![Application (introduction)
We use data of «nayn.co» a news portal in Turkish Language. Data is imported by url
«"https://raw.githubusercontent.com/naynco/nayn.data/master/classification_clean.c
sv"» as done in chapter one.
Head of data is presented below
There are 11622 documents («Title» column) with label («DÜNYA» (World), «SPOR» (Sports),
«SANAT»(Art) and «Teknoloji»(Technology)). But data is imbalanced in favor of category «DÜNYA» such
that the counts [and percentages] of categories 9226[%79] ,1967 [%17],285 [%2] and 144 [%1]
respectively.](https://image.slidesharecdn.com/episodetwocombinatorialapproach-211217124044/85/PREDICTION-MODELS-BASED-ON-MAX-STEMS-Episode-Two-Combinatorial-Approach-12-320.jpg)
![Application (computations)
Now Let’s show an example and compute its parameters (or compounds of models). We apply models to document,
used in chapter one, with index number 𝑖 = 38296 , 𝑟𝑎𝑛𝑘 𝑖𝑛 𝑡𝑒𝑠𝑡 𝑠𝑒𝑡 = 1356 (index number may not be related to
rank). We examine case 𝑠 = 2, because set of 𝑐𝑜𝑚𝑏𝑜𝑖𝑗
𝑠
of the document is empty for s > 2 .
𝑑𝑜𝑐𝑖: 2 𝑘𝑒𝑑𝑖 2 yıldır sanat müzesine girmeye çalışıyor. (𝑒𝑛: 2 𝑐𝑎𝑡𝑠 𝑡𝑟𝑦 𝑡𝑜 𝑒𝑛𝑡𝑒𝑟 𝑎𝑟𝑡 𝑚𝑢𝑠𝑒𝑢𝑚 𝑓𝑜𝑟 2 𝑦𝑒𝑎𝑟𝑠)
𝑙𝑎𝑏𝑒𝑙𝑖: 𝐷Ü𝑁𝑌𝐴 (𝑒𝑛: 𝑤𝑜𝑟𝑙𝑑)
𝑠𝑡𝑒𝑚𝑠: [′𝑘𝑒𝑑𝑖′, ′𝑦𝚤𝑙𝑑𝚤𝑟′, ′𝑠𝑎𝑛𝑎𝑡′, ′𝑚ü𝑧𝑒′, ′𝑔𝑖𝑟′, ′ç𝑎𝑙𝚤′]
Output of analyze_doc(doc,X_train,y_train): 𝑗 = 1, … , 𝑚𝑖
2
= 7
Output of analyze_doc_s(doc,X_train,y_train,2):𝑗 = 1, … , 7 𝑚𝑖 = 6
𝑐𝑜𝑚𝑏𝑜𝑖𝑗
2
𝜆𝑖𝑗
2
Σ𝑖𝑗
𝑝,2
Π𝑖𝑗
𝑝,2
Λ𝑖
𝑝,2 Category of
2nd max Σ𝑖𝑗
𝑝,2
(not used)
4/6/2022
EMREHAN 15](https://image.slidesharecdn.com/episodetwocombinatorialapproach-211217124044/85/PREDICTION-MODELS-BASED-ON-MAX-STEMS-Episode-Two-Combinatorial-Approach-15-320.jpg)
![Application (computations)
𝑖 = 38296, 𝑠 = 2
𝑐𝑜𝑚𝑏𝑜: comboi1
2
= [′sanat′,′müze′], comboi2
2
= [′kedi′,′gir′], comboi3
2
= [′müze′,′çalı′], comboi4
2
= [′kedi′,′yıldır′],
