r t tt - PowerPoint PPT Presentation

●r❡❡❞② ❢✉♥❝t✐♦♥ ♦♣t✐♠✐③❛t✐♦♥ ✐♥ ❧❡❛r♥✐♥❣ t♦ r❛♥❦ ➚♥❞r❡② ●✉❧✐♥✱ P❛✈❡❧ ❑❛r♣♦✈✐❝❤ P❡tr♦③❛✈♦❞s❦ ✷✵✵✾

❆♥♥♦t❛t✐♦♥ ●r❡❡❞② ❢✉♥❝t✐♦♥ ❛♣♣r♦①✐♠❛t✐♦♥ ❛♥❞ ❜♦♦st✐♥❣ ❛❧❣♦r✐t❤♠s ❛r❡ ✇❡❧❧ s✉✐t❡❞ ❢♦r s♦❧✈✐♥❣ ♣r❛❝t✐❝❛❧ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ t❛s❦s✳ ❲❡ ✇✐❧❧ ❞❡s❝r✐❜❡ ✇❡❧❧✲❦♥♦✇♥ ❜♦♦st✐♥❣ ❛❧❣♦r✐t❤♠s ❛♥❞ t❤❡✐r ♠♦❞✐✜❝❛t✐♦♥s ✉s❡❞ ❢♦r s♦❧✈✐♥❣ ❧❡❛r♥✐♥❣ t♦ r❛♥❦ ♣r♦❜❧❡♠s✳

❈♦♥t❡♥t ❼ ❙❡❛r❝❤ ❡♥❣✐♥❡ r❛♥❦✐♥❣✳ ❼ ❊✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s✳ ❼ ❋❡❛t✉r❡ ❜❛s❡❞ r❛♥❦✐♥❣ ♠♦❞❡❧✳ ❼ ▲❡❛r♥✐♥❣ t♦ r❛♥❦✳ ❖♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s✭❧✐st✇✐s❡✱ ♣♦✐t♥✇✐s❡✱ ♣❛✐r✇✐s❡ ❛♣♣r♦❛❝❤❡s✮✳ ❼ P♦✐♥t✇✐s❡ ❛♣♣r♦❛❝❤✳ ❇♦♦st✐♥❣ ❛❧❣♦r✐t❤♠s ❛♥❞ ❣r❡❡❞② ❢✉♥❝t✐♦♥ ❛♣♣r♦①✐♠❛t✐♦♥✳ ❼ ▼♦❞✐✜❝❛t✐♦♥ ▼❛tr✐①◆❡t✳ ❼ ▲✐st✇✐s❡ ❛♣♣r♦❛❝❤✳ ❆♣♣r♦①✐♠❛t✐♦♥s ♦❢ ❝♦♠♣❧❡① ❡✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s✭❉❈●✱ ♥❉❈●✮✳

❙❡❛r❝❤ ❡♥❣✐♥❡ r❛♥❦✐♥❣ ▼❛✐♥ ❣♦❛❧ ✿ t♦ r❛♥❦ ❞♦❝✉♠❡♥ts ❛❝❝♦r❞✐♥❣ t♦ t❤❡✐r q✉❛❧✐t② ♦❢ ❝♦♥❢♦r♠❛♥❝❡ t♦ t❤❡ s❡❛r❝❤ q✉❡r②✳ ❍♦✇ t♦ ❡✈❛❧✉❛t❡ r❛♥❦✐♥❣❄ Pr❡r❡q✉✐s✐t❡s✿ ❼ ❙❡t ♦❢ s❡❛r❝❤ q✉❡r✐❡s Q = { q 1 , .., q n } ✳ ❼ ❙❡t ♦❢ ❞♦❝✉♠❡♥ts ❝♦rr❡s♣♦♥❞✐♥❣ t♦ ❡❛❝❤ q✉❡r② q ∈ Q ✳ q → { d 1 , d 2 , ... } ❼ ❘❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥ts ❢♦r ❡❛❝❤ ♣❛✐r ( query, document ) ✭■♥ ♦✉r ♠♦❞❡❧ r❡❛❧ ♥✉♠❜❡rs rel ( q, d ) ∈ [0 , 1] ✮

❊✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s ❊✈❛❧✉❛t✐♦♥ ♠❛r❦ ❢♦r r❛♥❦✐♥❣ ✇✐❧❧ ❜❡ ❛♥ ❛✈❡r❛❣❡ ✈❛❧✉❡ ♦❢ ❡✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡ ♦✈❡r t❤❡ s❡t ♦❢ s❡❛r❝❤ q✉❡r✐❡s Q ✿ � EvMeas ( ranking for query q ) q ∈ Q n ❊①❛♠♣❧❡ ♦❢ ❡✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡ EvMeas ✿ ❼ Pr❡❝✐s✐♦♥✲✶✵ ✲ ♣❡r❝❡♥t ♦❢ ❞♦❝✉♠❡♥ts ✇✐t❤ r❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥ts ❣r❡❛t❡r t❤❛♥ ✵ ✐♥ t♦♣✲✶✵

