Instance Based Learning k-nn. YZM 3226 Makine Öğrenmesi

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1 Instance Based Learning k-nn YZM 3226 Makine Öğrenmesi

2 Outline Eager vs. Lazy Learning Instance Based Learning K-Nearest Neighbor Algorithm Nearest Neighbor Approach Basic k-nearest Neighbor Classification Distance Formula k-nn Variations k-nn Time Complexity Discussion: Advantages / Disadvantages

3 Eager vs. Lazy Learning Eager learning (eg. Decision trees, SVM, NN): Bir örneklemin sınıflandırılmasından önce, training set verilerine göre sınıflandırma modelinin oluşturulması. Lazy learning (e.g., instance-based learning): Bir örnek sınıflandırılacağı anda tarining veri setinin kullanılması.

4 Eager Learning Any random movement =>It s a mouse I saw a mouse!

5 Lazy Learning Its very similar to a Desktop!!

6 Eager Learning Bir örneklemin sınıflandırılmasından önce, training set verilerine göre sınıflandırma modelinin oluşturulması. Example models: Decision tree Neural Network Support Vector Machine

7 Lazy Learning Sınıflandırılacak bir örneklem gelene kadar training verisi saklanır. Training süresi kısa fakat tahminleme/sınıflandırma süresi daha fazladır.

8 Example Lazy Learning Study Learning of a Control Task for a LEGO Mindstorms Mobile Robot

9 Lazy Learner: Instance-Based Methods Instance-based learning is a kind of lazy learning.

10 Instance Based Learning No model is learned The training instances which have been stored in memory themselves represent the knowledge Training instances are searched for instance that most closely resembles new instance

11 Instance Based Learning Typical approaches k-nearest Neighbor Weighted regression Case-based reasoning

12 k-nearest Neighbor

13 k-nearest Neighbor Basit bir instance-based learning algoritması örneğidir. Özellikler Tüm kayıtlar n boyutlu bir uzay üzerinde temsil edilir. Yeni bir örneklem geldiği anda training veri setine bakılarak sınıflandırma işlemi gerçekleştirilir. Yeni gelen örneklemin vektör değerleri ile uzaydaki tüm kayıtların vektör değerleri karşılaştırılır _ + x q _ +

14 k-nearest Neighbor Classification Sınıflandırmada (classification) kullanılan bu algoritmaya göre, sınıflandırma sırasında çıkarılan özelliklerden (feature extraction), sınıflandırılmak istenen yeni bireyin daha önceki bireylerden k tanesine yakınlığına bakılmasıdır.

15 k-nearest Neighbor Genelde real valued attributeleri destekler. Genelde Euclidean distance formülü kullanılır. dist(x,y) (x i y i ) 2 Örneklemin sınıfı, kendisine en yakın k komşunun sahip olmuş olduğu çoğunluk sınıfıdır. m i 1 ^ f (xq ) argmax v V k i 1 (v, f (x i )) where (x,y) = 1 if x = y, else 0.

16 k-nearest Neighbor All instances correspond to points in the n-d space The nearest neighbor are defined in terms of Euclidean distance, dist(x 1, X 2 ) X Stored training set patterns X Input pattern for classification --- Euclidean distance measure to the nearest three patterns

örneklemine en yakın k training örneği ((x 1,y 1 ), (x

17 k-nearest Neighbor Classification Training method: Training verileri sakla Tahminleme zamanında: X örneklemine en yakın k training örneği ((x 1,y 1 ), (x k,y k ) ) bul. Tüm bu k örnek içerisindeki sınıf çoğunluğunu tahminle.

18 Example Application Document Classification (k=6) P(science )? Government Science Arts

pixel images: d = 784 60,000 training samples

19 Example Application Digit Recognition Yann LeCunn MNIST Digit Recognition Handwritten digits 28x28 pixel images: d = ,000 training samples 10,000 test samples Nearest neighbour is competitive

20 5-nearest neighbors: q1 is classified as negative Distance Formula Euclidian distance: square root of sum of squares of differences for two features: ( x) 2 + ( y) 2 Intuition: similar samples should be close to each other q

21 Other Distance Measures City-block distance (Manhattan dist) Cosine similarity Jaccard distance Others

22 Other Distance Measures

23 Non-Numeric Data Peki özellik değerleri sayısal değilse? Example Boolean values: Yes or no, presence or absence of an attribute Categories: Colors, educational attainment, gender Uzaklık nasıl hesaplanacak?

24 Dealing with Non-Numeric Data If the attribute a is discrete, then : da(xi,x j ) Boolean values => convert to 0 or 1 Applies to yes-no/presence-absence attributes 0, if a( xi ) a( x j ) 1, otherwise. Non-binary characterizations Use natural progression when applicable; e.g., educational attainment: GS, HS, College, MS, PHD => 1,2,3,4,5 Assign arbitrary numbers but be careful about distances; e.g., color: red, yellow, blue => 1,2,3 How about unavailable data? (0 value not always the answer)

25 Examples

26 X1 X2 Y 8 4? Euclidean distance dist(x,y) (x i y i ) 2 m i 1

27 K=3 X1 X2 Y 8 4?

28 K=3 X1 X2 Y 6 3 GOOD 10 2 BAD 9 7 BAD New instance X1 X2 Y 8 4 BAD

29 Discussion on k-nn

30 k-nn Time Complexity Suppose there are m instances and n features in the dataset Nearest neighbor algorithm requires computing m distances Each distance computation involves scanning through each feature value Running time complexity is proportional to m X n

31 Advantages Learning is very simple (fast learning) Robust to noisy data by averaging k-nearest neighbors Scales well with large number of classes In most cases it s more accurate than NB or Rocchio Easy to understand which facilitates implementation and modification.

32 Disadvantages Classification is time consuming Have to calculate the distance of the test case from all training cases Memory intensive: require significant storage The accuracy of the algorithm degrades with increase of irrelevant attributes.

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