comboi5
2
= [′gir′,′çalı′], comboi6
2
= [′yıldır′,′çalı′], comboi7
2
= [′sanat′,′çalı′]
𝑠𝑢𝑚 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑡𝑒𝑚𝑠 𝑖𝑛 𝑐𝑜𝑚𝑏𝑜𝑖𝑗
𝑠
∶ 𝜆𝑖1
2
= 9, 𝜆𝑖2
2
= 7, 𝜆𝑖3
2
= 8, 𝜆𝑖4
2
= 9, 𝜆𝑖5
2
= 7, 𝜆𝑖6
2
= 10, 𝜆𝑖7
2
= 9
Σ𝑖𝑗
𝑝,𝑠
: 𝑐𝑜𝑢𝑛𝑡𝑠 𝑜𝑓 𝑑𝑜𝑐𝑢𝑚𝑒𝑛𝑡𝑠, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑛𝑐𝑙𝑢𝑑𝑒 𝑎𝑙𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑜𝑓𝑐𝑜𝑚𝑏𝑜𝑖𝑗
𝑠
, 𝑙𝑎𝑏𝑒𝑙𝑙𝑒𝑑 𝑤𝑖𝑡ℎ 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝑤𝑖𝑡ℎ 𝑖𝑛𝑑𝑒𝑥 𝑝 𝑖𝑛 𝑡𝑟𝑎𝑖𝑛 𝑠𝑒𝑡
𝑓𝑜𝑟 𝑗 = 3 𝑎𝑛𝑑 𝑗 = 7 : Σ𝑖3
1,2
= 2,: Σ𝑖3
2,2
= 0, Σ𝑖3
3,2
= 1, Σ𝑖3
,4,2
= 0 , Σ𝑖7
1,2
= 1, Σ𝑖7
1,2
= 0, Σ𝑖7
1,2
= 0, Σ𝑖7
1,2
= 0
Λ𝑖𝑗: = 𝐿𝑎𝑏𝑒𝑙𝑞
𝑤ℎ𝑒𝑟𝑒 𝑞 = arg max
𝑝
Σ𝑖𝑗
𝑝
: Λi1 = "SANAT", Λi2 = "DÜNYA", Λi3 = "DÜNYA" , Λi4="DÜNYA",
Λi5="DÜNYA", Λi6 = "SPOR", Λi7="DÜNYA"
Λ𝑖
𝑝
: counts of Λ𝑖𝑗 𝑤ℎ𝑖𝑐ℎ 𝑒𝑞𝑢𝑎𝑙𝑠 𝑡𝑜 𝐿𝑎𝑏𝑒𝑙𝑝
, Λ𝑖
1
= 5, Λ𝑖
2
= 1, Λ𝑖
3
= 1, Λ𝑖
4
= 0
Π𝑖𝑗
𝑝
for j = 1 and j = 5 ∶ Π𝑖1
1,2
= 0, Π𝑖1
2,2
= 0, Π𝑖1
3,2
= 1, Π𝑖1
4,2
= 0, Π𝑖5
1,2
= 0.75, Π𝑖5
2,2
= 0.25, Π𝑖5
3,2
= 0, Π𝑖5
4,2
= 0
4/6/2022
EMREHAN 16](https://image.slidesharecdn.com/episodetwocombinatorialapproach-211217124044/85/PREDICTION-MODELS-BASED-ON-MAX-STEMS-Episode-Two-Combinatorial-Approach-16-320.jpg)
PREDICTION MODELS BASED ON MAX-STEMS Episode Two: Combinatorial Approach
- 1. PREDICTION MODELS BASED ON MAX-STEMS (or harnessing imbalanced data) Episode Two: A Combinatorial Approach Ahmet Furkan EMREHAN (matahmet@gmail.com)
- 2. MOTIVATION This study is an extension of previous study (chapter one) with combinatiorial approach. In chapter one, I examine five models using distribution of stems separately. Combination of stems with s-elements have a potential to help efficient prediction. Because documents including comination of stems may be semantically closer than one stem based prediction (defined in chapter one).