❊✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s ❊✈❛❧✉❛t✐♦♥ ♠❛r❦ ❢♦r r❛♥❦✐♥❣ ✇✐❧❧ ❜❡ ❛♥ ❛✈❡r❛❣❡ ✈❛❧✉❡ ♦❢ ❡✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡ ♦✈❡r t❤❡ s❡t ♦❢ s❡❛r❝❤ q✉❡r✐❡s Q ✿ � EvMeas ( ranking for query q ) q ∈ Q n ❊①❛♠♣❧❡ ♦❢ ❡✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡ EvMeas ✿ ❼ Pr❡❝✐s✐♦♥✲✶✵ ✲ ♣❡r❝❡♥t ♦❢ ❞♦❝✉♠❡♥ts ✇✐t❤ r❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥ts ❣r❡❛t❡r t❤❛♥ ✵ ✐♥ t♦♣✲✶✵

❊✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s ❼ ▼❆P ✲ ♠❡❛♥ ❛✈❡r❛❣❡ ♣r❡❝✐s✐♦♥ k MAP ( ranking for query q ) = 1 i � k n r ( i ) i =1 k ✲ ♥✉♠❜❡r ♦❢ ❞♦❝✉♠❡♥ts ✇✐t❤ ♣♦s✐t✐✈❡ r❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥ts ❝♦rr❡s♣♦♥❞✐♥❣ t♦ q✉❡r② q ✱ n r ( i ) ✲ ♣♦s✐t✐♦♥ ♦❢ t❤❡ i ✲t❤ ❞♦❝✉♠❡♥t ✇✐t❤ r❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥t ❣r❡❛t❡r t❤❛♥ ✵✳

❊✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s ❼ ❉❈● ✲ ❞✐s❝♦✉♥t❡❞ ❝✉♠✉❧❛t✐✈❡ ❣❛✐♥ N q rel j � DCG ( ranking for query q ) = log 2 j + 1 j =1 N q ✲ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❞♦❝✉♠❡♥ts ✐♥ r❛♥❦❡❞ ❧✐st✱ rel j ✲ r❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥t ❢♦r ❞♦❝✉♠❡♥t ♦♥ ♣♦s✐t✐♦♥ j ✳ ❼ ♥♦r♠❛❧✐③❡❞ ❉❈●✭♥❉❈●✮ DCG ( ranking for query q ) nDCG ( ... ) = DCG ( ideal ranking for query q )

❋❡❛t✉r❡ ❜❛s❡❞ r❛♥❦✐♥❣ ♠♦❞❡❧ ❼ ❊❛❝❤ ♣❛✐r ( query, document ) ✐s ❞❡s❝r✐❜❡❞ ❜② t❤❡ ✈❡❝t♦r ♦❢ ❢❡❛t✉r❡s✳ ( q, d ) → ( f 1 ( q, d ) , f 2 ( q, d ) , .. ) ❼ ❙❡❛r❝❤ r❛♥❦✐♥❣ ✐s t❤❡ s♦rt✐♥❣ ❜② t❤❡ ✈❛❧✉❡ ♦❢ ✧r❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥✧ ✳ ❘❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥ ✐s ❛ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ❢❡❛t✉r❡s✿ fr ( q, d ) = 3 . 14 · log 7 ( f 9 ( q, d )) + e f 66 ( q,d ) + ...

❋❡❛t✉r❡ ❜❛s❡❞ r❛♥❦✐♥❣ ♠♦❞❡❧ ❼ ❊❛❝❤ ♣❛✐r ( query, document ) ✐s ❞❡s❝r✐❜❡❞ ❜② t❤❡ ✈❡❝t♦r ♦❢ ❢❡❛t✉r❡s✳ ( q, d ) → ( f 1 ( q, d ) , f 2 ( q, d ) , .. ) ❼ ❙❡❛r❝❤ r❛♥❦✐♥❣ ✐s t❤❡ s♦rt✐♥❣ ❜② t❤❡ ✈❛❧✉❡ ♦❢ ✧r❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥✧ ✳ ❘❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥ ✐s ❛ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ❢❡❛t✉r❡s✿ fr ( q, d ) = 3 . 14 · log 7 ( f 9 ( q, d )) + e f 66 ( q,d ) + ...

