr❛♥s✐t✐♦♥ ❢♦r♠✉❧❛❡ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � �� � � � � � � � � � � � � � � � �� � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ✷✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▲✐♥❦ ❜❡t✇❡❡♥ t❤❡ t✇♦ r❡♣r❡s❡♥t❛t✐♦♥s✿ tr❛♥s✐t✐♦♥ ❢♦r♠✉❧❛❡ • ❙✉ = ❳ ′ ❳✉ = λ ✉ • ❳❳ ′ ❳✉ = ❳ λ ✉ → ❲ ( ❳✉ ) = λ ( ❳✉ ) • ❲❋ = λ ❋ ❛♥❞ s✐♥❝❡ ❲✈ = λ ✈ t❤❡♥ ❋ ❛♥❞ ✈ ❛r❡ ❝♦❧❧✐♥❡❛r • ❙✐♥❝❡✱ || ❋ || = λ ❛♥❞ || ✈ || = ✶ ✇❡ ❤❛✈❡✿ ✶ ⇒ ● = ❳ ′ ✈ = ✶ λ ❳ ′ ❋ ✈ = λ ❋ √ √ ✶ ✶ ⇒ ❋ = ❳✉ = ✉ = λ ● λ ❳● √ √ ❑ ■ ✶ ✶ � � ❋ ✐q = ① ✐❦ ● ❦q ● ❦q = ① ✐❦ ❋ ✐q � � λ q λ q ✐ = ✶ ❦ = ✶ ❋ . q ✿ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts✱ s❝♦r❡s ● . q ✿ ❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ ✈❛r✐❛❜❧❡s ❛♥❞ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ✷✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▲✐♥❦ ❜❡t✇❡❡♥ t❤❡ t✇♦ r❡♣r❡s❡♥t❛t✐♦♥s✿ tr❛♥s✐t✐♦♥ ❢♦r♠✉❧❛❡ ❑ ■ ✶ ✶ � � ❋ ✐q = ① ✐❦ ● ❦q ● ❦q = ① ✐❦ ❋ ✐q � � λ q λ q ❦ = ✶ ✐ = ✶ ❲❤❛t ❞♦❡s ✐t ♠❡❛♥❄ ❆♥ ✐♥❞✐✈✐❞✉❛❧ ✐s ❛t t❤❡ s❛♠❡ s✐❞❡ ❛s t❤❡ ✈❛r✐❛❜❧❡s ❢♦r ✇❤✐❝❤ ✐t t❛❦❡s ❤✐❣❤ ✈❛❧✉❡s Odor.Intensity.before.shaking 1.0 Odor.Intensity.after.shaking Expression Attack.intensity Aroma.persistency Bitterness Aroma.intensity Acidity V Aub Marigny O.wooded V Font Coteaux O.vanilla S Renaudie 0.5 O.alcohol 2 S Michaud Astringency S Trotignon Freshness Visual.intensity V Font Brûlés O.passion Grade Dim 2 (25.14%) 0 O.citrus Surface.feeling O.flower V Font Domaine 0.0 Dim 2 (25.14%) S Buisse Cristal Smoothness O.mushroom O.plante O.candied.fruit Oxidation O.fruity -2 S Buisse Domaine Typicity -0.5 -4 V Aub Silex Sweetness -6 -1.0 -1.0 -0.5 0.0 0.5 1.0 1.5 -6 -4 -2 0 2 4 ✷✻ ✴ ✾✽ Dim 1 (43.48%) Dim 1 (43.48%) ❋✐❣✉r❡✿ ■♥❞✐✈✐❞✉❛❧s ❛♥❞ ✈❛r✐❛❜❧❡s r❡♣r❡s❡♥t❛t✐♦♥s

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❙✉♣♣❧❡♠❡♥t❛r② ✐♥❢♦r♠❛t✐♦♥ • ❋♦r t❤❡ ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s✿ ♣r♦❥❡❝t✐♦♥ ♦❢ s✉♣♣❧❡♠❡♥t❛r② ✈❛r✐❛❜❧❡s ♦♥ t❤❡ ❞✐♠❡♥s✐♦♥s • ❋♦r t❤❡ ✐♥❞✐✈✐❞✉❛❧s✿ ♣r♦❥❡❝t✐♦♥ • ❋♦r t❤❡ ❝❛t❡❣♦r✐❡s✿ ♣r♦❥❡❝t✐♦♥ ❛t t❤❡ ❜❛r②❝❡♥tr❡ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ✇❤♦ t❛❦❡ t❤❡ ❝❛t❡❣♦r✐❡s Odor.Intensity.before.shaking 1.0 Odor.Intensity.after.shaking Sauvignon Expression V Aub Marigny Vouvray Attack.intensity Aroma.persistency Bitterness V Font Coteaux Acidity Aroma.intensity S Renaudie O.wooded 2 S Michaud O.vanilla S Trotignon 0.5 O.alcohol V Font Brûlés Sauvignon Astringency Freshness Odor.preferene Vouvray Visual.intensity 0 O.passion Grade Dim 2 (25.14%) V Font Domaine Dim 2 (25.14%) S Buisse Cristal O.citrus Surface.feeling 0.0 O.flower Smoothness O.mushroom -2 O.plante Overall.preference O.candied.fruit Oxidation S Buisse Domaine O.fruity Typicity -4 -0.5 V Aub Silex Sweetness -6 -1.0 -6 -4 -2 0 2 4 -1.0 -0.5 0.0 0.5 1.0 1.5 Dim 1 (43.48%) Dim 1 (43.48%) ⇒ ❙✉♣♣❧❡♠❡♥t❛r② ✐♥❢♦r♠❛t✐♦♥ ❞♦ ♥♦t ❝r❡❛t❡ t❤❡ ❞✐♠❡♥s✐♦♥s ✷✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❈❤♦♦s✐♥❣ t❤❡ ♥✉♠❜❡r ♦❢ ❝♦♠♣♦♥❡♥ts 3.0 ❇❛r ♣❧♦t✱ t❡st ♦♥ ❡✐❣❡♥✈❛❧✉❡s✱ ❝♦♥✜❞❡♥❝❡ ✐♥t❡r✲ 2.5 2.0 ✈❛❧✱ ❝r♦ss✲✈❛❧✐❞❛t✐♦♥ ✭❢✉♥❝t✐♦♥s ❡st✐♠❴♥❝♣P❈❆ 1.5 ❛♥❞ ❡st✐♠❴♥❝♣ ✮✱ ❡t❝✳ 1.0 0.5 0.0 1 2 3 4 5 6 7 8 9 10 � � � � � �� � � � �� � � � ❚✇♦ ♦❜❥❡❝t✐✈❡s✿ ⇒ ■♥t❡r♣r❡t❛t✐♦♥ PCA Data Structure Noise ⇒ ❙❡♣❛r❛t❡ str✉❝t✉r❡ ❛♥❞ ♥♦✐s❡ ✷✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❡r❝❡♥t❛❣❡ ♦❢ ✈❛r✐❛♥❝❡ ♦❜t❛✐♥❡❞ ✉♥❞❡r ✐♥❞❡♣❡♥❞❡♥❝❡ ⇒ ■s t❤❡r❡ ❛ str✉❝t✉r❡ ♦♥ ♠② ❞❛t❛❄ ◆✉♠❜❡r ♦❢ ✈❛r✐❛❜❧❡s ♥❜✐♥❞ ✹ ✺ ✻ ✼ ✽ ✾ ✶✵ ✶✶ ✶✷ ✶✸ ✶✹ ✶✺ ✶✻ ✺ ✾✻✳✺ ✾✸✳✶ ✾✵✳✷ ✽✼✳✻ ✽✺✳✺ ✽✸✳✹ ✽✶✳✾ ✽✵✳✼ ✼✾✳✹ ✼✽✳✶ ✼✼✳✹ ✼✻✳✻ ✼✺✳✺ ✻ ✾✸✳✸ ✽✽✳✻ ✽✹✳✽ ✽✶✳✺ ✼✾✳✶ ✼✻✳✾ ✼✺✳✶ ✼✸✳✷ ✼✷✳✷ ✼✵✳✽ ✻✾✳✽ ✻✽✳✼ ✻✽✳✵ ✼ ✾✵✳✺ ✽✹✳✾ ✽✵✳✾ ✼✼✳✹ ✼✹✳✹ ✼✷✳✵ ✼✵✳✶ ✻✽✳✸ ✻✼✳✵ ✻✺✳✸ ✻✹✳✸ ✻✸✳✷ ✻✷✳✷ ✽ ✽✽✳✶ ✽✷✳✸ ✼✼✳✷ ✼✸✳✽ ✼✵✳✼ ✻✽✳✷ ✻✻✳✶ ✻✹✳✵ ✻✷✳✽ ✻✶✳✷ ✻✵✳✵ ✺✾✳✵ ✺✽✳✵ ✾ ✽✻✳✶ ✼✾✳✺ ✼✹✳✽ ✼✵✳✼ ✻✼✳✹ ✻✺✳✶ ✻✷✳✾ ✻✶✳✶ ✺✾✳✹ ✺✼✳✾ ✺✻✳✺ ✺✺✳✹ ✺✹✳✸ ✶✵ ✽✹✳✺ ✼✼✳✺ ✼✷✳✸ ✻✽✳✷ ✻✺✳✵ ✻✷✳✹ ✻✵✳✶ ✺✽✳✸ ✺✻✳✺ ✺✺✳✶ ✺✸✳✼ ✺✷✳✺ ✺✶✳✺ ✶✶ ✽✷✳✽ ✼✺✳✼ ✼✵✳✸ ✻✻✳✸ ✻✷✳✾ ✻✵✳✶ ✺✽✳✵ ✺✻✳✵ ✺✹✳✹ ✺✷✳✼ ✺✶✳✸ ✺✵✳✶ ✹✾✳✷ ✶✷ ✽✶✳✺ ✼✹✳✵ ✻✽✳✻ ✻✹✳✹ ✻✶✳✷ ✺✽✳✸ ✺✺✳✽ ✺✹✳✵ ✺✷✳✹ ✺✵✳✾ ✹✾✳✸ ✹✽✳✷ ✹✼✳✷ ✶✸ ✽✵✳✵ ✼✷✳✺ ✻✼✳✷ ✻✷✳✾ ✺✾✳✹ ✺✻✳✼ ✺✹✳✹ ✺✷✳✷ ✺✵✳✺ ✹✽✳✾ ✹✼✳✼ ✹✻✳✻ ✹✺✳✹ ✶✹ ✼✾✳✵ ✼✶✳✺ ✻✺✳✼ ✻✶✳✺ ✺✽✳✶ ✺✺✳✶ ✺✷✳✽ ✺✵✳✽ ✹✾✳✵ ✹✼✳✺ ✹✻✳✷ ✹✺✳✵ ✹✹✳✵ ✶✺ ✼✽✳✶ ✼✵✳✸ ✻✹✳✻ ✻✵✳✸ ✺✼✳✵ ✺✸✳✾ ✺✶✳✺ ✹✾✳✹ ✹✼✳✽ ✹✻✳✶ ✹✹✳✾ ✹✸✳✻ ✹✷✳✺ ✶✻ ✼✼✳✸ ✻✾✳✹ ✻✸✳✺ ✺✾✳✷ ✺✺✳✻ ✺✷✳✾ ✺✵✳✸ ✹✽✳✸ ✹✻✳✻ ✹✺✳✷ ✹✸✳✻ ✹✷✳✹ ✹✶✳✹ ✶✼ ✼✻✳✺ ✻✽✳✹ ✻✷✳✻ ✺✽✳✷ ✺✹✳✼ ✺✶✳✽ ✹✾✳✸ ✹✼✳✶ ✹✺✳✺ ✹✹✳✵ ✹✷✳✻ ✹✶✳✹ ✹✵✳✸ ✶✽ ✼✺✳✺ ✻✼✳✻ ✻✶✳✽ ✺✼✳✶ ✺✸✳✼ ✺✵✳✽ ✹✽✳✹ ✹✻✳✸ ✹✹✳✻ ✹✸✳✵ ✹✶✳✻ ✹✵✳✹ ✸✾✳✸ ✶✾ ✼✺✳✶ ✻✼✳✵ ✻✵✳✾ ✺✻✳✺ ✺✷✳✽ ✹✾✳✾ ✹✼✳✹ ✹✺✳✺ ✹✸✳✼ ✹✷✳✶ ✹✵✳✼ ✸✾✳✻ ✸✽✳✹ ✷✵ ✼✹✳✶ ✻✻✳✶ ✻✵✳✶ ✺✺✳✻ ✺✷✳✶ ✹✾✳✶ ✹✻✳✻ ✹✹✳✼ ✹✷✳✾ ✹✶✳✸ ✸✾✳✽ ✸✽✳✼ ✸✼✳✺ ✷✺ ✼✷✳✵ ✻✸✳✸ ✺✼✳✶ ✺✷✳✺ ✹✽✳✾ ✹✻✳✵ ✹✸✳✹ ✹✶✳✹ ✸✾✳✻ ✸✽✳✶ ✸✻✳✼ ✸✺✳✺ ✸✹✳✺ ✸✵ ✻✾✳✽ ✻✶✳✶ ✺✺✳✶ ✺✵✳✸ ✹✻✳✼ ✹✸✳✻ ✹✶✳✶ ✸✾✳✶ ✸✼✳✸ ✸✺✳✼ ✸✹✳✹ ✸✸✳✷ ✸✷✳✶ ✸✺ ✻✽✳✺ ✺✾✳✻ ✺✸✳✸ ✹✽✳✻ ✹✹✳✾ ✹✶✳✾ ✸✾✳✺ ✸✼✳✹ ✸✺✳✻ ✸✹✳✵ ✸✷✳✼ ✸✶✳✻ ✸✵✳✹ ✹✵ ✻✼✳✺ ✺✽✳✸ ✺✷✳✵ ✹✼✳✸ ✹✸✳✹ ✹✵✳✺ ✸✽✳✵ ✸✻✳✵ ✸✹✳✶ ✸✷✳✼ ✸✶✳✸ ✸✵✳✶ ✷✾✳✶ ✹✺ ✻✻✳✹ ✺✼✳✶ ✺✵✳✽ ✹✻✳✶ ✹✷✳✹ ✸✾✳✸ ✸✻✳✾ ✸✹✳✽ ✸✸✳✶ ✸✶✳✺ ✸✵✳✷ ✷✾✳✵ ✷✼✳✾ ✺✵ ✻✺✳✻ ✺✻✳✸ ✹✾✳✾ ✹✺✳✷ ✹✶✳✹ ✸✽✳✹ ✸✺✳✾ ✸✸✳✾ ✸✷✳✶ ✸✵✳✺ ✷✾✳✷ ✷✽✳✶ ✷✼✳✵ ✶✵✵ ✻✵✳✾ ✺✶✳✹ ✹✹✳✾ ✹✵✳✵ ✸✻✳✸ ✸✸✳✸ ✸✶✳✵ ✷✽✳✾ ✷✼✳✷ ✷✺✳✽ ✷✹✳✺ ✷✸✳✸ ✷✷✳✸ ❚❛❜❧❡✿ ✾✺ ✪ q✉❛♥t✐❧❡ ✐♥❡rt✐❛ ♦♥ t❤❡ t✇♦ ✜rst ❞✐♠❡♥s✐♦♥s ♦❢ ✶✵✵✵✵ P❈❆ ♦♥ ❞❛t❛ ✇✐t❤ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s ✷✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❡r❝❡♥t❛❣❡ ♦❢ ✈❛r✐❛♥❝❡ ♦❜t❛✐♥❡❞ ✉♥❞❡r ✐♥❞❡♣❡♥❞❡♥❝❡ ◆✉♠❜❡r ♦❢ ✈❛r✐❛❜❧❡s ♥❜✐♥❞ ✶✼ ✶✽ ✶✾ ✷✵ ✷✺ ✸✵ ✸✺ ✹✵ ✺✵ ✼✺ ✶✵✵ ✶✺✵ ✷✵✵ ✺ ✼✹✳✾ ✼✹✳✷ ✼✸✳✺ ✼✷✳✽ ✼✵✳✼ ✻✽✳✽ ✻✼✳✹ ✻✻✳✹ ✻✹✳✼ ✻✷✳✵ ✻✵✳✺ ✺✽✳✺ ✺✼✳✹ ✻ ✻✼✳✵ ✻✻✳✸ ✻✺✳✻ ✻✹✳✾ ✻✷✳✸ ✻✵✳✹ ✺✽✳✾ ✺✼✳✻ ✺✺✳✽ ✺✷✳✾ ✺✶✳✵ ✹✾✳✵ ✹✼✳✽ ✼ ✻✶✳✸ ✻✵✳✼ ✺✾✳✼ ✺✾✳✶ ✺✻✳✹ ✺✹✳✸ ✺✷✳✻ ✺✶✳✹ ✹✾✳✺ ✹✻✳✹ ✹✹✳✻ ✹✷✳✹ ✹✶✳✷ ✽ ✺✼✳✵ ✺✻✳✷ ✺✺✳✹ ✺✹✳✺ ✺✶✳✽ ✹✾✳✼ ✹✼✳✽ ✹✻✳✼ ✹✹✳✻ ✹✶✳✻ ✸✾✳✽ ✸✼✳✻ ✸✻✳✹ ✾ ✺✸✳✻ ✺✷✳✺ ✺✶✳✽ ✺✶✳✷ ✹✽✳✶ ✹✺✳✾ ✹✹✳✹ ✹✷✳✾ ✹✶✳✵ ✸✽✳✵ ✸✻✳✶ ✸✹✳✵ ✸✷✳✼ ✶✵ ✺✵✳✻ ✹✾✳✽ ✹✾✳✵ ✹✽✳✸ ✹✺✳✷ ✹✷✳✾ ✹✶✳✹ ✹✵✳✶ ✸✽✳✵ ✸✺✳✵ ✸✸✳✷ ✸✶✳✵ ✷✾✳✽ ✶✶ ✹✽✳✶ ✹✼✳✷ ✹✻✳✺ ✹✺✳✽ ✹✷✳✽ ✹✵✳✻ ✸✾✳✵ ✸✼✳✼ ✸✺✳✻ ✸✷✳✻ ✸✵✳✽ ✷✽✳✼ ✷✼✳✺ ✶✷ ✹✻✳✷ ✹✺✳✷ ✹✹✳✹ ✹✸✳✽ ✹✵✳✼ ✸✽✳✺ ✸✻✳✾ ✸✺✳✺ ✸✸✳✺ ✸✵✳✺ ✷✽✳✽ ✷✻✳✼ ✷✺✳✺ ✶✸ ✹✹✳✹ ✹✸✳✹ ✹✷✳✽ ✹✶✳✾ ✸✾✳✵ ✸✻✳✽ ✸✺✳✶ ✸✸✳✾ ✸✶✳✽ ✷✽✳✽ ✷✼✳✶ ✷✺✳✵ ✷✸✳✾ ✶✹ ✹✷✳✾ ✹✷✳✵ ✹✶✳✸ ✹✵✳✹ ✸✼✳✹ ✸✺✳✷ ✸✸✳✻ ✸✷✳✸ ✸✵✳✹ ✷✼✳✹ ✷✺✳✼ ✷✸✳✻ ✷✷✳✹ ✶✺ ✹✶✳✻ ✹✵✳✼ ✸✾✳✽ ✸✾✳✶ ✸✻✳✷ ✸✹✳✵ ✸✷✳✹ ✸✶✳✶ ✷✾✳✵ ✷✻✳✵ ✷✹✳✸ ✷✷✳✹ ✷✶✳✷ ✶✻ ✹✵✳✹ ✸✾✳✺ ✸✽✳✼ ✸✼✳✾ ✸✺✳✵ ✸✷✳✽ ✸✶✳✶ ✷✾✳✽ ✷✼✳✾ ✷✹✳✾ ✷✸✳✷ ✷✶✳✷ ✷✵✳✶ ✶✼ ✸✾✳✹ ✸✽✳✺ ✸✼✳✻ ✸✻✳✾ ✸✸✳✽ ✸✶✳✼ ✸✵✳✶ ✷✽✳✽ ✷✻✳✽ ✷✸✳✾ ✷✷✳✷ ✷✵✳✸ ✶✾✳✷ ✶✽ ✸✽✳✸ ✸✼✳✹ ✸✻✳✼ ✸✺✳✽ ✸✷✳✾ ✸✵✳✼ ✷✾✳✶ ✷✼✳✽ ✷✺✳✾ ✷✷✳✾ ✷✶✳✸ ✶✾✳✹ ✶✽✳✸ ✶✾ ✸✼✳✹ ✸✻✳✺ ✸✺✳✽ ✸✹✳✾ ✸✷✳✵ ✷✾✳✾ ✷✽✳✸ ✷✼✳✵ ✷✺✳✶ ✷✷✳✷ ✷✵✳✺ ✶✽✳✻ ✶✼✳✺ ✷✵ ✸✻✳✼ ✸✺✳✽ ✸✹✳✾ ✸✹✳✷ ✸✶✳✸ ✷✾✳✶ ✷✼✳✺ ✷✻✳✷ ✷✹✳✸ ✷✶✳✹ ✶✾✳✽ ✶✽✳✵ ✶✻✳✾ ✷✺ ✸✸✳✺ ✸✷✳✺ ✸✶✳✽ ✸✶✳✶ ✷✽✳✶ ✷✻✳✵ ✷✹✳✺ ✷✸✳✸ ✷✶✳✹ ✶✽✳✻ ✶✼✳✵ ✶✺✳✷ ✶✹✳✷ ✸✵ ✸✶✳✷ ✸✵✳✸ ✷✾✳✺ ✷✽✳✽ ✷✻✳✵ ✷✸✳✾ ✷✷✳✸ ✷✶✳✶ ✶✾✳✸ ✶✻✳✻ ✶✺✳✶ ✶✸✳✹ ✶✷✳✺ ✸✺ ✷✾✳✺ ✷✽✳✻ ✷✼✳✾ ✷✼✳✶ ✷✹✳✸ ✷✷✳✷ ✷✵✳✼ ✶✾✳✻ ✶✼✳✽ ✶✺✳✷ ✶✸✳✼ ✶✷✳✶ ✶✶✳✶ ✹✵ ✷✽✳✶ ✷✼✳✸ ✷✻✳✺ ✷✺✳✽ ✷✸✳✵ ✷✶✳✵ ✶✾✳✺ ✶✽✳✹ ✶✻✳✻ ✶✹✳✶ ✶✷✳✼ ✶✶✳✶ ✶✵✳✷ ✹✺ ✷✼✳✵ ✷✻✳✶ ✷✺✳✹ ✷✹✳✼ ✷✶✳✾ ✷✵✳✵ ✶✽✳✺ ✶✼✳✹ ✶✺✳✼ ✶✸✳✷ ✶✶✳✽ ✶✵✳✸ ✾✳✹ ✺✵ ✷✻✳✶ ✷✺✳✸ ✷✹✳✻ ✷✸✳✽ ✷✶✳✶ ✶✾✳✶ ✶✼✳✼ ✶✻✳✻ ✶✹✳✾ ✶✷✳✺ ✶✶✳✶ ✾✳✻ ✽✳✼ ✶✵✵ ✷✶✳✺ ✷✵✳✼ ✶✾✳✾ ✶✾✳✸ ✶✻✳✼ ✶✹✳✾ ✶✸✳✻ ✶✷✳✺ ✶✶✳✵ ✽✳✾ ✼✳✼ ✻✳✹ ✺✳✼ ❚❛❜❧❡✿ ✾✺ ✪ q✉❛♥t✐❧❡ ✐♥❡rt✐❛ ♦♥ t❤❡ t✇♦ ✜rst ❞✐♠❡♥s✐♦♥s ♦❢ ✶✵✵✵✵ P❈❆ ♦♥ ❞❛t❛ ✇✐t❤ ✐♥❞❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡s ✸✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ◗✉❛❧✐t② ♦❢ t❤❡ r❡♣r❡s❡♥t❛t✐♦♥✿ ❝♦s ✷ • ❋♦r t❤❡ ✈❛r✐❛❜❧❡s✿ ♦♥❧② ✇❡❧❧ ♣r♦❥❡❝t❡❞ ✈❛r✐❛❜❧❡s ✭❤✐❣❤ ❝♦s ✷ ❜❡t✇❡❡♥ t❤❡ ✈❛r✐❛❜❧❡ ❛♥❞ ✐ts ♣r♦❥❡❝t✐♦♥✮ ❝❛♥ ❜❡ ✐♥t❡r♣r❡t❡❞✦ r♦✉♥❞✭r❡s✳♣❝❛✩✈❛r✩❝♦s✷✱✷✮ ❉✐♠✳✶ ❉✐♠✳✷ ❖❞♦r✳■♥t❡♥s✐t②✳❜❡❢♦r❡✳s❤❛❦✐♥❣ ✵✳✵✶ ✵✳✾✹ ❖❞♦r✳■♥t❡♥s✐t②✳❛❢t❡r✳s❤❛❦✐♥❣ ✵✳✵✶ ✵✳✽✾ ❊①♣r❡ss✐♦♥ ✵✳✶✶ ✵✳✼✶ • ❋♦r t❤❡ ✐♥❞✐✈✐❞✉❛❧s✿ ✭s❛♠❡ ✐❞❡❛✮ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ❝❛♥ ♦♥❧② ❜❡ ✐♥t❡r♣r❡t❡❞ ❢♦r ✇❡❧❧ ♣r♦❥❡❝t❡❞ ✐♥❞✐✈✐❞✉❛❧s r♦✉♥❞✭r❡s✳♣❝❛✩✐♥❞✩❝♦s✷✱✷✮ ❉✐♠✳✶ ❉✐♠✳✷ ❙ ▼✐❝❤❛✉❞ ✵✳✻✷ ✵✳✵✼ ❙ ❘❡♥❛✉❞✐❡ ✵✳✼✸ ✵✳✶✺ ❙ ❚r♦t✐❣♥♦♥ ✵✳✼✽ ✵✳✵✼ ✸✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❈♦♥tr✐❜✉t✐♦♥ ⇒ ❈♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ t❤❡ ❞✐♠❡♥s✐♦♥ ✭♣❡r❝❡♥t❛❣❡ ♦❢ ✈❛r✐❛❜✐❧✐t②✮✿ ❋ ✷ ❋ ✷ • ❢♦r ❡❛❝❤ ✐♥❞✐✈✐❞✉❛❧✿ ❈tr q ( ✐ ) = ✐q ✐q = ✐q � ■ ✐ = ✶ ❋ ✷ λ q ⇒ ■♥❞✐✈✐❞✉❛❧s ✇✐t❤ ❛ ❧❛r❣❡ ❝♦♦r❞✐♥❛t❡ ❝♦♥tr✐❜✉t❡ t❤❡ ♠♦st r♦✉♥❞✭r❡s✳♣❝❛✩✐♥❞✩❝♦♥tr✐❜✱✷✮ ❉✐♠✳✶ ❉✐♠✳✷ ❙ ▼✐❝❤❛✉❞ ✶✺✳✹✾ ✸✳✶✵ ❙ ❘❡♥❛✉❞✐❡ ✶✺✳✺✻ ✺✳✺✻ ❙ ❚r♦t✐❣♥♦♥ ✶✺✳✹✻ ✷✳✹✸ ● ✷ λ q = r ( ① . ❦ , ✈ q ) ✷ ❦q • ❢♦r ❡❛❝❤ ✈❛r✐❛❜❧❡✿ ❈tr q ( ❦ ) = λ q ⇒ ❱❛r✐❛❜❧❡s ❤✐❣❤❧② ❝♦rr❡❧❛t❡❞ ✇✐t❤ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ❝♦♥tr✐❜✉t❡ t❤❡ ♠♦st ✸✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❉❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❞✐♠❡♥s✐♦♥s ❇② t❤❡ ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s✿ • ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❡❛❝❤ ✈❛r✐❛❜❧❡ ❛♥❞ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ♦❢ r❛♥❦ q ✐s ❝❛❧❝✉❧❛t❡❞ • ❝♦rr❡❧❛t✐♦♥ ❝♦❡✣❝✐❡♥ts ❛r❡ s♦rt❡❞ ❛♥❞ s✐❣♥✐✜❝❛♥t ♦♥❡s ❛r❡ ❣✐✈❡♥ ❃ ❞✐♠❞❡s❝✭r❡s✳♣❝❛✮ ✩❉✐♠✳✶✩q✉❛♥t✐ ✩❉✐♠✳✷✩q✉❛♥t✐ ❝♦rr ♣✳✈❛❧✉❡ ❝♦rr ♣✳✈❛❧✉❡ ❖✳❝❛♥❞✐❡❞✳❢r✉✐t ✵✳✾✸ ✾✳✺❡✲✵✺ ❖❞♦r✳■♥t❡♥s✐t②✳❜❡❢♦r❡✳s❤❛❦✐♥❣ ✵✳✾✼ ✸✳✶❡✲✵✻ ●r❛❞❡ ✵✳✾✸ ✶✳✷❡✲✵✹ ❖❞♦r✳■♥t❡♥s✐t②✳❛❢t❡r✳s❤❛❦✐♥❣ ✵✳✾✺ ✸✳✻❡✲✵✺ ❙✉r❢❛❝❡✳❢❡❡❧✐♥❣ ✵✳✽✾ ✺✳✺❡✲✵✹ ❆tt❛❝❦✳✐♥t❡♥s✐t② ✵✳✽✺ ✶✳✼❡✲✵✸ ❚②♣✐❝✐t② ✵✳✽✻ ✶✳✹❡✲✵✸ ❊①♣r❡ss✐♦♥ ✵✳✽✹ ✷✳✷❡✲✵✸ ❖✳♠✉s❤r♦♦♠ ✵✳✽✹ ✷✳✸❡✲✵✸ ❆r♦♠❛✳♣❡rs✐st❡♥❝② ✵✳✼✺ ✶✳✸❡✲✵✷ ❱✐s✉❛❧✳✐♥t❡♥s✐t② ✵✳✽✸ ✸✳✶❡✲✵✸ ❇✐tt❡r♥❡ss ✵✳✼✶ ✷✳✸❡✲✵✷ ✳✳✳ ✳✳✳ ✳✳✳ ❆r♦♠❛✳✐♥t❡♥s✐t② ✵✳✻✻ ✹✳✵❡✲✵✷ ❖✳♣❧❛♥t❡ ✲✵✳✽✼ ✶✳✵❡✲✵✸ ❖✳❢❧♦✇❡r ✲✵✳✽✾ ✹✳✾❡✲✵✹ ❖✳♣❛ss✐♦♥ ✲✵✳✾✵ ✹✳✺❡✲✵✹ ❋r❡s❤♥❡ss ✲✵✳✾✶ ✷✳✾❡✲✵✹ ❙✇❡❡t♥❡ss ✲✵✳✼✽ ✽✳✵❡✲✵✸ ✸✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❉❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❞✐♠❡♥s✐♦♥s ❇② t❤❡ ❝❛t❡❣♦r✐❝❛❧ ✈❛r✐❛❜❧❡s✿ • P❡r❢♦r♠ ❛ ♦♥❡✲✇❛② ❛♥❛❧②s✐s ♦❢ ✈❛r✐❛♥❝❡ ✇✐t❤ t❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ✭ ❋ . q ✮ ❡①♣❧❛✐♥❡❞ ❜② t❤❡ ❝❛t❡❣♦r✐❝❛❧ ✈❛r✐❛❜❧❡ • ❛ ❋✲t❡st ❜② ✈❛r✐❛❜❧❡ • ❢♦r ❡❛❝❤ ❝❛t❡❣♦r②✱ ❛ ❙t✉❞❡♥t✬s t ✲t❡st t♦ ❝♦♠♣❛r❡ t❤❡ ❛✈❡r❛❣❡ ♦❢ t❤❡ ❝❛t❡❣♦r② ✇✐t❤ t❤❡ ❣❡♥❡r❛❧ ♠❡❛♥ ❃ ❞✐♠❞❡s❝✭r❡s✳♣❝❛✮ ❉✐♠✳✶✩q✉❛❧✐ ❘✷ ♣✳✈❛❧✉❡ ▲❛❜❡❧ ✵✳✽✼✹ ✼✳✸✵❡✲✵✺ ❉✐♠✳✶✩❝❛t❡❣♦r② ❊st✐♠❛t❡ ♣✳✈❛❧✉❡ ❱♦✉✈r❛② ✸✳✷✵✸ ✼✳✸✵❡✲✵✺ ❙❛✉✈✐❣♥♦♥ ✲✸✳✷✵✸ ✼✳✸✵❡✲✵✺ ✸✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr❛❝t✐❝❡ ✇✐t❤ ❘ ✶ ❈❤♦♦s❡ ❛❝t✐✈❡ ✈❛r✐❛❜❧❡s ✷ ❙❝❛❧❡ ♦r ♥♦t t❤❡ ✈❛r✐❛❜❧❡s ✸ P❡r❢♦r♠ P❈❆ ✹ ❈❤♦♦s❡ t❤❡ ♥✉♠❜❡r ♦❢ ❞✐♠❡♥s✐♦♥s t♦ ✐♥t❡r♣r❡t ✺ ❙✐♠✉❧t❛♥❡♦✉s❧② ✐♥t❡r♣r❡t t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❛♥❞ ✈❛r✐❛❜❧❡s ❣r❛♣❤s ✻ ❯s❡ ✐♥❞✐❝❛t♦rs t♦ ❡♥r✐❝❤ t❤❡ ✐♥t❡r♣r❡t❛t✐♦♥ ❧✐❜r❛r②✭❋❛❝t♦▼✐♥❡❘✮ ❊①♣❡rt ❁✲ r❡❛❞✳t❛❜❧❡✭✧❤tt♣✿✴✴❢❛❝t♦♠✐♥❡r✳❢r❡❡✳❢r✴✉s❡❘✷✵✶✵✴❊①♣❡rt❴✇✐♥❡✳❝s✈✧✱ ❤❡❛❞❡r❂❚❘❯❊✱ s❡♣❂✧❀✧✱r♦✇✳♥❛♠❡s❂✶✮ r❡s✳♣❝❛ ❁✲ P❈❆✭❊①♣❡rt✱s❝❛❧❡❂❚✱q✉❛♥t✐✳s✉♣❂✷✾✿✸✵✱q✉❛❧✐✳s✉♣❂✶✮ r❡s✳♣❝❛ ①✶✶✭✮ ❜❛r♣❧♦t✭r❡s✳♣❝❛✩❡✐❣❬✱✶❪✱♠❛✐♥❂✧❊✐❣❡♥✈❛❧✉❡s✧✱♥❛♠❡s✳❛r❣❂✶✿♥r♦✇✭r❡s✳♣❝❛✩❡✐❣✮✮ ♣❧♦t✳P❈❆✭r❡s✳♣❝❛✱❤❛❜✐❧❧❛❣❡❂✶✮ r❡s✳♣❝❛✩✐♥❞✩❝♦♦r❞ r❡s✳♣❝❛✩✐♥❞✩❝♦s✷ r❡s✳♣❝❛✩✐♥❞✩❝♦♥tr✐❜ ♣❧♦t✳P❈❆✭r❡s✳♣❝❛✱❛①❡s❂❝✭✸✱✹✮✱❤❛❜✐❧❧❛❣❡❂✶✮ ❞✐♠❞❡s❝✭r❡s✳♣❝❛✮ ✇r✐t❡✳✐♥❢✐❧❡✭r❡s✳♣❝❛✱❢✐❧❡❂✧♠②❴❋❛❝t♦▼✐♥❡❘❴r❡s✉❧ts✳❝s✈✧✮ ★t♦ ❡①♣♦rt ❛ ❧✐st ✸✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr❛❝t✐❝❡ ✇✐t❤ ●❯■ s♦✉r❝❡✭✧❤tt♣✿✴✴❢❛❝t♦♠✐♥❡r✳❢r❡❡✳❢r✴✐♥st❛❧❧✲❢❛❝t♦✳r✧✮ ✸✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❍❛♥❞❧✐♥❣ ♠✐ss✐♥❣ ✈❛❧✉❡s✿ ♠✐ss▼❉❆ ♣❛❝❦❛❣❡ ⇒ ❖❜t❛✐♥ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ❢r♦♠ ♦❜s❡r✈❡❞ ❞❛t❛ ✇✐t❤ ❛♥ ❊▼✲t②♣❡ ❛❧❣♦r✐t❤♠ • ■♠♣✉t❡ ♠✐ss✐♥❣ ✈❛❧✉❡s ✇✐t❤ P❈❆ ✉s✐♥❣ ✐♠♣✉t❡P❈❆ ❢✉♥❝t✐♦♥ ✭t✉♥✐♥❣ ♣❛r❛♠❡t❡r✿ ♥✉♠❜❡r ♦❢ ❝♦♠♣♦♥❡♥ts✮ • P❡r❢♦r♠ t❤❡ ✉s✉❛❧ P❈❆ ♦♥ t❤❡ ❝♦♠♣❧❡t❡❞ ❞❛t❛ s❡t ❧✐❜r❛r②✭♠✐ss▼❉❆✮ ❞❛t❛✭♦r❛♥❣❡✮ ♥❜✳❞✐♠ ❁✲ ❡st✐♠❴♥❝♣P❈❆✭♦r❛♥❣❡✱♥❝♣✳♠❛①❂✺✮ r❡s✳❝♦♠♣ ❁✲ ✐♠♣✉t❡P❈❆✭♦r❛♥❣❡✱♥❝♣❂✷✮ r❡s✳♣❝❛ ❁✲ P❈❆✭r❡s✳❝♦♠♣✩❝♦♠♣❧❡t❡❖❜s✮ ✸✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼❈❆✿ ♣r♦❜❧❡♠s ✲ ♦❜❥❡❝t✐✈❡s • ■♥❞✐✈✐❞✉❛❧s st✉❞②✿ s✐♠✐❧❛r✐t② ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ✭❢♦r ❛❧❧ t❤❡ ✈❛r✐❛❜❧❡s✮ → ♣❛rt✐t✐♦♥ ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ■♥❞✐✈✐❞✉❛❧s ❛r❡ ❞✐✛❡r❡♥t ✐❢ t❤❡② ❞♦♥✬t t❛❦❡ t❤❡ s❛♠❡ ❧❡✈❡❧s • ❱❛r✐❛❜❧❡s st✉❞②✿ ✜♥❞ s♦♠❡ s②♥t❤❡t✐❝ ✈❛r✐❛❜❧❡s ✭❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s t❤❛t s✉♠ ✉♣ ❝❛t❡❣♦r✐❝❛❧ ✈❛r✐❛❜❧❡s✮❀ ❧✐♥❦ ❜❡t✇❡❡♥ ✈❛r✐❛❜❧❡s ⇒ ❧❡✈❡❧s st✉❞② • ❈❛t❡❣♦r✐❡s st✉❞②✿ • t✇♦ ❧❡✈❡❧s ♦❢ ❞✐✛❡r❡♥t ✈❛r✐❛❜❧❡s ❛r❡ s✐♠✐❧❛r ✐❢ ✐♥❞✐✈✐❞✉❛❧s t❤❛t t❛❦❡ t❤❡s❡ ❧❡✈❡❧s ❛r❡ t❤❡ s❛♠❡ ✭❡①✿ ✻✺ ②❡❛rs ❛♥❞ r❡t✐r❡❞✮ • t✇♦ ❧❡✈❡❧s ❛r❡ s✐♠✐❧❛r ✐❢ ✐♥❞✐✈✐❞✉❛❧s t❛❦✐♥❣ t❤❡s❡ ❧❡✈❡❧s ❜❡❤❛✈❡ t❤❡ s❛♠❡ ✇❛②✱ t❤❡② t❛❦❡ t❤❡ s❛♠❡ ❧❡✈❡❧s ❢♦r t❤❡ ♦t❤❡r ✈❛r✐❛❜❧❡s ✭❡①✿ ✻✵ ②❡❛rs ❛♥❞ ✻✺ ②❡❛rs✮ • ▲✐♥❦ ❜❡t✇❡❡♥ t❤❡s❡ st✉❞✐❡s✿ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ t❤❡ ❣r♦✉♣s ♦❢ ✐♥❞✐✈✐❞✉❛❧s ❜② t❤❡ ❧❡✈❡❧s ✭❡①✿ ❡①❡❝✉t✐✈❡ ❞②♥❛♠✐❝ ✇♦♠❡♥✮ ✸✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼❈❆✿ ❛ P❈❆ ♦♥ ❛♥ ✐♥❞✐❝❛t♦r ♠❛tr✐① • ❇✐♥❛r② ❝♦❞✐♥❣ ♦❢ t❤❡ ❢❛❝t♦rs✿ ❛ ❢❛❝t♦r ✇✐t❤ ❑ ❥ ❧❡✈❡❧s → ❑ ❥ ❝♦❧✉♠♥s ❝♦♥t❛✐♥✐♥❣ ❜✐♥❛r② ✈❛❧✉❡s✱ ❛❧s♦ ❝❛❧❧❡❞ ❞✉♠♠② ✈❛r✐❛❜❧❡s variable j variable J variable 1 1 individuals 0 1 0 0 0 0 0 1 0 ❑ ❥ ❏ ❞ ✷ ( ✐ , ✐ ′ ) = ■ ✶ � � ( ① ✐❦ − ① ✐ ′ ❦ ) ✷ ❏ ■ ❦ ❥ = ✶ ❦ = ✶ ✸✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼❈❆✿ t❤❡ s✉♣❡r✐♠♣♦s❡❞ r❡♣r❡s❡♥t❛t✐♦♥ ■ ✶ ❑ ① ✐❦ � ✶ ① ✐❦ � ❋ ✐q = ❏ ● ❦q ● ❦q = ❋ ✐q � � λ q ■ ❦ λ q ❦ = ✶ ✐ = ✶ ⇒ ■♥❞✐✈✐❞✉❛❧ ✐ ❛t t❤❡ ❜❛r②❝❡♥t❡r ⇒ ▲❡✈❡❧ ❦ ❛t t❤❡ ❜❛r②❝❡♥t❡r ♦❢ ♦❢ ✐ts ❧❡✈❡❧s t❤❡ ✐♥❞✐✈✐❞✉❛❧s ✇❤♦ t❛❦❡ t❤✐s ❧❡✈❡❧ tea shop 2 unpackaged p_upscale Dim 2 (8.103%) ● ● ● ● ● ● ● ● 1 ● green ● dinner ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● black ● ● ● ● ● ● lemon tearoom ● ● ● ● ● ● ● ● Not.friends ● ● ● No.sugar ● ● ● ● Not.resto Not.breakfast Not.work ● ● Not.tea time ● ● ● ● chain store+tea shop ● Not.lunch alone ● ● Not.evening Not.pub ● ● ● ● ● ● always tea bag+unpackaged ● ● ● ● home ● ● other Not.always ● ● ● ● ● Not.home ● ● ● Not.dinner ● ● evening ● Not.tearoom ● ● ● ● friends tea time ● ● ● ● ● ● ● ● ● ● 0 ● ● ● ● ● ● ● breakfast ● ● ● pub ● ● ● ● ● ● ● ● sugar ● ● ● ● ● ● ● ● ● ● ● ● ● ● p_variable ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● p_cheap ● ● ● ● ● ● ● ● ● Earl Grey ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● work ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● milk ● ● ● ● ● ● ● lunch ● ● ● ● p_branded chain store tea bag ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● resto ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● p_private label ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● p_unknown −1 −1 0 1 2 ✹✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ✶ ❉❛t❛ ✲ ■ss✉❡s ✷ ❈♦♠♠♦♥ ❙tr✉❝t✉r❡ ✸ ●r♦✉♣s ❙t✉❞② ✹ P❛rt✐❛❧ ❆♥❛❧②s❡s ✺ ❊①❛♠♣❧❡ ✧❉♦✐♥❣ ❛ ❞❛t❛ ❛♥❛❧②s✐s✱ ✐♥ ❣♦♦❞ ♠❛t❤❡♠❛t✐❝s✱ ✐s s✐♠♣❧② s❡❛r❝❤✐♥❣ ❡✐❣❡♥✈❡❝t♦rs✱ ❛❧❧ t❤❡ s❝✐❡♥❝❡ ♦❢ ✐t ✭t❤❡ ❛rt✮ ✐s ❥✉st t♦ ✜♥❞ t❤❡ r✐❣❤t ♠❛tr✐① t♦ ❞✐❛❣♦♥❛❧✐③❡✧ ❇❡♥③é❝r✐ ✹✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼✉❧t✐✇❛② ❞❛t❛ s❡t ❊①❛♠♣❧❡s ✇✐t❤ ❝♦♥t✐♥✉♦✉s ❛♥❞✴♦r ❝❛t❡❣♦r✐❝❛❧ s❡ts ♦❢ ✈❛r✐❛❜❧❡s✿ • ❣❡♥♦♠✐❝✿ ❉◆❆✱ ♣r♦t❡✐♥ • s❡♥s♦r② ❛♥❛❧②s✐s✿ s❡♥s♦r✐❛❧✱ ♣❤②s✐❝♦✲❝❤❡♠✐❝❛❧ • s✉r✈❡②✿ st✉❞❡♥t ❤❡❛❧t❤ ✭❛❞❞✐❝t❡❞ ❝♦♥s✉♠♣t✐♦♥s✱ ♣s②❝❤♦❧♦❣✐❝❛❧ ❝♦♥❞✐t✐♦♥s✱ s❧❡❡♣✱ ✐❞❡♥t✐✜❝❛t✐♦♥✱ ❡t❝✳✮ • ❡❝♦♥♦♠②✿ ❡❝♦♥♦♠✐❝ ✐♥❞✐❝❛t♦rs ❢♦r ❝♦✉♥tr✐❡s ❜② ②❡❛r ✹✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❊①❛♠♣❧❡✿ ❣❧✐♦♠❛s ❜r❛✐♥ t✉♠♦rs Gliomas: Brain tumors, WHO classification - astrocytoma (A) ……….