Klasifikasi. Data Mining

Transkripsi

1 Klasifikasi Data Mining 1

2 Klasifikasi 1 Decision Tree Induction 2 Bayesian Classification 3 Neural Network 4 Model Evaluation and Selection 5 Techniques to Improve Classification Accuracy: Ensemble Methods 2

3 1 Decision Tree 3

4 Tahapan Algoritma Decision Tree 1. Siapkan data training 2. Pilih atribut sebagai akar Entropy( S) n i 1 pi*log 2 pi Gain( S, A) Entropy( S) n i 1 S i S * Entropy( S i ) 3. Buat cabang untuk tiap-tiap nilai 4. Ulangi proses untuk setiap cabang sampai semua kasus pada cabang memiliki kelas yg sama 4

5 1. Siapkan data training 5

6 2. Pilih atribut sebagai akar Untuk memilih atribut akar, didasarkan pada nilai Gain tertinggi dari atribut-atribut yang ada. Untuk mendapatkan nilai Gain, harus ditentukan terlebih dahulu nilai Entropy Rumus Entropy: S = Himpunan Kasus n = Jumlah Partisi S pi = Proporsi dari Si terhadap S Entropy( S) n i 1 pi*log 2 pi Rumus Gain: Gain( S, A) S = Himpunan Kasus A = Atribut n = Jumlah Partisi Atribut A Si = Jumlah Kasus pada partisi ke-i S = Jumlah Kasus dalam S Entropy( S) n i 1 S i S * Entropy( S i ) 6

7 Perhitungan Entropy dan Gain Akar 7

8 Penghitungan Entropy Akar Entropy Total Entropy (Outlook) Entropy (Temperature) Entropy (Humidity) Entropy (Windy) 8

9 Penghitungan Entropy Akar NODE ATRIBUT JML KASUS TIDAK YA (Si) ENTROPY (S) (Si) 1 TOTAL ,86312 OUTLOOK CLOUDY RAINY ,72193 SUNNY ,97095 GAIN TEMPERATURE HUMADITY WINDY COOL HOT MILD ,91830 HIGH ,98523 NORMAL FALSE ,81128 TRUE ,

10 Penghitungan Gain Akar 10

11 Penghitungan Gain Akar NODE ATRIBUT JML KASUS TIDAK YA (Si) (S) (Si) ENTROPY GAIN 1 TOTAL ,86312 OUTLOOK 0,25852 CLOUDY RAINY ,72193 SUNNY ,97095 TEMPERATURE 0,18385 COOL HOT MILD ,91830 HUMIDITY 0,37051 HIGH ,98523 NORMAL WINDY 0,00598 FALSE ,81128 TRUE ,

12 Gain Tertinggi Sebagai Akar Dari hasil pada Node 1, dapat diketahui bahwa atribut dengan Gain tertinggi adalah HUMIDITY yaitu sebesar Dengan demikian HUMIDITY dapat menjadi node akar Ada 2 nilai atribut dari HUMIDITY yaitu HIGH dan NORMAL. Dari kedua nilai atribut tersebut, nilai atribut NORMAL sudah mengklasifikasikan kasus menjadi 1 yaitu keputusan-nya Yes, sehingga tidak perlu dilakukan perhitungan lebih lanjut Tetapi untuk nilai atribut HIGH masih perlu dilakukan perhitungan lagi High 1. HUMIDITY Normal 1.1????? Yes 12

13 2. Buat cabang untuk tiap-tiap nilai Untuk memudahkan, dataset di-filter dengan mengambil data yang memiliki kelembaban HUMIDITY=HIGH untuk membuat Tabel Node 1.1 OUTLOOK TEMPERATURE HUMIDITY WINDY PLAY Sunny Hot High FALSE No Sunny Hot High TRUE No Cloudy Hot High FALSE Yes Rainy Mild High FALSE Yes Sunny Mild High FALSE No Cloudy Mild High TRUE Yes Rainy Mild High TRUE No 13

14 Perhitungan Entropi Dan Gain Cabang NODE ATRIBUT JML KASUS YA (Si) TIDAK (S) (Si) ENTROPY GAIN 1.1 HUMIDITY ,98523 OUTLOOK 0,69951 CLOUDY RAINY SUNNY TEMPERATURE 0,02024 COOL HOT ,91830 MILD WINDY 0,02024 FALSE TRUE ,

15 Gain Tertinggi Sebagai Node 1.1 Dari hasil pada Tabel Node 1.1, dapat diketahui bahwa atribut dengan Gain tertinggi adalah OUTLOOK yaitu sebesar Dengan demikian OUTLOOK dapat menjadi node kedua Artibut CLOUDY = YES dan SUNNY= NO sudah mengklasifikasikan kasus menjadi 1 keputusan, sehingga tidak perlu dilakukan perhitungan lebih lanjut Tetapi untuk nilai atribut RAINY masih perlu dilakukan perhitungan lagi Cloudy High 1.1 OUTLOOK Rainy 1. HUMIDITY Sunny Normal Yes Yes 1.1.2????? No 15

