ID3 (Iterative Dichotomiser 3 - Tekrarlanan ikili yapi)

Ozunde Entropy hesaplamasi kullanan bir algoritmadir. Entropy, bir veri kumesindeki verilerin belirsizliginin sayisallastirilmasi demektir.  Algoritmanin amaci, egitim kumesindeki verilerin agacin olusturulmasi esnasinda birbirine benzetilmesi gerekiyor, agac derinliginin minimum olmasi, karmasikliginda minimum olmasini saglarken kazancin maksimum olmasi gozle gorulur bir fark alacaktir.

ID3 (Iterative Dichotomiser 3 - Tekrarlanan ikili yapi ) :

Ozunde Entropy hesaplamasi kullanan bir algoritmadir. Entropy, bir veri kumesindeki verilerin belirsizliginin sayisallastirilmasi demektir.  Algoritmanin amaci, egitim kumesindeki verilerin agacin olusturulmasi esnasinda birbirine benzetilmesi gerekiyor, agac derinliginin minimum olmasi, karmasikliginda minimum olmasini saglarken kazancin maksimum olmasi gozle gorulur bir fark alacaktir. Entropy deger araligi 0 < entropy < log2n arasinda olmalidir. Entropy degeri log2n'e yaklastikca belirsizligin artmasi, 0'a yaklasmasiyla belirsizligin azalmasi olarak bilinecektir. Ilk hesaplanmasi gereken entropy, tum data setin hesaplanmasi ile olusur. Sonrasinda datasetin farkli nitelikleri icinde entropy hesaplanmaktadir. Tum bu islemleri bilgi edinim icin kullanilmaktadir. Bu kavramdaki kazanc ise, ilk hesaplanan entropy ile her bir alt kumenin olusumundaki entropylerin arasindaki fark hesaplandiktan sonra, farki buyuk olan karar agacinin sagligi acisindan en dogru dallanmayi yapmis olacaktir. Avantaj : Olasilik kurallari icin egitim verileri kullanilir ve tum data set'teki veriler agac olusturulmasi icin analiz edilir, sonucta kisa agaclar olusturdugu icin en hizli yapiya sahip olmus olur. Bu da, Test sayilarinin azalmasi ve test verilerinin budanmasini saglamaktadir. Dezavantaj : Dataset'ten aldigimiz egitim verilerimizin boyutu kucukse agac test edildiginde cikan sonucun basarisiz olma olasiligi cok yuksektir.

ID3 UYGULAMASI

1.Adim : Dataset Week    Weather    Temperatures (Isi)    Wetness     Wind (Ruzgar)    Game W1    Sunny    Warm    High    Slightly    No W2    Sunny    Warm    High    Strong    No W3    Cloudy    Warm    High    Slightly    Yes W4    Rainy    Warmish    High    Slightly    Yes W5    Rainy    Cold    Normal    Slightly    Yes W6    Rainy    Cold    Normal    Strong    No W7    Cloudy    Cold    Normal    Strong    Yes W8    Sunny    Warmish    High    Slightly    No W9    Sunny    Cold    Normal    Slightly    Yes W10    Rainy    Warmish    Normal    Slightly    Yes W11    Sunny    Warmish    Normal    Strong    Yes W12    Cloudy    Warmish    High    Strong    Yes W13    Cloudy    Warm    Normal    Slightly    Yes W14    Rainy    Warmish    High    Strong    No Game = {No, No, Yes, Yes, Yes, No, Yes, No, Yes, Yes, Yes, Yes, Yes, No} P(Game,No) = 5/14 P(Game,Yes) = 9/14 E(Game) = - ( P (Game,No) log2 P (Game, No) + P (Game,Yes) log2 P (Game,Yes) ) E(Game) = - ( 5/14 log2 5/14 + 9/14 log2 9/14 ) E(Game) = 0.940 1. Adim – Isi niteligi Entropy - Gain Cozumu

= 4

= 6

= 4 E(Game) = 0.940 E(Temp,Game) = P(Temp,Cold) * E(Temp,Cold) + P(Temp,Warmish) * E(Temp,Warmish) + P(Temp,Warm) * E(Temp,Warm) E(Temp,Game) = 4/14 E(Temp,Cold) + 6/14 E(Temp,Warmish) + 4/14 E(Temp,Warm) E(Temp,Cold) = - (1/4 log2 1/4 + 3/4 log2 3/4 ) E(Temp,Cold) = 0.811 E(Temp,Warmish) = - (2/6 log2 2/6+ 4/6 log2 4/6 ) E(Temp,Warmish) = 0.918 E(Temp,Warm) = - (2/4 log2 2/4 + 2/4 log2 2/4 ) E(Temp,Warm) = 1.00 E(Temp,Game) = 4/14 * 0.811 + 6/14 * 0.918 + 4/14 * 1.00 E(Temp,Game) = 0.911 Gain(Temp,Game) = E(Game) - E(Temp,Game) Gain(Temp,Game) = 0.940 – 0.911 Gain(Temp,Game) = 0.029 1. Adim – Hava niteligi Entropy - Gain Cozumu