❖♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s ❍♦✇ t♦ ❣❡t ❛ ❣♦♦❞ r❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥❄ ●❡t ❧❡❛r♥✐♥❣ s❡t ♦❢ ❡①❛♠♣❧❡s P l ✲ s❡t ♦❢ ♣❛✐rs ( q, d ) ✇✐t❤ r❡❧❡✈❛♥❝❡ ❥✉❞❣♠❡♥ts rel ( q, d ) ✳ ❯s❡ ❧❡❛r♥✐♥❣ t♦ r❛♥❦ ♠❡t❤♦❞s t♦ ♦❜t❛✐♥ fr ✳

❖♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s ✭❧✐st✇✐s❡ ❛♣♣r♦❛❝❤✮ ❼ ❙♦❧✈❡ ❞✐r❡❝t ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠✿ � EvMeas ( ranking for query q with fr ) q ∈ Q l arg max fr ∈ F = n F ✲ s❡t ♦❢ ♣♦ss✐❜❧❡ r❛♥❦✐♥❣ ❢✉♥❝t✐♦♥s✳ Q l ✲ s❡t ♦❢ ❞✐✛❡r❡♥t q✉❡r✐❡s ✐♥ ❧❡❛r♥✐♥❣ s❡t P l ❉✐✣❝✉❧t② ✐♥ s♦❧✈✐♥❣✿ ♠♦st ♦❢ ❡✈❛❧✉❛t✐♦♥ ♠❡❛s✉r❡s ❛r❡ ♥♦♥✲❝♦♥t✐♥✉♦✉s ❢✉♥❝t✐♦♥s✳

❖♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s ✭♣♦✐♥t✇✐s❡ ❛♣♣r♦❛❝❤✮ ❼ ❙✐♠♣❧✐❢② ♦♣t✐♠✐③❛t✐♦♥ t❛s❦ t♦ r❡❣r❡ss✐♦♥ ♣r♦❜❧❡♠ ❛♥❞ ♠✐♥✐♠✐③❡ s✉♠ ♦❢ ❧♦ss ❢✉♥❝t✐♦♥s✿ � L ( fr ( q, d ) , rel ( q, d )) ( q,d ) ∈ P l arg min fr ∈ F L t ( fr ) = n L ( fr ( q, d ) , rel ( q, d )) ✲ ❧♦ss ❢✉♥❝t✐♦♥✱ F ✲ s❡t ♦❢ ♣♦ss✐❜❧❡ r❛♥❦✐♥❣ ❢✉♥❝t✐♦♥s✳ ❊①❛♠♣❧❡s ♦❢ ❧♦ss ❢✉♥❝t✐♦♥s✿ ❼ L ( fr, rel ) = ( fr − rel ) 2 ❼ L ( fr, rel ) = | fr − rel |

❖♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠ ✭♣❛✐r✇✐s❡ ❛♣♣r♦❛❝❤✮ ❼ ❚r② t♦ ✉s❡ ✇❡❧❧✲❦♥♦✇♥ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s t♦ s♦❧✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ ❝❧❛ss✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠✿ ❼ ❛♥ ♦r❞❡r❡❞ ♣❛✐r ♦❢ ❞♦❝✉♠❡♥ts ( d 1 , d 2 ) ✭❝♦rr❡s♣♦♥❞✐♥❣ t♦ q✉❡r② q ✮ ❜❡❧♦♥❣s t♦ ✜rst ❝❧❛ss ✐✛ rel ( q, d 1 ) > rel ( q, d 2 ) ❼ ❛♥ ♦r❞❡r❡❞ ♣❛✐r ♦❢ ❞♦❝✉♠❡♥ts ( d 1 , d 2 ) ✭❝♦rr❡s♣♦♥❞✐♥❣ t♦ q✉❡r② q ✮ ❜❡❧♦♥❣s t♦ s❡❝♦♥❞ ❝❧❛ss ✐✛ rel ( q, d 1 ) ≤ rel ( q, d 2 )

❇♦♦st✐♥❣ ❛❧❣♦r✐t❤♠s ❛♥❞ ❣r❡❡❞② ❢✉♥❝t✐♦♥ ❛♣♣r♦①✐♠❛t✐♦♥ ❲❡ ✇✐❧❧ s♦❧✈❡ r❡❣r❡ss✐♦♥ ♣r♦❜❧❡♠✿ � L ( fr ( q, d ) , rel ( q, d )) ( q,d ) ∈ P l arg min n fr ∈ F ❲❡ ✇✐❧❧ s❡❛r❝❤ r❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ❢♦r♠✿ M � fr ( q, d ) = α k h k ( q, d ) k =1 ❘❡❧❡✈❛♥❝❡ ❢✉♥❝t✐♦♥ ✇✐❧❧ ❜❡ ❛ ❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ❢✉♥❝t✐♦♥s h k ( q, d ) ✱ ❢✉♥❝t✐♦♥s h k ( q, d ) ❜❡❧♦♥❣ t♦ s✐♠♣❧❡ ❢❛♠✐❧② H ✭✇❡❛❦ ❧❡❛r♥❡rs ❢❛♠✐❧②✮ ✳