LETTER IMAGE RECOGNITION

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1 LETTER IMAGE RECOGNITION

2 1. Introducton.

3 1. Introducton. Objectve: desgn classfers for letter mage recognton. consder accuracy and tme n takng the decson. 20,000 samples: Startng set: mages based on 20 dfferent fonts (20x26 samples) Data set: each letter was randomly dstorted to produce our data set (the 20,000 samples) we dd not have ths ntal set free of nose. 16 numercal features: statstcal moments and edge counts scaled to ft nto a range of nteger values from 0 through 15. We use H, R or L method to estmate the error of the classfer. 3

4 1. Introducton. Attrbute Informaton: Captal Letter: (26 Values From A To Z) X-Box: Horzontal Poston Of Box Y-Box: Vertcal Poston Of Box Wdth: Wdth Of Box Hgh: Heght Of Box Onpx: Total # On Pxels X-Bar: Mean X Of On Pxels In Box Y-Bar: Mean Y Of On Pxels In Box 4

5 1. Introducton. Y2bar: Mean X Varance Y2bar: Mean Y Varance Xybar: Mean X Y Correlaton X2ybr: Mean Of X * X * Y Xy2br: Mean Of X * Y * Y X-Ege: Mean Edge Count Left To Rght Xegvy: Correlaton Of X-Ege Wth Y Y-Ege: Mean Edge Count Bottom To Top Yegvx: Correlaton Of Y-Ege Wth X 5

6 2. Eucldean dstance classfer.

7 2. Eucldean dstance classfer. The decson rule: x ω x µ < x µ j j Estmate the means for each category: µ ^ 1 = n n k = 1 x k 7

8 2. Eucldean dstance classfer. Estmate the error wth R method: Average Decson Tme (ms) Accuracy (%) NC (%) Error (%)

9 3. Gaussan classfer.

10 3. Gaussan classfer. Assume Gaussan dstrbuton. Estmate the mean and covarance matrx for each class, wth these estmators: ^ C = n 1 1 n k = 1 ( X k ^ µ )( X k ^ µ ) t ^ 1 µ = n n k = 1 x k 10

11 11 3. Gaussan classfer. Decson rule: Where g(x) are the dscrmnant functons: j x g x g x j > ) ( ) ( ω t t t LnP Ln x x x g 2 2 ) ( Σ Σ Σ + Σ = µ µ µ

12 3. Gaussan classfer. We can estmate the error of the classfer wth the R method. The result: Average Decson Tme Accuracy NC Error

13 4. KNN classfer.

14 4. KNN classfer. We wll use the KNN rule, for each testsample we fnd K nearest neghbors: K = The decson rule: K x ω K > K j j 14

15 4. KNN classfer. 1st approach: compute the dstance to all the tranngsamples for each test-sample. not optmum n the sense of decson tme for each sample. 15

16 4. KNN classfer. 2nd Approach: The features are numbers from 0 to 15. We can order the tranng-samples by ther dstance to the orgn. Gven a test-sample, we measure ts dstance to the orgn and look for ts knn only n tranng-samples wth a smlar dstance. Suppose that the samples wll be equally dstrbuted n the 16D space use more tranng samples for furthest samples and less for closest samples (a smallest wndow for close samples and a bg wndow for far samples). Optmum wndow: lnearly from 50 to

17 4. KNN classfer. 26 classes: we wll get tes whether K s odd or even. Two optons: not to take a decson break the te gve more mportance to the closer samples (k votes for the nn, 1 vote for the knn). Example 4nn: AABB -> A:1+1, B:1+1 AABB -> A:4+3, B:2+1 ABBA -> A:5, B:5 17

18 4. KNN classfer. K=1 Average Decson Tme Accuracy NC Error W= W= W= OW

19 4. KNN classfer. K=3 Average Decson Tme Accuracy NC Error ,TB ,TB ,TB TB,OW

20 4. KNN classfer. K=4 Average Decson Tme Accuracy NC Error ,TB ,TB ,TB TB,OW

21 21 4. KNN classfer TB,OW (50, 2000) TB,OW ,TB ,TB ,TB ,TB Error NC Acc Decson Tme K=5

22 5. Neural Network classfer.

23 5. Neural Network classfer. Multlayer neural network wth backpropagaton algorthm. We used the reslent backpropagaton tranng algorthm. Faster. Many parameters of the networks and tranng method where changed to fnd the optmum classfer: Number of neurons n the hdden layer. Number of hdden layers. Functons n the layers: hyperbolc tangent, logstc, lneal. Learnng rate. 23

24 5. Neural Network classfer. Number of tranng samples. Preprocessng of the nput data: mean and SD normalzaton, prncpal components analyss (take out the components that contrbute less than 2% n the total varaton of the data set). Tranng algorthms. Targets vectors: 0..1 (logstc), (hyperbolc tangent), (hyperbolc tangent), (lneal). Performance functons. 24

25 5. Neural Network classfer. The network that had better performance was the followng one: 25

26 5. Neural Network classfer. The hdden layer has 15 neurons, and both layers use the logstc functon. Rule of thumb: around 30 neurons the performance was better wth 15 neurons The output layer had 26 neurons as the number of classes 26

27 5. Neural Network classfer. We dd not preprocess the nputs: no scalng (actually the data was already normalzed) no prncpal components analyss. The target vector was a a j a r : r = 0 p ω r = 0.9 p ω j 27

28 5. Neural Network classfer tranng-samples: randomly dstrbuted accordng to ther class. the performance was not better usng more samples 1000 valdaton-samples early stop of 50 (f n 50 teratons the performance measured wth the valdaton data was worse, then we stop to avod overfttng) 2000 teratons maxmum Learnng rate: η=0.1 28

29 29

30 5. Neural Network classfer. We could compare ths to the performance of other network: Input preprocessng: scaled and prncpal components (11 over 16) Tranng data: 2000 Hdden neurons: 10 Hdden layer functon: hyperbolc tangent Learnng rate:

31 31

32 5. Neural Network classfer. H method: test the performance of the classfer wth 5000 new samples 2000 from the valdaton set and 3000 dfferent one. The decson rule was: x ω a > a j j 32

33 5. Neural Network classfer. The results: Average Decson Tme Accuracy NC Error Probably better f we could tran wth the set wthout nose. 33

34 6. Summary and concluson.

35 6. Summary and concluson. The best accuracy was acheved wth the 5nn classfer If we consder the tme n takng the decson, the best classfer s the Gaussan. Classfer Tme Accuracy NC Error Eucldean Gaussan NN NN N. Network

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