= 5

= 5

= 4 E(Game) = 0.940 E(Weather,Game) = P(Weather,Sunny) * E(Weather,Sunny) + P(Weather,Cloudy) * E(Weather,Cloudy) + P(Weather,Rainy) * E(Weather,Rainy) E(Weather,Game) = 5/14 E(Weather,Sunny) + 4/14 E(Weather,Cloudy) + 5/14 E(Weather,Rainy) E(Weather,Sunny) = - (3/5 log2 3/5 + 2/5 log2 2/5 ) E(Weather,Sunny) = 0.971 E(Weather,Rainy) = - (2/5 log2 2/5+ 3/5 log2 3/5) E(Weather,Rainy) = 0.971 E(Weather,Cloudy) = - (4/4 log2 4/4) E(Weather,Cloudy) = 0 E(Weather,Game) = 5/14 * 0.971+ 5/14 * 0.971 + 4/14 * 0 E(Weather,Game) = 0.694 Gain(Weather,Game) = E(Game) - E(Weather,Game) Gain(Weather,Game) = 0.940 – 0.694 Gain(Weather,Game) = 0.247 1. Adim – Nem niteligi Entropy - Gain Cozumu

= 7

= 7 E(Game) = 0.940 E(Wetness,Game) = P(Wetness,High) * E(Wetness,High) + P(Wetness,Normal) * E(Wetness,Normal) E(Wetness,Game) = 7/14 E(Wetness,High) + 7/14 E(Wetness,Normal) E(Wetness,Sunny) = - (4/7 log2 4/7 + 3/7 log2 3/7 ) E(Wetness,Sunny) = 0.985 E(Wetness,Rainy) = - (1/7 log2 1/7+ 6/7 log2 6/7) E(Wetness,Rainy) = 0.592 E(Wetness,Game) = 7/14 * 0.985+ 7/14 * 0.592 E(Wetness,Game) = 0.789 Gain(Wetness,Game) = E(Game) - E(Wetness,Game) Gain(Wetness,Game) = 0.940 – 0.789 Gain(Wetness,Game) = 0.151 1. Adim – Ruzgar niteligi Entropy - Gain Cozumu

= 8

= 6 E(Game) = 0.940 E(Wind,Game) = P(Wind,Slightly) * E(Wind,Slightly) + P(Wind,Strong) * E(Wind,Strong) E(Wind,Game) = 8/14 E(Wind,Slightly) + 6/14 E(Wind,Strong) E(Wind,Slightly) = - (2/8 log2 2/8 + 6/8 log2 6/8 ) E(Wind,Slightly) = 0.811 E(Wind,Strong) = - (3/6 log2 3/6+ 3/6 log2 3/6) E(Wind,Strong) = 1.00 E(Wind,Game) = 8/14 * 0.811 + 6/14 * 1.00 E(Wind,Game) = 0.892 Gain(Wind,Game) = E(Game) - E(Wind,Game) Gain(Wind,Game) = 0.940 – 0.892 Gain(Wind,Game) = 0.0.48 1. Adim – Birinci Dallanma Sonucu *weather : 0.246 temperature : 0.029 weatness : 0.151 wind : 0.048 2. Adim Hava ozniteliginin gunesli degeri icin dallanma degerleri Game = {No, No, No, Yes, Yes} P(Game,No) = 3/5 P(Game,Yes) = 2/5 E(Game) = - ( P (Game,No) log2 P (Game, No) + P (Game,Yes) log2 P (Game,Yes) ) E(Game) = - ( 3/5 log2 3/5 + 2/5 log2 2/5 ) E(Game) = 0.970 2. Adim – Isi niteligi Entropy - Gain Cozumu

= 1

= 2

= 2 E(Game) = 0.970 E(Temp,Game) = P(Temp,Cold) * E(Temp,Cold) + P(Temp,Warmish) * E(Temp,Warmish) + P(Temp,Warm) * E(Temp,Warm) E(Temp,Game) = 1/15 E(Temp,Cold) + 2/5 E(Temp,Warmish) + 2/5 E(Temp,Warm) E(Temp,Cold) = - (1/1 log2 1/1) E(Temp,Cold) = 0 E(Temp,Warm) = - (2/2 log2 2/2) E(Temp,Warm) = 0 E(Temp,Warmish) = - (1/2 log2 1/2 + 1/2 log2 1/2 ) E(Temp,Warmish) = 1.00 E(Temp,Game) = 1/5 * 0 + 2/5 * 0 + 2/5 * 1 E(Temp,Game) = 0.4 Gain(Temp,Game) = E(Game) - E(Temp,Game) Gain(Temp,Game) = 0.970 – 0.4 Gain(Temp,Game) = 0.570 2. Adim – Nem niteligi Entropy - Gain Cozumu