- 3. ADAPTATION OF COMPONENTS OF MODELS 𝑝, 𝐿𝑎𝑏𝑒𝑙𝑝 , 𝑛, 𝑑𝑜𝑐𝑖 𝑎𝑛𝑑 Σ𝑝 , components of general parameters, are defined in Chapter One−Slide 8 𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 ∶ 𝑐𝑜𝑚𝑏𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑒𝑚𝑠 𝑖𝑛𝑑𝑒𝑥𝑒𝑑 𝑗 𝑤𝑖𝑡ℎ 𝑠 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑜𝑓𝑑𝑜𝑐𝑖 𝑠𝑡𝑒𝑚 𝑐𝑎𝑛 𝑏𝑒 𝑐ℎ𝑜𝑠𝑒𝑛 𝑎𝑠 𝑚𝑎𝑥 − 𝑠𝑡𝑒𝑚 𝑚𝑒𝑛𝑡𝑖𝑜𝑛𝑒𝑑 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑠𝑙𝑖𝑑𝑒𝑠. 𝑚𝑖 𝑠 : 𝑐𝑜𝑢𝑛𝑡𝑠 𝑜𝑓𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 Σ𝑖𝑗 𝑝,𝑠 : 𝑐𝑜𝑢𝑛𝑡𝑠 𝑜𝑓 𝑑𝑜𝑐𝑢𝑚𝑒𝑛𝑡𝑠, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑛𝑐𝑙𝑢𝑑𝑒 𝑎𝑙𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑜𝑓𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 , 𝑙𝑎𝑏𝑒𝑙𝑙𝑒𝑑 𝑤𝑖𝑡ℎ 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝑤𝑖𝑡ℎ 𝑖𝑛𝑑𝑒𝑥 𝑝 𝑖𝑛 𝑡𝑟𝑎𝑖𝑛 𝑠𝑒𝑡 Λ𝑖𝑗 𝑠 : = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg max 𝑝 Σ𝑖𝑗 𝑝,𝑠 Λ𝑖 𝑝,𝑠 : counts of Λ𝑖𝑗 𝑠 𝑤ℎ𝑖𝑐ℎ 𝑒𝑞𝑢𝑎𝑙𝑠 𝑡𝑜 𝐿𝑎𝑏𝑒𝑙𝑝
- 4. ADAPTATION OF COMPONENTS OF MODELS 𝜆𝑖𝑗 𝑠 : 𝑠𝑢𝑚 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑡𝑒𝑚𝑠 𝑖𝑛 𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 𝜌𝑖 𝑝,𝑠 ≔ 𝑗=1 𝑚𝑖 Σ𝑖𝑗 𝑝,𝑠 Σ𝑝 * ∗ 𝑖𝑛 𝑐𝑎𝑠𝑒 𝑡ℎ𝑎𝑡 Σ𝑝=0, 𝜌𝑖 𝑝 =0 Π𝑖𝑗 𝑝,𝑠 ≔ Σ𝑖𝑗 𝑝,𝑠 𝑞=1 𝑛 Σ𝑖𝑗 𝑞 (𝑖𝑡 𝑐𝑎𝑛 𝑏𝑒 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑒𝑑 𝑎𝑠 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 , 𝑙𝑎𝑏𝑒𝑙𝑙𝑒𝑑 𝑤𝑖𝑡ℎ 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝑤𝑖𝑡ℎ 𝑝 𝑖𝑛𝑑𝑒𝑥) Π𝑖 𝑝,𝑠 : = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒𝑗∗ Π𝑖𝑗∗ 𝑝,𝑠 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑎𝑙𝑙 "j∗"s 𝑚𝑒𝑒𝑡 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 Π𝑖𝑗∗ 𝑝,𝑠 > 0 * ∗ in case that Σ𝑖𝑗 𝑝,𝑠 = 0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑝 = 1,2, … 𝑛, Π𝑖 𝑝,𝑠 =0 Π𝑖 𝑝,𝑠 ≔ max 𝑗(Π𝑖𝑗 𝑝,𝑠 )