……… x5 - oligodendroglioma (O) ……… x8 43 tumor samples - oligo-astrocytoma (OA) …… x6 - glioblastoma (GBM) ………… x24 (Bredel et al., 2005) • ❚r❛♥s❝r✐♣t✐♦♥❛❧ ♠♦❞✐✜❝❛t✐♦♥ ✭❘◆❆✮✱ ♠✐❝r♦❛rr❛②s✿ ✹✽✾ ✈❛r✐❛❜❧❡s • ❉❛♠❛❣❡ t♦ ❉◆❆ ✭❈●❍ ❛rr❛②✮✿ ✶✶✸ ✈❛r✐❛❜❧❡s <Transcriptome> <Genome alteration> 1 j 2 J 2 1 j 1 J 1 1 s r o i m u T I ‘-omics’ data ✹✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❖❜❥❡❝t✐✈❡s • ❙t✉❞② t❤❡ s✐♠✐❧❛r✐t✐❡s ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ✇✐t❤ r❡s♣❡❝t t♦ ❛❧❧ t❤❡ ✈❛r✐❛❜❧❡s • ❙t✉❞② t❤❡ ❧✐♥❡❛r r❡❧❛t✐♦♥s❤✐♣s ❜❡t✇❡❡♥ ✈❛r✐❛❜❧❡s ⇒ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ str✉❝t✉r❡ ♦♥ t❤❡ ❞❛t❛ ✭❜❛❧❛♥❝✐♥❣ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❡❛❝❤ ❣r♦✉♣✮ • ❋✐♥❞ t❤❡ ❝♦♠♠♦♥ str✉❝t✉r❡ ✇✐t❤ r❡s♣❡❝t t♦ ❛❧❧ t❤❡ ❣r♦✉♣s ✲ ❤✐❣❤❧✐❣❤t t❤❡ s♣❡❝✐✜❝✐t✐❡s ♦❢ ❡❛❝❤ ❣r♦✉♣ • ❈♦♠♣❛r❡ t❤❡ t②♣♦❧♦❣✐❡s ♦❜t❛✐♥❡❞ ❢r♦♠ ❡❛❝❤ ❣r♦✉♣ ♦❢ ✈❛r✐❛❜❧❡s ✭s❡♣❛r❛t❡ ❛♥❛❧②s❡s✮ ✹✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❇❛❧❛♥❝✐♥❣ t❤❡ ❣r♦✉♣s ♦❢ ✈❛r✐❛❜❧❡s ▼❋❆ ✐s ❛ ✇❡✐❣❤t❡❞ P❈❆✿ • ❝♦♠♣✉t❡ t❤❡ ✜rst ❡✐❣❡♥✈❛❧✉❡ λ ❥ ✶ ♦❢ ❡❛❝❤ ❣r♦✉♣ ♦❢ ✈❛r✐❛❜❧❡s • ♣❡r❢♦r♠ ❛ ❣❧♦❜❛❧ P❈❆ ♦♥ t❤❡ ✇❡✐❣❤t❡❞ ❞❛t❛ t❛❜❧❡✿    ❳ ✶ ; ❳ ✷ ; ... ; ❳ ❏  � � � λ ✶ λ ✷ λ ❏ ✶ ✶ ✶ ⇒ ❙❛♠❡ ✐❞❡❛ ❛s ✐♥ P❈❆ ✇❤❡♥ ✈❛r✐❛❜❧❡s ❛r❡ st❛♥❞❛r❞✐③❡❞✿ ✈❛r✐❛❜❧❡s ❛r❡ ✇❡✐❣❤t❡❞ t♦ ❝♦♠♣✉t❡ ❞✐st❛♥❝❡s ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ✐ ❛♥❞ ✐ ′ 8 variables 2 var highly � correlated � ′ ✹✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❇❛❧❛♥❝✐♥❣ t❤❡ ❣r♦✉♣s ♦❢ ✈❛r✐❛❜❧❡s ❚❤✐s ✇❡✐❣❤t✐♥❣ ❛❧❧♦✇s t❤❛t✿ • s❛♠❡ ✇❡✐❣❤t ❢♦r ❛❧❧ t❤❡ ✈❛r✐❛❜❧❡s ♦❢ ♦♥❡ ❣r♦✉♣✿ t❤❡ str✉❝t✉r❡ ♦❢ t❤❡ ❣r♦✉♣ ✐s ♣r❡s❡r✈❡❞ • ❢♦r ❡❛❝❤ ❣r♦✉♣ t❤❡ ✈❛r✐❛♥❝❡ ♦❢ t❤❡ ♠❛✐♥ ❞✐♠❡♥s✐♦♥ ♦❢ ✈❛r✐❛❜✐❧✐t② ✭✜rst ❡✐❣❡♥✈❛❧✉❡✮ ✐s ❡q✉❛❧ t♦ ✶ • ♥♦ ❣r♦✉♣ ❝❛♥ ❣❡♥❡r❛t❡ ❜② ✐ts❡❧❢ t❤❡ ✜rst ❣❧♦❜❛❧ ❞✐♠❡♥s✐♦♥ • ❛ ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ ❣r♦✉♣ ✇✐❧❧ ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ ♠♦r❡ ❞✐♠❡♥s✐♦♥s t❤❛♥ ❛ ♦♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❣r♦✉♣ ✹✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ■♥❞✐✈✐❞✉❛❧s ❛♥❞ ✈❛r✐❛❜❧❡s r❡♣r❡s❡♥t❛t✐♦♥s A 2 GBM ● ● O OA ● ● 1 ● ● ● O ● ● ● ● ● ● GBM ● ● ● ● ● ● ● ● Dimension 2 (13.51%) ● ● ● ● ● ● 0 ● ● ● ● ● ● ● OA ● A −1 ● ● ● ● ● ● ● −2 ● −3 ● −2 −1 0 1 2 3 Dimension 1 (20.99%) ❙❛♠❡ r❡♣r❡s❡♥t❛t✐♦♥s ❛♥❞ s❛♠❡ ✐♥t❡r♣r❡t❛t✐♦♥ ❛s ✐♥ P❈❆ ✹✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ●r♦✉♣s st✉❞② ⇒ ❙②♥t❤❡t✐❝ ❝♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❣r♦✉♣s ⇒ ❆r❡ t❤❡ r❡❧❛t✐✈❡ ♣♦s✐t✐♦♥s ♦❢ ✐♥❞✐✈✐❞✉❛❧s ❣❧♦❜❛❧❧② s✐♠✐❧❛r ❢r♦♠ ♦♥❡ ❣r♦✉♣ t♦ ❛♥♦t❤❡r❄ ❆r❡ t❤❡ ♣❛rt✐❛❧ ❝❧♦✉❞s s✐♠✐❧❛r❄ ⇒ ❉♦ t❤❡ ❣r♦✉♣s ❜r✐♥❣ t❤❡ s❛♠❡ ✐♥❢♦r♠❛t✐♦♥❄ ✹✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❙✐♠✐❧❛r✐t② ❜❡t✇❡❡♥ t✇♦ ❣r♦✉♣s ▼❡❛s✉r❡ ♦❢ s✐♠✐❧❛r✐t② ❜❡t✇❡❡♥ ❣r♦✉♣s ❑ ❥ ❛♥❞ ❑ ♠ ✿    ① . ❦ , ① . ❧ � � ❝♦✈ ✷ L ❣ ( ❑ ❥ , ❑ ♠ ) =  � � λ ❦ λ ❧ ❦ ∈ ❑ ❥ ❧ ∈ ❑ ♠ ✶ ✶ ▼❋❆ ❂ ✇❡✐❣❤t❡❞ P❈❆ ⇒ ✜rst ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ♦❢ ▼❋❆ ♠❛①✐♠✐③❡s   ❏ ❏  ① . ❦ � � � ❝♦✈ ✷ L ❣ ( ✈ ✶ , ❑ ❥ ) = , ✈ ✶  � λ ❥ ❥ = ✶ ❥ = ✶ ❦ ∈ ❑ ❥ ✶ ■♥❡rt✐❛ ♦❢ ❑ ❥ ♣r♦❥❡❝t❡❞ ♦♥ ✈ ✶ ✹✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❣r♦✉♣s ●r♦✉♣ ❥ ❤❛s t❤❡ ❝♦♦r❞✐♥❛t❡s ( L ❣ ( ✈ ✶ , ❑ ❥ ) , L ❣ ( ✈ ✷ , ❑ ❥ )) 1.0 CGH • ✷ ❣r♦✉♣s ❛r❡ ❛❧❧ t❤❡ ♠♦r❡ 0.8 ❝❧♦s❡ t❤❛t t❤❡② ✐♥❞✉❝❡ t❤❡ Dim 2 (13.51 %) 0.6 s❛♠❡ str✉❝t✉r❡ • ❚❤❡ ✶st ❞✐♠❡♥s✐♦♥ ✐s 0.4 ❝♦♠♠♦♥ t♦ ❛❧❧ t❤❡ ❣r♦✉♣s 0.2 • ✷♥❞ ❞✐♠❡♥s✐♦♥ ♠❛✐♥❧② ❞✉❡ WHO expr t♦ ❈●❍ 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Dim 1 (20.99 %) ✵ ≤ L ❣ ( ✈ ✶ , ❑ ❥ ) = ✶ � ❝♦✈ ✷ ( ① . ❦ , ✈ ✶ ) ≤ ✶ λ ❥ ✶ ❦ ∈ ❑ ❥ � �� � ≤ λ ❥ ✶ ✺✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ◆✉♠❡r✐❝ ✐♥❞✐❝❛t♦rs ❃ r❡s✳♠❢❛✩❣r♦✉♣✩▲❣ ❈●❍ ❡①♣r ❲❍❖ ▼❋❆ � ❑ ❥ � ❑ ❥ ❦ = ✶ ( λ ❥ ❦ = ✷ ( λ ❥ ❦ ) ✷ ❦ ) ✷ ❈●❍ ✷✳✺✶ ✵✳✻✵ ✵✳✹✻ ✶✳✾✻ L ❣ ( ❑ ❥ , ❑ ❥ ) = = ✶ + ❡①♣r ✵✳✻✵ ✶✳✶✵ ✵✳✸✻ ✶✳✵✼ ( λ ❥ ( λ ❥ ✶ ) ✷ ✶ ) ✷ ❲❍❖ ✵✳✹✻ ✵✳✸✻ ✵✳✺✵ ✵✳✺✶ ▼❋❆ ✶✳✾✻ ✶✳✵✼ ✵✳✺✶ ✶✳✾✶ • ❈●❍ ❣✐✈❡s r✐❝❤❡r ❞❡s❝r✐♣t✐♦♥ ✭ L ❣ ❣r❡❛t❡r✮ ❃ r❡s✳♠❢❛✩❣r♦✉♣✩❘❱ • ❘❱✿ ❛ st❛♥❞❛r❞✐③❡❞ L ❣ ❈●❍ ❡①♣r ❲❍❖ ▼❋❆ • ❈●❍ ❛♥❞ ❡①♣r ❛r❡ ♥♦t ❧✐♥❦❡❞ ✭❘❱❂✵✳✸✻✮ ❈●❍ ✶✳✵✵ ✵✳✸✻ ✵✳✹✶ ✵✳✾✵ ❡①♣r ✵✳✸✻ ✶✳✵✵ ✵✳✹✽ ✵✳✼✹ • ❈●❍ ❝❧♦s❡st t♦ t❤❡ ♦✈❡r❛❧❧ ✭❘❱❂✵✳✾✵✮ ❲❍❖ ✵✳✹✶ ✵✳✹✽ ✶✳✵✵ ✵✳✺✸ ▼❋❆ ✵✳✾✵ ✵✳✼✹ ✵✳✺✸ ✶✳✵✵ ❈♦♥tr✐❜✉t✐♦♥ ♦❢ ❡❛❝❤ ❣r♦✉♣ t♦ ❡❛❝❤ ❝♦♠♣♦♥❡♥t ♦❢ t❤❡ ▼❋❆ • ❙✐♠✐❧❛r ❝♦♥tr✐❜✉t✐♦♥ ♦❢ t❤❡ ✷ ❣r♦✉♣s t♦ ❃ r❡s✳♠❢❛✩❣r♦✉♣✩❝♦♥tr✐❜ t❤❡ ✜rst ❞✐♠❡♥s✐♦♥ ❉✐♠✳✶ ❉✐♠✳✷ ❉✐♠✳✸ ❈●❍ ✹✺✳✽ ✾✸✳✸ ✼✽✳✶ • ❙❡❝♦♥❞ ❞✐♠❡♥s✐♦♥ ♦♥❧② ❞✉❡ t♦ ❈●❍ ❡①♣r ✺✹✳✷ ✻✳✼ ✷✶✳✾ ✺✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❚❤❡ ❘❱ ❝♦❡✣❝✐❡♥t ❳ ❥ ( ■ × ❑❥ ) ❛♥❞ ❳ ♠ ( ■ × ❑♠ ) ♥♦t ❞✐r❡❝t❧② ❝♦♠♣❛r❛❜❧❡ ❲ ❥ ( ■ × ■ ) = ❳ ❥ ❳ ′ ❥ ❛♥❞ ❲ ♠ ( ■ × ■ ) = ❳ ♠ ❳ ′ ♠ ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞ ■♥♥❡r ♣r♦❞✉❝t ♠❛tr✐❝❡s ❂ r❡❧❛t✐✈❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❈♦✈❛r✐❛♥❝❡ ❜❡t✇❡❡♥ t✇♦ ❣r♦✉♣s✿ � � ❝♦✈ ✷ ( ① . ❦ , ① . ❧ ) < ❲ ❥ , ❲ ♠ > = ❦ ∈ ❑ ❥ ❧ ∈ ❑ ♠ ❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t✇♦ ❣r♦✉♣s✿ ❘❱ ( ❑ ❥ , ❑ ♠ ) = < ❲ ❥ , ❲ ♠ > ✵ ≤ ❘❱ ≤ ✶ � ❲ ❥ � � ❲ ♠ � ❘❱ = ✵✿ ✈❛r✐❛❜❧❡s ♦❢ ❑ ❥ ❛r❡ ✉♥❝♦rr❡❧❛t❡❞ ✇✐t❤ ✈❛r✐❛❜❧❡s ♦❢ ❑ ♠ ❘❱ = ✶✿ t❤❡ t✇♦ ❝❧♦✉❞s ♦❢ ♣♦✐♥ts ❛r❡ ❤♦♠♦t❤❡t✐❝ ✺✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❛rt✐❛❧ ❛♥❛❧②s❡s • ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❣r♦✉♣s t❤r♦✉❣❤ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ⇒ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ t②♣♦❧♦❣✐❡s ♣r♦✈✐❞❡❞ ❜② ❡❛❝❤ ❣r♦✉♣ ✐♥ ❛ ❝♦♠♠♦♥ s♣❛❝❡ ⇒ ❆r❡ t❤❡r❡ ✐♥❞✐✈✐❞✉❛❧s ✈❡r② ♣❛rt✐❝✉❧❛r ✇✐t❤ r❡s♣❡❝t t♦ ♦♥❡ ❣r♦✉♣❄ • ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ s❡♣❛r❛t❡ P❈❆ ✺✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr♦❥❡❝t✐♦♥ ♦❢ ♣❛rt✐❛❧ ♣♦✐♥ts G1 G2 G3 MFA individuals configuration xxxxxxxx xxxxx xxxxx xxxxxxxx xxxxx xxxxx xxxxxxxx xxxxx xxxxx � � � ⊕ � �� xxxxx xxxxx Data xxxxxxxx xxxxx xxxxxxxx xxxxx xxxxx � xxxxxxxx xxxxx � xxxxx xxxxxxxx xxxxx xxxxxxxx 00000 00000 xxxxxxxx 00000 00000 xxxxxxxx 00000 00000 xxxxxxxx 00000 Projection of group 1 00000 xxxxxxxx 00000 00000 � � xxxxxxxx 00000 00000 xxxxxxxx 00000 00000 xxxxx 00000000 00000 Partial point 1 xxxxx 00000000 00000 xxxxx 00000000 00000 Partial point 2 Projection of group 2 00000000 xxxxx 00000 00000000 xxxxx 00000 � � 00000000 xxxxx 00000 Mean point xxxxx 00000 00000000 00000 xxxxx 00000000 xxxxx 00000000 00000 Partial point 3 xxxxx 00000000 00000 Projection of group 3 xxxxx 00000000 00000 xxxxx 00000000 00000 � � xxxxx 00000000 00000 xxxxx 00000000 00000 ✺✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❛rt✐❛❧ ♣♦✐♥ts opinion attitude individuals � � What you think behavioral conflict individual i What you do � � ✺✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❛rt✐❛❧ ♣♦✐♥ts Tutorial participants What you expected What you have learned for the tutorial during the tutorial � � � � � � � � What you expected for the tutorial What you expected What you have learned for the tutorial during the tutorial What you have learned during the tutorial � � � � � � � � ✺✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❛rt✐❛❧ ♣♦✐♥ts Tutorial participants What you expected What you have learned for the tutorial during the tutorial � � � � � � � � What you expected for the tutorial What you expected What you have learned Happy learner for the tutorial during the tutorial Disappointed What you have learned learner during the tutorial � � � � � � � � ✺✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣❛rt✐❛❧ ♣♦✐♥ts CGH CGH 1.5 4 expr expr ● ● 1.0 GBM30 ● O4 ● 2 O GBM22 ● ● O1 ● ● ● ● GBM28 O5 GS2 JPA2 GBM31 O3 ● GBM21 ● ● O2 O 0.5 ● GBM6 GBM23 GBM25 ● GBM27 ● GBM4 GBM11 GBM15 ● ● ● sGBM3 ● AO1 ● ● GBM9 GBM ● ● AO3 GBM GBM5 GBM26 ● LGG1 AOA6 ● ● GS1 AOA4 ● ● Dim 2 (13.51 %) GBM29 ● sGBM1 ● ● ● Dim 2 (13.51 %) ● ● ● ● AOA3 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● AO2 ● ● ● 0 ● ● ● ● ● ● GBM1 ● ● ● ● ● ● ● ● ● ● ● ● ● OA ● ● 0.0 ● ● ● ● ● ● ● ● ● GBM24 JPA3 ● ● A ● ● ● ● ● ● ● ● GBM16 ● AOA7 AOA2 ● GBM3 ● ● ● AA3 ● AOA1 ● −0.5 ● ● −2 ● ● ● ● OA GNN1 ● ● A ● −1.0 ● ● ● ● −4 −1.5 ● −2.0 −6 −4 −2 0 2 4 6 −1 0 1 2 Dim 1 (20.99 %) Dim 1 (20.99 %) • ❛♥ ✐♥❞✐✈✐❞✉❛❧ ✐s ❛t t❤❡ ❜❛r②❝❡♥tr❡ ♦❢ ✐ts ♣❛rt✐❛❧ ♣♦✐♥ts • ❛♥ ✐♥❞✐✈✐❞✉❛❧ ✐s ❛❧❧ t❤❡ ♠♦r❡ ✧❤♦♠♦❣❡♥❡♦✉s✧ t❤❛t ✐ts s✉♣❡r♣♦s❡❞ r❡♣r❡s❡♥t❛t✐♦♥s ❛r❡ ❝❧♦s❡ ✭ r❡s✳♠❢❛✩✐♥❞✩✇✐t❤✐♥✳✐♥❡rt✐❛ ✮ ✺✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣❛rt✐❛❧ ❝♦♠♣♦♥❡♥ts ❉♦ t❤❡ s❡♣❛r❛t❡ ❛♥❛❧②s❡s ❣✐✈❡ s✐♠✐❧❛r ❞✐♠❡♥s✐♦♥s ❛s ▼❋❆❄ � � � PCA � � � � � � ✺✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣❛rt✐❛❧ ❝♦♠♣♦♥❡♥ts CGH 1.0 expr Dim1.CGH WHO 0.5 • ❚❤❡ ✜rst ❞✐♠❡♥s✐♦♥ ♦❢ Dim 2 (13.51 %) Dim1.WHO ❡❛❝❤ ❣r♦✉♣ ✐s ✇❡❧❧ Dim1.expr 0.0 Dim3.CGH ● ♣r♦❥❡❝t❡❞ Dim3.expr Dim3.WHO Dim2.expr −0.5 Dim2.WHO • ❈●❍ ❤❛s s❛♠❡ Dim2.CGH ❞✐♠❡♥s✐♦♥s ❛s ▼❋❆ −1.0 −1.0 −0.5 0.0 0.5 1.0 Dim 1 (20.99 %) ✺✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣❛rt✐❛❧ ❝♦♠♣♦♥❡♥ts PCA on the CGH group of variables PCA on the expression group of variables A GBM A O GBM OA O 10 OA 5 5 Dim 2 (15.78%) Dim 2 (10.01%) 0 0 -5 -10 -5 -15 -20 -10 0 10 20 Dim 1 (45.67%) -10 -5 0 5 10 Dim 1 (18.63%) ❙❡♣❛r❛t❡ P❈❆ ♠❛♣s t❤❛t ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞ t♦ t❤❡ ▼❋❆ ♠❛♣ s❧✐❞❡ ✼ ✺✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❯s❡ ♦❢ ❜✐♦❧♦❣✐❝❛❧ ❦♥♦✇❧❡❞❣❡ ●❡♥❡s ❝❛♥ ❜❡ ❣r♦✉♣❡❞ ❜② ❣❡♥❡ ♦♥t♦❧♦❣② ✭●❖✮ ❜✐♦❧♦❣✐❝❛❧ ♣r♦❝❡ss GO:0009966 GO:0052276 GO:0006928 regulation of signal chromosome cell motility transduction organisation and biogenesis ANXA1 CASP1 CALD1 EDG2 CBX6 EGFR F2R NUSAP1 ENPP2 HCLS1 PCOLN3 FN1 HMOX1 PTTG1 FPRL2 IGFBP3 SUV39H1 LSP1 IQSEC1 TCF7L1 MSN LYN TSPYL1 PDPN MALT1 PLAUR TCF7L1 PRSS3 TNFAIP3 SAA2 TRIO SPINT2 VEGF TNFRSF12A YWHAG VEGF YWHAH WASF1 YARS ✻✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❯s❡ ♦❢ ❜✐♦❧♦❣✐❝❛❧ ❦♥♦✇❧❡❞❣❡ • ❇✐♦❧♦❣✐❝❛❧ ♣r♦❝❡ss❡s ❝♦♥s✐❞❡r❡❞ ❛s s✉♣♣❧❡♠❡♥t❛r② ❣r♦✉♣s ♦❢ ✈❛r✐❛❜❧❡s <MODULES of GENES> Modular approach 1 j 1 J 1 1 j 2 J 2 1 Tumors ….. M1 M2 M3 i I Modules ‘-omics’ data ✻✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❯s❡ ♦❢ ❜✐♦❧♦❣✐❝❛❧ ❦♥♦✇❧❡❞❣❡ 1.0 CGH 0.8 ● ● ● Dim 2 (13.51 %) ● ● ● 