= 3

= 2 E(Game) = 0.970 E(Wetness,Game) = P(Wetness,High) * E(Wetness,High) + P(Wetness,Normal) * E(Wetness,Normal) E(Wetness,Game) = 3/5 E(Wetness,High) + 2/5 E(Wetness,Normal) E(Wetness,Sunny) = - (3/3 log2 3/3) E(Wetness,Sunny) = 0 E(Wetness,Rainy) = - (2/2 log2 2/2) E(Wetness,Rainy) = 0 E(Wetness,Game) = 3/5 * 0 + 2/5 * 0 E(Wetness,Game) = 0 Gain(Wetness,Game) = E(Game) - E(Wetness,Game) Gain(Wetness,Game) = 0.970 – 0 Gain(Wetness,Game) = 0.970 2. Adim – Ruzgar niteligi Entropy - Gain Cozumu

= 3

= 2 E(Game) = 0.970 E(Wind,Game) = P(Wind,Slightly) * E(Wind,Slightly) + P(Wind,Strong) * E(Wind,Strong) E(Wind,Game) = 3/5 E(Wind,Slightly) + 2/5 E(Wind,Strong) E(Wind,Slightly) = - (2/3 log2 2/3 + 1/3 log2 1/3 ) E(Wind,Slightly) = 0.918 E(Wind,Strong) = - (1/2 log2 1/2+ 1/2 log2 1/2) E(Wind,Strong) = 1.00 E(Wind,Game) = 3/5 * 0.918 + 2/5 * 1.00 E(Wind,Game) = 0.951 Gain(Wind,Game) = E(Game) - E(Wind,Game) Gain(Wind,Game) = 0.970 – 0.951 Gain(Wind,Game) = 0.019 2. Adim – Ikinci Dallanma Sonucu temperature : 0.570 *weatness : 0.970 wind : 0.019 3. Adim Hava ozniteliginin bulutlu degeri icin dallanma degerleri Game = {Yes, Yes, Yes, Yes} P(Game,Yes) = 4/4 E(Game) = - ( P (Game, Yes) log2 P (Game, Yes) ) E(Game) = - ( 4/4 log2 4/4) E(Game) = 1 4. Adim Hava ozniteliginin yagmurlu degeri icin dallanma degerleri Game = {Yes, Yes, No, Yes, No} P(Game,No) = 2/5 P(Game,Yes) = 3/5 E(Game) = - ( P (Game,No) log2 P (Game, No) + P (Game,Yes) log2 P (Game,Yes) ) E(Game) = - ( 2/5 log2 2/5 + 3/5 log2 3/5 ) E(Game) = 0.970 4. Adim – Isi niteligi Entropy - Gain Cozumu

= 2

= 3 E(Game) = 0.970 E(Temp,Game) = P(Temp,Cold) * E(Temp,Cold) + P(Temp,Warmish) * E(Temp,Warmish) E(Temp,Game) = 2/5 E(Temp,Cold) + 3/5 E(Temp,Warmish) E(Temp,Cold) = - (1/2 log2 1/2 + 1/2 log2 1/2 ) E(Temp,Cold) = 1 E(Temp,Warmish) = - (2/3 log2 2/3 + 1/3 log2 1/3 ) E(Temp,Warmish) = 0.918 E(Temp,Game) = 2/5 * 1 + 3/5 * 0.918 E(Temp,Game) = 0.951 Gain(Temp,Game) = E(Game) - E(Temp,Game) Gain(Temp,Game) = 0.970 – 0.951 Gain(Temp,Game) = 0.019 4. Adim – Ruzgar niteligi Entropy - Gain Cozumu

= 3

= 2 E(Game) = 0.970 E(Wind,Game) = P(Wind,Slightly) * E(Wind,Slightly) + P(Wind,Strong) * E(Wind,Strong) E(Wind,Game) = 3/5 E(Wind,Slightly) + 2/5 E(Wind,Strong) E(Wind,Slightly) = - (3/3 log2 3/3) E(Wind,Slightly) = 0 E(Wind,Strong) = - (2/2 log2 2/2) E(Wind,Strong) = 0 E(Wind,Game) = 3/5 * 0 + 2/5 * 0 E(Wind,Game) = 0 Gain(Wind,Game) = E(Game) - E(Wind,Game) Gain(Wind,Game) = 0.970 – 0 Gain(Wind,Game) = 0.970 4. Adim – Dorduncu Dallanma Sonucu temperature : 0.019 *wind : 0.970 Keyifli Calismalar Dilerim.