- 5. General Scheme for Prediction Models with Combinatorial Approach X_test 𝑑𝑜𝑐𝑖 𝑑𝑜𝑐𝑖 = 𝑙𝑜𝑤𝑒𝑟(𝑑𝑜𝑐𝑖) 𝑡𝑜𝑘𝑒𝑛𝑖 = 𝑐𝑙𝑒𝑎𝑛(𝑑𝑜𝑐𝑖) 𝑑𝑜𝑐𝑖 = 𝑐𝑙𝑒𝑎𝑛(𝑑𝑜𝑐𝑖) 𝑠𝑡𝑒𝑚𝑠𝑖 = max _𝑠𝑡𝑒𝑚𝑠(𝑡𝑜𝑘𝑒𝑛𝑖) 𝑐𝑜𝑚𝑏𝑜𝑖𝑖1 𝑐𝑜𝑚𝑏𝑜𝑖𝑖2 𝑐𝑜𝑚𝑏𝑜𝑖𝑖𝑚𝑖 𝑠 . . . Σ𝑖1 𝑝,𝑠 , Π𝑖1 𝑝,𝑠 , Λ𝑖1 𝑠 ,𝜆𝑖1 𝑠 Σ𝑖2 𝑝,𝑠 , Π𝑖2 𝑝,𝑠 , Λ𝑖2 𝑠 ,𝜆𝑖2 𝑠 Σ𝑖𝑚𝑖 𝑝,𝑠 , Π𝑖𝑚𝑖 𝑝,𝑠 , , Λ𝑖𝑚𝑖 𝑠 𝑠 , 𝜆𝑖𝑚𝑖 𝑠 𝑠 . . . Analyze_word_s Predictions With Combinatiorial Approach X_train, y_train Evaluations (accuracy, confusion etc.) y_test 𝑐𝑜𝑚𝑏𝑜𝑖 𝑠 = get_combo(𝑠𝑡𝑒𝑚𝑠𝑖)
- 6. Model 1 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏1 𝑑𝑜𝑐𝑖, 𝑠 = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑖𝑓 Σ𝑖𝑗 𝑝,𝑠 = 0 < Σ𝑖𝑗 𝑞,𝑠 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑝 ≠ 𝑞 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg 2𝑛𝑑 𝑚𝑎𝑥𝑝 Λ𝑖 𝑝,𝑠 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 ∗ ∗ 𝑖𝑛 𝑐𝑎𝑠𝑒 𝑡ℎ𝑎𝑡 𝑞 𝑖𝑠 𝑛𝑜𝑡 𝑢𝑛𝑖𝑞𝑒, 𝑞 𝑖𝑠 𝑐ℎ𝑜𝑠𝑒𝑛 𝑎𝑠 𝑡ℎ𝑒 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑖𝑛𝑑𝑒𝑥 𝑚𝑒𝑒𝑡𝑖𝑛𝑔 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 4/6/2022 EMREHAN 6
- 7. Model 2 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏2 𝑑𝑜𝑐𝑖, 𝑠 = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg 𝑚𝑎𝑥𝑝 𝜌𝑖 𝑝,𝑠 4/6/2022 EMREHAN 7
- 8. Model 3 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏3 𝑑𝑜𝑐𝑖, 𝑠 = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg 𝑚𝑎𝑥𝑝Π𝑖 𝑝,𝑠 4/6/2022 EMREHAN 8
- 9. Model 4 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏4 𝑑𝑜𝑐𝑖, 𝑠 = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg 𝑚𝑎𝑥𝑝Π𝑖 𝑝,𝑠 ∗ 𝑖𝑛 𝑐𝑎𝑠𝑒 𝑡ℎ𝑎𝑡 𝑞 𝑖𝑠 𝑛𝑜𝑡 𝑢𝑛𝑖𝑞𝑒, 𝑞 𝑖𝑠 𝑐ℎ𝑜𝑠𝑒𝑛 𝑎𝑠 𝑡ℎ𝑒 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑖𝑛𝑑𝑒𝑥 𝑚𝑒𝑒𝑡𝑖𝑛𝑔 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 4/6/2022 EMREHAN 9
- 10. Model 5 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏5 𝑑𝑜𝑐𝑖, 𝑠 = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg 𝑚𝑎𝑥𝑝 (𝑚𝑎𝑥𝑗 𝜆𝑖𝑗 ∗ Σ𝑖𝑗 𝑝 Σ𝑝 ) 4/6/2022 EMREHAN 10
- 11. A Trivial Result 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏𝑘 𝑑𝑜𝑐𝑖, 1 = 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑘 𝑑𝑜𝑐𝑖 𝑓𝑜𝑟 𝑘 = 1,2, … , 5 Moreover all parameters in case s = 1, equal to corresponding parameters in chapter one (slides 8-10) For example 𝑚𝑖 𝑠 = 𝑚𝑖, Σ𝑖𝑗 𝑝,1 = Σ𝑖𝑗 𝑝 and Π𝑖 𝑝,1 = Π𝑖 𝑝 .