0.6 ● ● ● ▼❛♥② ❜✐♦❧♦❣✐❝❛❧ ♣r♦❝❡ss❡s ● ● ● ● ● ● ● ✐♥❞✉❝❡ t❤❡ s❛♠❡ str✉❝t✉r❡ ● ● 0.4 ● ● ● ● ● ● ● ♦♥ t❤❡ ✐♥❞✐✈✐❞✉❛❧s t❤❛♥ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ▼❋❆ ● ● ● ● ● ● ● ● ● ● ● 0.2 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● WHO ● ● ● ● ● ● ● ● expr ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 0.2 0.4 0.6 0.8 1.0 Dim 1 (20.99 %) ✻✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❇❛❝❦ t♦ t❤❡ ✇✐♥❡ ❡①❛♠♣❧❡✦ Continuous variables Categorical Expert Consu Student Preference Label (27) mer (15) (60) (1) (15) wine 1 wine 2 … wine 10 ❖❜❥❡❝t✐✈❡s✿ • ❍♦✇ ❛r❡ t❤❡ ♣r♦❞✉❝ts ❞❡s❝r✐❜❡❞ ❜② t❤❡ ♣❛♥❡❧s❄ • ❉♦ t❤❡ ♣❛♥❡❧s ❞❡s❝r✐❜❡ t❤❡ ♣r♦❞✉❝ts ✐♥ ❛ s❛♠❡ ✇❛②❄ ■s t❤❡r❡ ❛ s♣❡❝✐✜❝ ❞❡s❝r✐♣t✐♦♥ ❞♦♥❡ ❜② ♦♥❡ ♣❛♥❡❧❄ ✻✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr❛❝t✐❝❡ ✇✐t❤ ❘ ✶ ❉❡✜♥❡ ❣r♦✉♣s ♦❢ ❛❝t✐✈❡ ❛♥❞ s✉♣♣❧❡♠❡♥t❛r② ✈❛r✐❛❜❧❡s ✷ ❙❝❛❧❡ ♦r ♥♦t t❤❡ ✈❛r✐❛❜❧❡s ✸ P❡r❢♦r♠ ▼❋❆ ✹ ❈❤♦♦s❡ t❤❡ ♥✉♠❜❡r ♦❢ ❞✐♠❡♥s✐♦♥s t♦ ✐♥t❡r♣r❡t ✺ ❙✐♠✉❧t❛♥❡♦✉s❧② ✐♥t❡r♣r❡t t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❛♥❞ ✈❛r✐❛❜❧❡s ❣r❛♣❤s ✻ ❙t✉❞② t❤❡ ❣r♦✉♣s ♦❢ ✈❛r✐❛❜❧❡s ✼ ❙t✉❞② t❤❡ ♣❛rt✐❛❧ r❡♣r❡s❡♥t❛t✐♦♥s ✽ ❯s❡ ✐♥❞✐❝❛t♦rs t♦ ❡♥r✐❝❤ t❤❡ ✐♥t❡r♣r❡t❛t✐♦♥ ✻✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s Pr❛❝t✐❝❡ ✇✐t❤ ❘ ❧✐❜r❛r②✭❋❛❝t♦▼✐♥❡❘✮ ❊①♣❡rt ❁✲ r❡❛❞✳t❛❜❧❡✭✧❤tt♣✿✴✴❢❛❝t♦♠✐♥❡r✳❢r❡❡✳❢r✴✉s❡❘✷✵✶✵✴❊①♣❡rt❴✇✐♥❡✳❝s✈✧✱ ❤❡❛❞❡r❂❚❘❯❊✱ s❡♣❂✧❀✧✱ r♦✇✳♥❛♠❡s❂✶✮ ❈♦♥s✉ ❁✲ r❡❛❞✳t❛❜❧❡✭✧✳✳✳✴❈♦♥s✉♠❡r❴✇✐♥❡✳❝s✈✧✱❤❡❛❞❡r❂❚✱s❡♣❂✧❀✧✱r♦✇✳♥❛♠❡s❂✶✮ ❙t✉❞ ❁✲ r❡❛❞✳t❛❜❧❡✭✧✳✳✳✴❙t✉❞❡♥t❴✇✐♥❡✳❝s✈✧✱❤❡❛❞❡r❂❚✱s❡♣❂✧❀✧✱r♦✇✳♥❛♠❡s❂✶✮ Pr❡❢ ❁✲ r❡❛❞✳t❛❜❧❡✭✧✳✳✳✴Pr❡❢❴✇✐♥❡✳❝s✈✧✱❤❡❛❞❡r❂❚✱s❡♣❂✧❀✧✱r♦✇✳♥❛♠❡s❂✶✮ ♣❛❧❡tt❡✭❝✭✧❜❧❛❝❦✧✱✧r❡❞✧✱✧❜❧✉❡✧✱✧♦r❛♥❣❡✧✱✧❞❛r❦❣r❡❡♥✧✱✧♠❛r♦♦♥✧✱✧❞❛r❦✈✐♦❧❡t✧✮✮ ❝♦♠♣❧❡t ❁✲ ❝❜✐♥❞✳❞❛t❛✳❢r❛♠❡✭❊①♣❡rt❬✱✶✿✷✽❪✱❈♦♥s✉❬✱✷✿✶✻❪✱❙t✉❞❬✱✷✿✶✻❪✱Pr❡❢✮ r❡s✳♠❢❛ ❁✲ ▼❋❆✭❝♦♠♣❧❡t✱❣r♦✉♣❂❝✭✶✱✷✼✱✶✺✱✶✺✱✻✵✮✱t②♣❡❂❝✭✧♥✧✱r❡♣✭✧s✧✱✹✮✮✱ ♥✉♠✳❣r♦✉♣✳s✉♣❂❝✭✶✱✺✮✱❣r❛♣❤❂❋❆▲❙❊✱ ♥❛♠❡✳❣r♦✉♣❂❝✭✧▲❛❜❡❧✧✱✧❊①♣❡rt✧✱✧❈♦♥s✉♠❡r✧✱✧❙t✉❞❡♥t✧✱✧Pr❡❢❡r❡♥❝❡✧✮✮ ♣❧♦t✭r❡s✳♠❢❛✱❝❤♦✐①❂✧❣r♦✉♣✧✱♣❛❧❡tt❡❂♣❛❧❡tt❡✭✮✮ ♣❧♦t✭r❡s✳♠❢❛✱❝❤♦✐①❂✧✈❛r✧✱✐♥✈✐s✐❜❧❡❂✧s✉♣✧✱❤❛❜❂✧❣r♦✉♣✧✱♣❛❧❡tt❡❂♣❛❧❡tt❡✭✮✮ ♣❧♦t✭r❡s✳♠❢❛✱❝❤♦✐①❂✧✈❛r✧✱✐♥✈✐s✐❜❧❡❂✧❛❝t✐❢✧✱❧❛❜✳✈❛r❂❋❆▲❙❊✱♣❛❧❡tt❡❂♣❛❧❡tt❡✭✮✮ ♣❧♦t✭r❡s✳♠❢❛✱❝❤♦✐①❂✧✐♥❞✧✱♣❛rt✐❛❧❂✧❛❧❧✧✱❤❛❜✐❧❧❛❣❡❂✧❣r♦✉♣✧✱♣❛❧❡tt❡❂♣❛❧❡tt❡✭✮✮ ♣❧♦t✭r❡s✳♠❢❛✱❝❤♦✐①❂✧❛①❡s✧✱❤❛❜✐❧❧❛❣❡❂✧❣r♦✉♣✧✱♣❛❧❡tt❡❂♣❛❧❡tt❡✭✮✮ ❞✐♠❞❡s❝✭r❡s✳♠❢❛✮ ✇r✐t❡✳✐♥❢✐❧❡✭r❡s✳♣❝❛✱❢✐❧❡❂✧♠②❴❋❛❝t♦▼✐♥❡❘❴r❡s✉❧ts✳❝s✈✧✮ ★t♦ ❡①♣♦rt ❛ ❧✐st ✻✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧s Sauvignon S Trotignon Vouvray S Renaudie S Michaud 1 • ❚❤❡ t✇♦ ❧❛❜❡❧s ❛r❡ Sauvignon V Aub Marigny S Buisse Cristal ✇❡❧❧ s❡♣❛r❛t❡❞ Dim 2 (24.42 %) V Font Coteaux 0 • ❱♦✉✈r❛② ❛r❡ S Buisse Domaine Vouvray s❡♥s♦r✐❛❧❧② ♠♦r❡ V Font Domaine -1 V Font Brûlés ❞✐✛❡r❡♥t -2 • ❙❡✈❡r❛❧ ❣r♦✉♣s ♦❢ V Aub Silex ✇✐♥❡s✱ ✳✳✳ -3 -2 -1 0 1 2 3 Dim 1 (42.52 %) ✻✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❛❝t✐✈❡ ✈❛r✐❛❜❧❡s Expert O.Intensity.before.shaking_S Consumer 1.0 Attack.intensity Expression O.Intensity.before.shaking Student Acidity Freshness O.Intensity.after.shaking O.passion O.Intensity.before.shaking_C O.Intensity.after.shaking_S O.plante_C O.Intensity.after.shaking_C O.passion_S Astringency_S O.passion_C A.persistency O.flower 0.5 Bitterness O.citrus Astringency_C Bitterness_C Balance_S A.intensity Acidity_S O.plante Smoothness Dim 2 (24.42 %) Acidity_C A.intensity_C Bitterness_S O.mushroom_S O.fruity A.alcohol_C O.Typicity_S A.intensity_S O.vanilla 0.0 O.wooded A.alcohol_S Typical_S O.mushroom_C Balance_C O.alcohol Typical_C Astringency O.Typicity_C Visual.intensity Grade Sweetness_C Surface.feeling -0.5 O.candied.fruit Sweetness_S O.mushroom Oxidation Sweetness O.alcohol_C Typicity O.plante_S O.alcohol_S -1.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Dim 1 (42.52 %) ✻✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❛❝t✐✈❡ ✈❛r✐❛❜❧❡s Expert Consumer 1.0 Student Acidity O.passion O.passion_S O.passion_C 0.5 Acidity_S Dim 2 (24.42 %) Acidity_C 0.0 Sweetness_C -0.5 Sweetness_S Sweetness -1.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Dim 1 (42.52 %) ✻✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❣r♦✉♣s • ✷ ❣r♦✉♣s ❛r❡ ❛❧❧ t❤❡ 1.0 ♠♦r❡ ❝❧♦s❡ t❤❛t t❤❡② ✐♥❞✉❝❡ t❤❡ s❛♠❡ 0.8 Expert str✉❝t✉r❡ Preference 0.6 Dim 2 (24.42 %) • ❚❤❡ ✶st ❞✐♠❡♥s✐♦♥ ✐s Student Label ❝♦♠♠♦♥ t♦ ❛❧❧ t❤❡ Consumer 0.4 ♣❛♥❡❧s • ✷♥❞ ❞✐♠❡♥s✐♦♥ ♠❛✐♥❧② 0.2 ❞✉❡ t♦ t❤❡ ❡①♣❡rts 0.0 • Pr❡❢❡r❡♥❝❡ ❧✐♥❦❡❞ t♦ 0.0 0.2 0.4 0.6 0.8 1.0 s❡♥s♦r② ❞❡s❝r✐♣t✐♦♥ Dim 1 (42.52 %) ✻✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣❛rt✐❛❧ ♣♦✐♥ts Expert Consumer Student 2 S Trotignon S Renaudie S Michaud 1 Sauvignon S Buisse Cristal V Font Coteaux V Aub Marigny Dim 2 (24.42 %) 0 S Buisse Domaine Vouvray V Font Domaine -1 V Font Brûlés -2 V Aub Silex -3 -4 -2 0 2 4 Dim 1 (42.52 %) ✻✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ♣❛rt✐❛❧ ❞✐♠❡♥s✐♦♥s Expert Dim2.Student 1.0 Consumer Student Dim2.Consumer Dim2.Expert Preference Label Dim1.Label 0.5 • ❚❤❡ t✇♦ ✜rst Dim1.Consumer Dim 2 (24.42 %) ❞✐♠❡♥s✐♦♥s ♦❢ ❡❛❝❤ 0.0 Dim1.Student ❣r♦✉♣ ❛r❡ ✇❡❧❧ ♣r♦❥❡❝t❡❞ • ❈♦♥s✉♠❡r ❤❛s s❛♠❡ -0.5 Dim1.Expert Dim1.Preference Dim2.Preference ❞✐♠❡♥s✐♦♥s ❛s ▼❋❆ -1.