- 12. Application (introduction) We use data of «nayn.co» a news portal in Turkish Language. Data is imported by url «"https://raw.githubusercontent.com/naynco/nayn.data/master/classification_clean.c sv"» as done in chapter one. Head of data is presented below There are 11622 documents («Title» column) with label («DÜNYA» (World), «SPOR» (Sports), «SANAT»(Art) and «Teknoloji»(Technology)). But data is imbalanced in favor of category «DÜNYA» such that the counts [and percentages] of categories 9226[%79] ,1967 [%17],285 [%2] and 144 [%1] respectively.
- 13. General Scheme for Application of Prediction Models with Combinatorial Approach X_test 𝑑𝑜𝑐𝑖 𝑑𝑜𝑐𝑖 = 𝑙𝑜𝑤𝑒𝑟(𝑑𝑜𝑐𝑖) 𝑡𝑜𝑘𝑒𝑛𝑖 = 𝑐𝑙𝑒𝑎𝑛(𝑑𝑜𝑐𝑖) 𝑑𝑜𝑐𝑖 = 𝑐𝑙𝑒𝑎𝑛(𝑑𝑜𝑐𝑖) 𝑠𝑡𝑒𝑚𝑠𝑖 = max _𝑠𝑡𝑒𝑚𝑠(𝑡𝑜𝑘𝑒𝑛𝑖) 𝑐𝑜𝑚𝑏𝑜𝑖𝑖1 𝑐𝑜𝑚𝑏𝑜𝑖𝑖2 𝑐𝑜𝑚𝑏𝑜𝑖𝑖𝑚𝑖 𝑠 . . . Σ𝑖1 𝑝,𝑠 , Π𝑖1 𝑝,𝑠 , Λ𝑖1 𝑠 ,𝜆𝑖1 𝑠 Σ𝑖2 𝑝,𝑠 , Π𝑖2 𝑝,𝑠 , Λ𝑖2 𝑠 ,𝜆𝑖2 𝑠 Σ𝑖𝑚𝑖 𝑝,𝑠 , Π𝑖𝑚𝑖 𝑝,𝑠 , , Λ𝑖𝑚𝑖 𝑠 𝑠 , 𝜆𝑖𝑚𝑖 𝑠 𝑠 . . . Analyze_word_s Predictions With Combinatiorial Approach X_train, y_train Evaluations (accuracy, confusion etc.) y_test 𝑐𝑜𝑚𝑏𝑜𝑖 𝑠 = get_combo(𝑠𝑡𝑒𝑚𝑠𝑖) Turkish Stem List (32001 stems) (for application) Step2_Preprocess_word.ipynb Step3_Classifier_V10.ipynb Step4_Prediction_Models_cb.ipynb Step6_Run_Integrated_Model_cb.ipynb 13
- 14. Application (computations) Pandas and Sklearn libraries in Python is used for application of methods. Test size is chosen as 0.2 and random_state parameter for partition as 57. Values of parameters in model are computed below Counts of categories: 𝑛 = 4 Indexes and name of categories: 𝑝 = 1,2,3 𝑎𝑛𝑑 4 , 𝐿𝑎𝑏𝑒𝑙𝑝 = "DÜNYA","SPOR","SANAT and "Teknoloji", 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦 Counts of categories in train set : Σ1 = 7384, Σ2 = 1568, Σ3 = 229 𝑎𝑛𝑑 Σ4 = 116 4/6/2022 EMREHAN 14
- 15. Application (computations) Now Let’s show an example and compute its parameters (or compounds of models). We apply models to document, used in chapter one, with index number 𝑖 = 38296 , 𝑟𝑎𝑛𝑘 𝑖𝑛 𝑡𝑒𝑠𝑡 𝑠𝑒𝑡 = 1356 (index number may not be related to rank). We examine case 𝑠 = 2, because set of 𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 of the document is empty for s > 2 . 𝑑𝑜𝑐𝑖: 2 𝑘𝑒𝑑𝑖 2 yıldır sanat müzesine girmeye çalışıyor. (𝑒𝑛: 2 𝑐𝑎𝑡𝑠 𝑡𝑟𝑦 𝑡𝑜 𝑒𝑛𝑡𝑒𝑟 𝑎𝑟𝑡 𝑚𝑢𝑠𝑒𝑢𝑚 𝑓𝑜𝑟 2 𝑦𝑒𝑎𝑟𝑠) 𝑙𝑎𝑏𝑒𝑙𝑖: 𝐷Ü𝑁𝑌𝐴 (𝑒𝑛: 𝑤𝑜𝑟𝑙𝑑) 𝑠𝑡𝑒𝑚𝑠: [′𝑘𝑒𝑑𝑖′, ′𝑦𝚤𝑙𝑑𝚤𝑟′, ′𝑠𝑎𝑛𝑎𝑡′, ′𝑚ü𝑧𝑒′, ′𝑔𝑖𝑟′, ′ç𝑎𝑙𝚤′] Output of analyze_doc(doc,X_train,y_train): 𝑗 = 1, … , 𝑚𝑖 2 = 7 Output of analyze_doc_s(doc,X_train,y_train,2):𝑗 = 1, … , 7 𝑚𝑖 = 6 𝑐𝑜𝑚𝑏𝑜𝑖𝑗 2 𝜆𝑖𝑗 2 Σ𝑖𝑗 𝑝,2 Π𝑖𝑗 𝑝,2 Λ𝑖 𝑝,2 Category of 2nd max Σ𝑖𝑗 𝑝,2 (not used) 4/6/2022 EMREHAN 15
- 16. Application (computations) 𝑖 = 38296, 𝑠 = 2 𝑐𝑜𝑚𝑏𝑜: comboi1 2 = [′sanat′,′müze′], comboi2 2 = [′kedi′,′gir′], comboi3 2 = [′müze′,′çalı′], comboi4 2 = [′kedi′,′yıldır′], comboi5 2 = [′gir′,′çalı′], comboi6 2 = [′yıldır′,′çalı′], comboi7 2 = [′sanat′,′çalı′] 𝑠𝑢𝑚 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑡𝑒𝑚𝑠 𝑖𝑛 𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 ∶ 𝜆𝑖1 2 = 9, 𝜆𝑖2 2 = 7, 𝜆𝑖3 2 = 8, 𝜆𝑖4 2 = 9, 𝜆𝑖5 2 = 7, 𝜆𝑖6 2 = 10, 𝜆𝑖7 2 = 9 Σ𝑖𝑗 𝑝,𝑠 : 𝑐𝑜𝑢𝑛𝑡𝑠 𝑜𝑓 𝑑𝑜𝑐𝑢𝑚𝑒𝑛𝑡𝑠, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑛𝑐𝑙𝑢𝑑𝑒 𝑎𝑙𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑜𝑓𝑐𝑜𝑚𝑏𝑜𝑖𝑗 𝑠 , 𝑙𝑎𝑏𝑒𝑙𝑙𝑒𝑑 𝑤𝑖𝑡ℎ 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝑤𝑖𝑡ℎ 𝑖𝑛𝑑𝑒𝑥 𝑝 𝑖𝑛 𝑡𝑟𝑎𝑖𝑛 𝑠𝑒𝑡 𝑓𝑜𝑟 𝑗 = 3 𝑎𝑛𝑑 𝑗 = 7 : Σ𝑖3 1,2 = 2,: Σ𝑖3 2,2 = 0, Σ𝑖3 3,2 = 1, Σ𝑖3 ,4,2 = 0 , Σ𝑖7 1,2 = 1, Σ𝑖7 1,2 = 0, Σ𝑖7 1,2 = 0, Σ𝑖7 1,2 = 0 Λ𝑖𝑗: = 𝐿𝑎𝑏𝑒𝑙𝑞 𝑤ℎ𝑒𝑟𝑒 𝑞 = arg max 𝑝 Σ𝑖𝑗 𝑝 : Λi1 = "SANAT", Λi2 = "DÜNYA", Λi3 = "DÜNYA" , Λi4="DÜNYA", Λi5="DÜNYA", Λi6 = "SPOR", Λi7="DÜNYA" Λ𝑖 𝑝 : counts of Λ𝑖𝑗 𝑤ℎ𝑖𝑐ℎ 𝑒𝑞𝑢𝑎𝑙𝑠 𝑡𝑜 𝐿𝑎𝑏𝑒𝑙𝑝 , Λ𝑖 1 = 5, Λ𝑖 2 = 1, Λ𝑖 3 = 1, Λ𝑖 4 = 0 Π𝑖𝑗 𝑝 for j = 1 and j = 5 ∶ Π𝑖1 1,2 = 0, Π𝑖1 2,2 = 0, Π𝑖1 3,2 = 1, Π𝑖1 4,2 = 0, Π𝑖5 1,2 = 0.75, Π𝑖5 2,2 = 0.25, Π𝑖5 3,2 = 0, Π𝑖5 4,2 = 0 4/6/2022 EMREHAN 16