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 Dim 1 (42.52 %) ✼✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❘❡♣r❡s❡♥t❛t✐♦♥ ♦❢ s✉♣♣❧❡♠❡♥t❛r② ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s 1.0 0.5 Dim 2 (24.42 %) 0.0 -0.5 -1.0 -1.0 -0.5 0.0 0.5 1.0 Dim 1 (42.52 %) Pr❡❢❡r❡♥❝❡s ❛r❡ ❧✐♥❦❡❞ t♦ s❡♥s♦r② ❞❡s❝r✐♣t✐♦♥ ❚❤❡ ❢❛✈♦✉r✐t❡ ✇✐♥❡ ✐s ❱♦✉✈r❛② ❆✉❜✉ss✐èr❡ ❙✐❧❡① ✼✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❍❡❧♣s t♦ ✐♥t❡r♣r❡t • ❈♦♥tr✐❜✉t✐♦♥ ♦❢ ❡❛❝❤ ❣r♦✉♣ ♦❢ ✈❛r✐❛❜❧❡s t♦ ❡❛❝❤ ❝♦♠♣♦♥❡♥t ♦❢ t❤❡ ▼❋❆ • ❙✐♠✐❧❛r ❝♦♥tr✐❜✉t✐♦♥ ♦❢ t❤❡ ✸ ❣r♦✉♣s ❃ r❡s✳♠❢❛✩❣r♦✉♣✩❝♦♥tr✐❜ ❉✐♠✳✶ ❉✐♠✳✷ ❉✐♠✳✸ t♦ t❤❡ ✜rst ❞✐♠❡♥s✐♦♥ ❊①♣❡rt ✸✵✳✺ ✹✻✳✵ ✸✸✳✼ • ❙❡❝♦♥❞ ❞✐♠❡♥s✐♦♥ ♠❛✐♥❧② ❞✉❡ t♦ t❤❡ ❈♦♥s✉♠❡r ✸✸✳✷ ✷✸✳✶ ✸✶✳✷ ❙t✉❞❡♥t ✸✻✳✸ ✸✵✳✾ ✸✺✳✶ ❡①♣❡rt • ❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ❣❧♦❜❛❧ ❝❧♦✉❞ ❛♥❞ ❡❛❝❤ ♣❛rt✐❛❧ ❝❧♦✉❞ ❃ r❡s✳♠❢❛✩❣r♦✉♣✩❝♦rr❡❧❛t✐♦♥ ❋✐rst ❝♦♠♣♦♥❡♥ts ❛r❡ ❤✐❣❤❧② ❧✐♥❦❡❞ t♦ ❉✐♠✳✶ ❉✐♠✳✷ ❉✐♠✳✸ t❤❡ ✸ ❣r♦✉♣s✿ t❤❡ ✸ ❝❧♦✉❞s ♦❢ ♣♦✐♥ts ❊①♣❡rt ✵✳✾✺ ✵✳✾✺ ✵✳✾✻ ❈♦♥s✉♠❡r ✵✳✾✺ ✵✳✽✸ ✵✳✽✼ ❛r❡ ♥❡❛r❧② ❤♦♠♦t❤❡t✐❝ ❙t✉❞❡♥t ✵✳✾✾ ✵✳✾✾ ✵✳✽✹ ✼✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❙✐♠✐❧❛r✐t② ♠❡❛s✉r❡s ❜❡t✇❡❡♥ ❣r♦✉♣s ❃ r❡s✳♠❢❛✩❣r♦✉♣✩▲❣ ❊①♣❡rt ❈♦♥s✉♠❡r ❙t✉❞❡♥t Pr❡❢❡r❡♥❝❡ ▲❛❜❡❧ ▼❋❆ ❊①♣❡rt ✶✳✹✺ ✵✳✾✹ ✶✳✶✼ ✶✳✵✶ ✵✳✽✾ ✶✳✸✸ ❈♦♥s✉♠❡r ✵✳✾✹ ✶✳✷✺ ✶✳✵✹ ✶✳✶✶ ✵✳✷✽ ✶✳✷✶ ❙t✉❞❡♥t ✶✳✶✼ ✶✳✵✹ ✶✳✷✾ ✶✳✵✸ ✵✳✻✷ ✶✳✸✶ Pr❡❢❡r❡♥❝❡ ✶✳✵✶ ✶✳✶✶ ✶✳✵✸ ✶✳✹✼ ✵✳✸✼ ✶✳✶✽ ▲❛❜❡❧ ✵✳✽✾ ✵✳✷✽ ✵✳✻✷ ✵✳✸✼ ✶✳✵✵ ✵✳✻✼ ▼❋❆ ✶✳✸✸ ✶✳✷✶ ✶✳✸✶ ✶✳✶✽ ✵✳✻✼ ✶✳✹✹ ❃ r❡s✳♠❢❛✩❣r♦✉♣✩❘❱ ❊①♣❡rt ❈♦♥s✉♠❡r ❙t✉❞❡♥t Pr❡❢❡r❡♥❝❡ ▲❛❜❡❧ ▼❋❆ ❊①♣❡rt ✶✳✵✵ ✵✳✼✵ ✵✳✽✺ ✵✳✻✾ ✵✳✼✹ ✵✳✾✷ ❈♦♥s✉♠❡r ✵✳✼✵ ✶✳✵✵ ✵✳✽✷ ✵✳✽✷ ✵✳✷✺ ✵✳✾✵ ❙t✉❞❡♥t ✵✳✽✺ ✵✳✽✷ ✶✳✵✵ ✵✳✼✺ ✵✳✺✺ ✵✳✾✻ Pr❡❢❡r❡♥❝❡ ✵✳✻✾ ✵✳✽✷ ✵✳✼✺ ✶✳✵✵ ✵✳✸✶ ✵✳✽✶ ▲❛❜❡❧ ✵✳✼✹ ✵✳✷✺ ✵✳✺✺ ✵✳✸✶ ✶✳✵✵ ✵✳✺✻ ▼❋❆ ✵✳✾✷ ✵✳✾✵ ✵✳✾✻ ✵✳✽✶ ✵✳✺✻ ✶✳✵✵ • ❊①♣❡rt ❣✐✈❡s ❛ r✐❝❤❡r ❞❡s❝r✐♣t✐♦♥ ✭ L ❣ ❣r❡❛t❡r✮ • ●r♦✉♣s ❙t✉❞❡♥t ❛♥❞ ❊①♣❡rt ❛r❡ ❧✐♥❦❡❞ ✭❘❱ ❂ ✵✳✽✺✮ • ●r♦✉♣ ❙t✉❞❡♥t ✐s t❤❡ ❝❧♦s❡st t♦ t❤❡ ♦✈❡r❛❧❧ ✭❘❱ ❂ ✵✳✾✻✮ ✼✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❚♦ ❣♦ ❢✉rt❤❡r • ▼✐①❡❞ ❞❛t❛✿ ▼❋❆ ✇✐t❤ ✶ ❣r♦✉♣ ❂ ✶ ✈❛r✐❛❜❧❡ ✐❢ t❤❡r❡ ❛r❡ ♦♥❧② ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s✱ P❈❆ ✐s r❡❝♦✈❡r❡❞❀ ✐❢ t❤❡r❡ ❛r❡ ♦♥❧② ❝❛t❡❣♦r✐❝❛❧ ✈❛r✐❛❜❧❡s✱ ▼❈❆ ✐s r❡❝♦✈❡r❡❞ ❛ s♣❡❝✐✜❝ ❢✉♥❝t✐♦♥✿ ❆❋❉▼ • ▼❋❆ ✉s❡❞ ❢♦r ♠❡t❤♦❞♦❧♦❣✐❝❛❧ ♣✉r♣♦s❡s✿ • ❝♦♠♣❛r✐s♦♥ ♦❢ ❝♦❞✐♥❣ ✭❝♦♥t✐♥✉♦✉s ♦r ❝❛t❡❣♦r✐❝❛❧✮ • ❝♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ♣r❡♣r♦❝❡ss✐♥❣ ✭st❛♥❞❛r❞✐③❡❞ P❈❆ ❛♥❞ ✉♥st❛♥❞❛r❞✐③❡❞ P❈❆✮ • ❝♦♠♣❛r✐s♦♥ ♦❢ r❡s✉❧ts ❢r♦♠ ❞✐✛❡r❡♥t ❛♥❛❧②s❡s • ❍✐❡r❛r❝❤✐❝❛❧ ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❚❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t ❛ ❤✐❡r❛r❝❤② ♦♥ t❤❡ ✈❛r✐❛❜❧❡s✿ ✈❛r✐❛❜❧❡s ❛r❡ ❣r♦✉♣❡❞ ❛♥❞ s✉❜❣r♦✉♣❡❞ ✭❧✐❦❡ ✐♥ q✉❡st✐♦♥♥❛✐r❡s str✉❝t✉r❡❞ ✐♥ t♦♣✐❝s ❛♥❞ s✉❜t♦♣✐❝s✮ ✼✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ✶ ❈❧✉st❡r✐♥❣ ▼❡t❤♦❞s ✷ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥ts ▼❡t❤♦❞s ❛s ❛ Pr❡♣r♦❝❡ss✐♥❣ ❙t❡♣ ✸ ●r❛♣❤✐❝❛❧ ❈♦♠♣❧❡♠❡♥t❛r✐t② ✼✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❯♥s✉♣❡r✈✐s❡❞ ❝❧❛ss✐✜❝❛t✐♦♥ • ❉❛t❛ s❡t✿ t❛❜❧❡ ✐♥❞✐✈✐❞✉❛❧s × ✈❛r✐❛❜❧❡s ✭♦r ❛ ❞✐st❛♥❝❡ ♠❛tr✐①✮ • ❖❜❥❡❝t✐✈❡✿ t♦ ♣r♦❞✉❝❡ ❤♦♠♦❣❡♥❡♦✉s ❣r♦✉♣s ♦❢ ✐♥❞✐✈✐❞✉❛❧s ✭♦r ❣r♦✉♣s ♦❢ ✈❛r✐❛❜❧❡s✮ • ❚✇♦ ❦✐♥❞s ♦❢ ❝❧✉st❡r✐♥❣ t♦ ❞❡✜♥❡ t✇♦ str✉❝t✉r❡s ♦♥ ✐♥❞✐✈✐❞✉❛❧s✿ ❤✐❡r❛r❝❤② ♦r ♣❛rt✐t✐♦♥ ✼✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❍✐❡r❛r❝❤✐❝❛❧ ❈❧✉st❡r✐♥❣ Pr✐♥❝✐♣❧❡✿ s❡q✉❡♥t✐❛❧❧② ❛❣❣❧♦♠❡r❛t❡ ✭❝❧✉st❡rs ♦❢✮ ✐♥❞✐✈✐❞✉❛❧s ✉s✐♥❣ • ❛ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s✿ ❈✐t② ❜❧♦❝❦✱ ❊✉❝❧✐❞❡❛♥ • ❛♥ ❛❣❣❧♦♠❡r❛t✐✈❡ ❝r✐t❡r✐♦♥✿ s✐♥❣❧❡ ❧✐♥❦❛❣❡✱ ❝♦♠♣❧❡t❡ ❧✐♥❦❛❣❡✱ ❛✈❡r❛❣❡ ❧✐♥❦❛❣❡✱ ❲❛r❞✬s ❝r✐t❡r✐♦♥ Single linkage Euclidean City-block Complete linkage ❘❡♣r❡s❡♥t❛t✐♦♥ ✇✐t❤ ❛ ❞❡♥❞r♦❣r❛♠ ⇒ ❊✉❧✐❞❡❛♥ ❞✐st❛♥❝❡ ✐s ✉s❡❞ ✐♥ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ♠❡t❤♦❞s ⇒ ❲❛r❞✬s ❝r✐t❡r✐♦♥ ✐s ❜❛s❡❞ ♦♥ ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ ✈❛r✐❛♥❝❡ ✭✐♥❡rt✐❛✮ ✇❤✐❝❤ ✐s t❤❡ ❝♦r❡ ♦❢ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ♠❡t❤♦❞s ✼✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❆s❝❡♥❞✐♥❣ ❍✐❡r❛r❝❤✐❝❛❧ ❈❧✉st❡r✐♥❣ ❆❍❈ ❛❧❣♦r✐t❤♠✿ • ❈♦♠♣✉t❡ t❤❡ ❊✉❝❧✐❞❡❛♥ ❞✐st❛♥❝❡ ♠❛tr✐① ✭ ■ × ■ ✮ • ❈♦♥s✐❞❡r ❡❛❝❤ ✐♥❞✐✈✐❞✉❛❧ ❛s ❛ ❝❧✉st❡r • ▼❡r❣❡ t❤❡ t✇♦ ❝❧✉st❡rs ❆ ❛♥❞ ❇ ✇❤✐❝❤ ❛r❡ t❤❡ ❝❧♦s❡st ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ❲❛r❞✬s ❝r✐t❡r✐♦♥✿ ■ ❆ ■ ❇ ❞ ✷ ( µ ❆ , µ ❇ ) ∆ ✇❛r❞ ( ❆ , ❇ ) = ■ ❆ + ■ ❇ ✇✐t❤ ❞ t❤❡ ❊✉❝❧✐❞❡❛♥ ❞✐st❛♥❝❡✱ µ ❆ t❤❡ ❜❛r②❝❡♥tr❡ ❛♥❞ ■ ❆ t❤❡ ❝❛r❞✐♥❛❧✐t② ♦❢ t❤❡ s❡t ❆ • ❘❡♣❡❛t ✉♥t✐❧ t❤❡ ♥✉♠❜❡r ♦❢ ❝❧✉st❡rs ✐s ❡q✉❛❧ t♦ ♦♥❡ ✼✽ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❲❛r❞✬s ❝r✐t❡r✐♦♥ • ■♥❞✐✈✐❞✉❛❧s ❝❛♥ ❜❡ r❡♣r❡s❡♥t❡❞ ❜② ❛ ❝❧♦✉❞ ♦❢ ♣♦✐♥ts ✐♥ R ❑ • ❚♦t❛❧ ✐♥❡rt✐❛ ❂ ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ ✈❛r✐❛♥❝❡ ❲✐t❤ ◗ ❣r♦✉♣s ♦❢ ✐♥❞✐✈✐❞✉❛❧s✱ ✐♥❡rt✐❛ ❝❛♥ ❜❡ ❞❡❝♦♠♣♦s❡❞ ❛s✿ ■ q ■ q ❑ ◗ ❑ ◗ ❑ ◗ � � � � � � � � ① ❦ ) ✷ = ① ❦ ) ✷ + ① q❦ ) ✷ ( ① ✐q❦ − ¯ ① q❦ − ¯ ( ① ✐q❦ − ¯ ■ q (¯ ❦ = ✶ q = ✶ ✐ = ✶ ❦ = ✶ q = ✶ ❦ = ✶ q = ✶ ✐ = ✶ ❚♦t❛❧ ✐♥❡rt✐❛ = ❇❡t✇❡❡♥ ✐♥❡rt✐❛ + ❲✐t❤✐♥ ✐♥❡rt✐❛ ✼✾ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❲❛r❞✬s ❝r✐t❡r✐♦♥ Step 1: 1 cluster = 1 individual Within = 0 Between = Total Step I-2 : 3 clusters ? ? ? Step I-1 : 2 clusters to define Step I : only 1 cluster Within = Total Between = 0 ⇒ ❲❛r❞ ♠✐♥✐♠✐③❡s t❤❡ ✐♥❝r❡❛s✐♥❣ ♦❢ ✇✐t❤✐♥ ✐♥❡rt✐❛ ✽✵ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❑✲♠❡❛♥s ❛❧❣♦r✐t❤♠ ✶ ❈❤♦♦s❡ ◗ ♣♦✐♥ts ❛t r❛♥❞♦♠ ✭t❤❡ ❜❛r②❝❡♥tr❡✮ ✷ ❆✛❡❝t t❤❡ ♣♦✐♥ts t♦ t❤❡ ❝❧♦s❡st ❜❛r②❝❡♥tr❡ ✸ ❈♦♠♣✉t❡ t❤❡ ♥❡✇ ❜❛r②❝❡♥tr❡ ✹ ■t❡r❛t❡ ✷ ❛♥❞ ✸ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡ ✽✶ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❈❆ ❛s ❛ ♣r❡♣r♦❝❡ss✐♥❣ ❲✐t❤ ❝♦♥t✐♥✉♦✉s ✈❛r✐❛❜❧❡s✿ ⇒ ❆❍❈ ❛♥❞ ❦✲♠❡❛♥s ♦♥t♦ t❤❡ r❛✇ ❞❛t❛ ⇒ ❆❍❈ ♦r ❦✲♠❡❛♥s ♦♥t♦ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts P❈❆ tr❛♥s❢♦r♠s t❤❡ r❛✇ ✈❛r✐❛❜❧❡s ✐♥t♦ ♦rt❤♦❣♦♥❛❧ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ❋ . ✶ , ..., ❋ . ❑ ✇✐t❤ ❞❡❝r❡❛s✐♥❣ ✈❛r✐❛♥❝❡ λ ✶ ≥ λ ✷ ≥ ...λ ❑ � � � � � �� � � � �� � � � PCA Data Structure Noise ⇒ ❑❡❡♣✐♥❣ t❤❡ ✜rst ❝♦♠♣♦♥❡♥ts ♠❛❦❡s t❤❡ ❝❧✉st❡r✐♥❣ ♠♦r❡ r♦❜✉st ⇒ ❇✉t✱ ❤♦✇ ♠❛♥② ❝♦♠♣♦♥❡♥ts ❞♦ ②♦✉ ❦❡❡♣ t♦ ❞❡♥♦✐s❡❄ ✽✷ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼❈❆ ❛s ❛ ♣r❡♣r♦❝❡ss✐♥❣ ❈❧✉st❡r✐♥❣ ♦♥ ❝❛t❡❣♦r✐❝❛❧ ✈❛r✐❛❜❧❡s✿ ✇❤✐❝❤ ❞✐st❛♥❝❡ t♦ ✉s❡❄ • ✇✐t❤ t✇♦ ❝❛t❡❣♦r✐❡s✿ ❏❛❝❝❛r❞ ✐♥❞❡①✱ ❉✐❝❡✬s ❝♦❡✣❝✐❡♥t✱ s✐♠♣❧❡ ♠❛t❝❤✱ ❡t❝✳ ■♥❞✐❝❡s ✇❡❧❧✲✜tt❡❞ ❢♦r ♣r❡s❡♥❝❡✴❛❜s❡♥❝❡ ❞❛t❛ • ✇✐t❤ ♠♦r❡ t❤❛♥ ✷ ❝❛t❡❣♦r✐❡s✿ ✉s❡ ❢♦r ❡①❛♠♣❧❡ t❤❡ χ ✷ ✲❞✐st❛♥❝❡ ❯s✐♥❣ t❤❡ χ ✷ ✲❞✐st❛♥❝❡ ⇔ ❝♦♠♣✉t✐♥❣ ❞✐st❛♥❝❡s ❢r♦♠ ❛❧❧ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ♦❜t❛✐♥❡❞ ❢r♦♠ ▼❈❆ ■♥ ♣r❛❝t✐❝❡✱ ▼❈❆ ✐s ✉s❡❞ ❛s ❛ ♣r❡♣r♦❝❡ss✐♥❣ ✐♥ ♦r❞❡r t♦ • tr❛♥s❢♦r♠ ❝❛t❡❣♦r✐❝❛❧ ✈❛r✐❛❜❧❡s ✐♥ ❝♦♥t✐♥✉♦✉s ♦♥❡s • ❞❡❧❡t❡ t❤❡ ❧❛st ❞✐♠❡♥s✐♦♥s t♦ ♠❛❦❡ t❤❡ ❝❧✉st❡r✐♥❣ ♠♦r❡ r♦❜✉st ✽✸ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ▼❋❆ ❛s ❛ ♣r❡♣r♦❝❡ss✐♥❣ X1 X2 i i’ ▼❋❆ ❜❛❧❛♥❝❡s t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❣r♦✉♣s ✇❤❡♥ ❝♦♠♣✉t✐♥❣ ❞✐st❛♥❝❡s ❜❡t✇❡❡♥ ✐♥❞✐✈✐❞✉❛❧s ❑ ❥ ❏ ✶ � � ❞ ✷ ( ✐ , ✐ ′ ) = ( ① ✐❦ − ① ✐ ′ ❦ ) ✷ � λ ❥ ❥ = ✶ ❦ = ✶ ❆❍❈ ♦r ❦✲♠❡❛♥s ♦♥t♦ t❤❡ ✜rst ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ✭ ❋ . ✶ , ..., ❋ . ◗ ✮ ♦❜t❛✐♥❡❞ ❢r♦♠ ▼❋❆ ❛❧❧♦✇s t♦ • t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❣r♦✉♣s str✉❝t✉r❡ ✐♥ t❤❡ ❝❧✉st❡r✐♥❣ • ♠❛❦❡ t❤❡ ❝❧✉st❡r✐♥❣ ♠♦r❡ r♦❜✉st ❜② ❞❡❧❡t✐♥❣ t❤❡ ❧❛st ❞✐♠❡♥s✐♦♥s ✽✹ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❇❛❝❦ t♦ t❤❡ ✇✐♥❡ ❞❛t❛✦ ❆❍❈ ♦♥t♦ t❤❡ ✜rst ✺ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥ts ❢r♦♠ ▼❋❆ Hierarchical Clustering Hierarchical Classification 2.0 1.5 1.0 0.5 0.0 V Aub Silex S Michaud S Buisse Domaine S Buisse Cristal V Font Brûlés V Font Domaine V Aub Marigny V Font Coteaux S Trotignon S Renaudie ■♥❞✐✈✐❞✉❛❧s ❛r❡ s♦rt❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡✐r ❝♦♦r❞✐♥❛t❡ ❋ . ✶ ✽✺ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❲❤② s♦rt✐♥❣ t❤❡ tr❡❡❄ ❳ ❁✲ ❝✭✻✱✼✱✷✱✵✱✸✱✶✺✱✶✶✱✶✷✮ ♥❛♠❡s✭❳✮ ❁✲ ❳ ❧✐❜r❛r②✭❝❧✉st❡r✮ ♣❛r✭♠❢r♦✇❂❝✭✶✱✷✮✮ ♣❧♦t✭❛s✳❞❡♥❞r♦❣r❛♠✭❛❣♥❡s✭❳✮✮✮ ♣❧♦t✭❛s✳❞❡♥❞r♦❣r❛♠✭❛❣♥❡s✭s♦rt✭❳✮✮✮✮ 8 8 6 6 4 4 2 2 0 0 6 7 2 3 0 15 11 12 0 2 3 6 7 11 12 15 ✽✻ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❛rt✐t✐♦♥ ❢r♦♠ t❤❡ tr❡❡ ❲ q − ❲ q + ✶ ❆♥ ❡♠♣✐r✐❝❛❧ ♥✉♠❜❡r ♦❢ ❝❧✉st❡rs ✐s s✉❣❣❡st❡❞ ✭♠✐♥ q ❲ q − ✶ − ❲ q ✮ Hierarchical Clustering 2.0 1.5 Hierarchical Classification 1.0 0.5 2.0 0.0 inertia gain 1.5 1.0 0.5 0.0 V Aub Silex S Michaud S Buisse Domaine S Buisse Cristal V Font Brûlés V Font Domaine V Aub Marigny V Font Coteaux S Trotignon S Renaudie ✽✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s P❛rt✐t✐♦♥ ❢r♦♠ t❤❡ tr❡❡ ❲ q − ❲ q + ✶ ❆♥ ❡♠♣✐r✐❝❛❧ ♥✉♠❜❡r ♦❢ ❝❧✉st❡rs ✐s s✉❣❣❡st❡❞ ✭♠✐♥ q ❲ q − ✶ − ❲ q ✮ Hierarchical Clustering 2.0 1.5 Hierarchical Classification 1.0 0.5 2.0 0.0 inertia gain 1.5 1.0 0.5 0.0 V Aub Silex S Michaud S Buisse Domaine S Buisse Cristal V Font Brûlés V Font Domaine V Aub Marigny V Font Coteaux S Trotignon S Renaudie ✽✼ ✴ ✾✽

Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s ▼✉❧t✐♣❧❡ ❋❛❝t♦r ❆♥❛❧②s✐s ❈❧✉st❡r✐♥❣ ❛♥❞ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ▼❡t❤♦❞s ❍✐❡r❛r❝❤✐❝❛❧ tr❡❡ ♦♥ t❤❡ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ♠❛♣ cluster 1 cluster 1 Hierarchical clustering on the factor map Hierarchical clustering on the factor map cluster 2 cluster 2 cluster 3 cluster 3 cluster 4 cluster 4 cluster 5 cluster 5 2.5 2.5 2.0 2.0 1.5 1.5 Dim 2 (24.42%) Dim 2 (24.42%) height height S Trotignon S Trotignon 2 2 1.0 1.0 S Renaudie S Renaudie V Aub Marigny V Aub Marigny 1 1 S Michaud S Michaud 0 0 S Buisse Cristal S Buisse Cristal V Font Coteaux V Font Coteaux 0.5 0.5 -1 -1 V Font Domaine V Font Domaine S Buisse Domaine S Buisse Domaine V Font Brûlés V Font Brûlés -2 -2 V Aub Silex V Aub Silex -3 -3 0.0 0.0 -2 -2 -1 -1 0 0 1 1 2 2 3 3 Dim 1 (42.52%) Dim 1 (42.52%) ❍✐❡r❛r❝❤✐❝❛❧ tr❡❡ ❣✐✈❡s ❛♥ ✐❞❡❛ ♦❢ t❤❡ ♦t❤❡r ❞✐♠❡♥s✐♦♥s ✽✽ ✴ ✾✽