- 17. Application (computations) 𝜌𝑖 𝑝 : 𝜌𝑖 1 = 8 7384 = 0.001, 𝜌𝑖 2 = 3 1568 = 0.002, 𝜌𝑖 3 = 3 229 = 0.013, 𝜌𝑖 4 = 0 116 = 0 Π𝑖 𝑝 : Π𝑖 1 = 1+0.67+1+0.75+1 4 = 0.884, Π𝑖 2 = 0.25+1 2 = 0.625, Π𝑖 3 = 1+0.33 2 = 0.665, Π𝑖 4 = 0 Π𝑖 𝑝 : Π𝑖 1 = 1, Π𝑖 2 = 1, Π𝑖 3 = 1, Π𝑖 4 = 0 4/6/2022 EMREHAN 17
- 18. Application (Predictions) 𝑓𝑜𝑟 𝑖 = 38296 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏1 𝑑𝑜𝑐𝑖, 2 = SPOR 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏2 𝑑𝑜𝑐𝑖, 2 = SANAT 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏3 𝑑𝑜𝑐𝑖, 2 = DÜNYA 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏4 𝑑𝑜𝑐𝑖, 2 = DÜNYA 𝑝𝑟𝑒𝑑𝑖𝑐𝑡_𝑐𝑏5 𝑑𝑜𝑐𝑖, 2 = SANAT
- 19. Application (Results) Confusion Matrix for Model 1 (count) s= 2 Confusion Matrix for Model 1 (percentage) Prediction Prediction (rounded to 2 digits) DÜNYA SANAT SPOR Teknoloji No Prediction Total DÜNYA SANAT SPOR Teknoloji No Prediction Total Observed DÜNYA 1204 47 519 47 25 1842 0.65 0.03 0.28 0.03 0.01 1 SANAT 15 23 15 0 3 56 0.27 0.41 0.27 0 0.05 1 SPOR 201 3 182 0 13 399 0.5 0.01 0.46 0 0.03 1 Teknoloji 18 0 8 2 0 28 0.64 0 0.29 0.07 0 1 Accuracy Rate For Model 1 0.61 Confusion Matrix for Model 2 (count) s= 2 Confusion Matrix for Model 2 (percentage) Prediction Prediction (rounded to 2 digits) DÜNYA SANAT SPOR Teknoloji No Prediction Total DÜNYA SANAT SPOR Teknoloji No Prediction Total Observed DÜNYA 1286 174 130 227 25 1842 0.7 0.09 0.07 0.12 0.01 1 SANAT 3 41 9 0 3 56 0.05 0.73 0.16 0 0.05 1 SPOR 30 18 324 14 13 399 0.08 0.05 0.81 0.04 0.03 1 Teknoloji 14 0 2 12 0 28 0.5 0 0.07 0.43 0 1 Accuracy Rate For Model 2 0.72
- 20. Application (Results) Confusion Matrix for Model 3 (count) s= 2 Confusion Matrix for Model 3 (percentage) Prediction Prediction (rounded to 2 digits) DÜNYA SANAT SPOR Teknoloji No Prediction Total DÜNYA SANAT SPOR Teknoloji No Prediction Total Observed DÜNYA 1755 17 25 20 25 1842 0.95 0.01 0.01 0.01 0.01 1 SANAT 39 8 6 0 3 56 0.7 0.14 0.11 0 0.05 1 SPOR 159 8 214 5 13 399 0.4 0.02 0.54 0.01 0.03 1 Teknoloji 28 0 0 0 0 28 1 0 0 0 0 1 Accuracy Rate For Model 3 0.85 Confusion Matrix for Model 4 (count) s= 2 Confusion Matrix for Model 4 (percentage) Prediction Prediction (rounded to 2 digits) DÜNYA SANAT SPOR Teknoloji No Prediction Total DÜNYA SANAT SPOR Teknoloji No Prediction Total Observed DÜNYA 1805 3 7 2 25 1842 0.98 0 0 0 0.01 1 SANAT 47 2 4 0 3 56 0.84 0.04 0.07 0 0.05 1 SPOR 284 0 102 0 13 399 0.71 0 0.26 0 0.03 1 Teknoloji 28 0 0 0 0 28 1 0 0 0 0 1 Accuracy Rate For Model 4 0.82
- 21. Application (Results) Confusion Matrix for Model 5 (count) s= 2 Confusion Matrix for Model 5 (percentage) Prediction Prediction (rounded to 2 digits) DÜNYA SANAT SPOR Teknoloji No Prediction Total DÜNYA SANAT SPOR Teknoloji No Prediction Total Observed DÜNYA 977 289 189 362 25 1842 0.53 0.16 0.1 0.2 0.01 1 SANAT 3 40 10 0 3 56 0.05 0.71 0.18 0 0.05 1 SPOR 25 27 308 26 13 399 0.06 0.07 0.77 0.07 0.03 1 Teknoloji 10 0 3 15 0 28 0.36 0 0.11 0.54 0 1 Accuracy Rate For Model 5 0.58 A Note: All predictions of 25,2,13 documents labelled with «DÜNYA», «SANAT» and «SPOR» respectively are «No prediction». Because no combinations, with s = 2 stems,of those documents in test set are covered by a document in train set. Trivially prediction based combinations of stems of these documents, with s > 2 stems, are «No Predidiction». End of Chapter Two