16 3. Ulangi proses untuk setiap cabang sampai semua kasus pada cabang memiliki kelas yg sama OUTLOOK TEMPERATURE HUMIDITY WINDY PLAY Rainy Mild High FALSE Yes Rainy Mild High TRUE No NODE ATRIBUT JML KASUS (S) YA (Si) TIDAK (Si) ENTROPY GAIN HUMADITY HIGH & OUTLOOK RAINY TEMPERATURE 0 COOL HOT MILD WINDY 1 FALSE TRUE

17 Gain Tertinggi Sebagai Node Dari tabel, Gain Tertinggi adalah WINDY dan menjadi node cabang dari atribut RAINY High 1.1 OUTLOOK 1. HUMIDIT Y Normal Yes Karena semua kasus sudah masuk dalam kelas Jadi, pohon keputusan pada Gambar merupakan pohon keputusan terakhir yang terbentuk Yes Cloudy False WINDY Rainy True Sunny No Yes No 17

18 Decision Tree Induction: An Example Training data set: Buys_computer age income student credit_rating buys_computer <=30 high no fair no <=30 high no excellent no high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes medium no excellent yes high yes fair yes >40 medium no excellent no 18

19 Overfitting and Tree Pruning Overfitting: An induced tree may overfit the training data Too many branches, some may reflect anomalies due to noise or outliers Poor accuracy for unseen samples Two approaches to avoid overfitting 1. Prepruning: Halt tree construction early do not split a node if this would result in the goodness measure falling below a threshold Difficult to choose an appropriate threshold 2. Postpruning: Remove branches from a fully grown tree -get a sequence of progressively pruned trees Use a set of data different from the training data to decide which is the best pruned tree 19

20 Pruning 20

21 Why is decision tree induction popular? Relatively faster learning speed (than other classification methods) Convertible to simple and easy to understand classification rules Can use SQL queries for accessing databases Comparable classification accuracy with other methods 21

22 Latihan Lakukan eksperimen untuk mengumpulkan dataset yang memiliki 4-5 atribut dan analisis dengan decision tree pada dataset tersebut. 22

23 2 Bayesian Classification 23

24 Bayesian Classification: Why? A statistical classifier: performs probabilistic prediction, i.e., predicts class membership probabilities Foundation: Based on Bayes Theorem. Performance: A simple Bayesian classifier, naïve Bayesian classifier, has comparable performance with decision tree and selected neural network classifiers Incremental: Each training example can incrementally increase/decrease the probability that a hypothesis is correct prior knowledge can be combined with observed data Standard: Even when Bayesian methods are computationally intractable, they can provide a standard of optimal decision making against which other methods can be measured 24

25 Tahapan Algoritma Naïve Bayes 1. Baca Data Training 2. Hitung jumlah class 3. Hitung jumlah kasus yang sama dengan class yang sama 4. Kalikan semua nilai hasil sesuai dengan data X yang dicari class-nya 25

26 1. Baca Data Training 26

27 Teorema Bayes P( X H ) P( H ) P( H X) P( X H ) P( H ) / P( X) P( X) X Data dengan class yang belum diketahui H Hipotesis data X yang merupakan suatu class yang lebih spesifik P (H X) Probabilitas hipotesis H berdasarkan kondisi X (posteriori probability) P (H) Probabilitas hipotesis H (prior probability) P (X H) Probabilitas X berdasarkan kondisi pada hipotesis H P (X) Probabilitas X 27

28 2. Hitung jumlah class/label Terdapat 2 class dari data training tersebut, yaitu: C1 (Class 1) Play = yes 9 record C2 (Class 2) Play = no 5 record Total = 14 record Maka: P (C1) = 9/14 = P (C2) = 5/14 = Pertanyaan: Data X = (outlook=rainy, temperature=cool, humidity=high, windy=true) Naik gunung atau tidak? 28

29 3. Hitung jumlah kasus yang sama dengan class yang sama Untuk P(Ci) yaitu P(C1) dan P(C2) sudah diketahui hasilnya di langkah sebelumnya. Selanjutnya Hitung P(X Ci) untuk i = 1 dan 2 P(outlook= sunny play= yes )=2/9= P(outlook= sunny play= no )=3/5=0.6 P(outlook= overcast play= yes )=4/9= P(outlook= overcast play= no )=0/5=0 P(outlook= rainy play= yes )=3/9= P(outlook= rainy play= no )=2/5=0.4 29

30 3. Hitung jumlah kasus yang sama dengan class yang sama Jika semua atribut dihitung, maka didapat hasil akhirnya seperti berikut ini: Atribute Parameter No Yes Outlook value=sunny Outlook value=overcast Outlook value=rainy Temperature value=hot Temperature value=mild Temperature value=cool Humidity value=high Humidity value=normal Windy value=false Windy value=true

31 4. Kalikan semua nilai hasil sesuai dengan data X yang dicari class-nya Pertanyaan: Data X = (outlook=rainy, temperature=cool, humidity=high, windy=true) Naik gunung atau tidak? Kalikan semua nilai hasil dari data X P(X play= yes ) = * * * = P(X play= no ) = 0.4*0.2*0.8*0.6= P(X play= yes )*P(C1) = * = P(X play= no )*P(C2) = * = Nilai no lebih besar dari nilai yes maka class dari data X tersebut adalah No 31

32 Avoiding the Zero-Probability Problem Naïve Bayesian prediction requires each conditional prob. be non-zero. Otherwise, the predicted prob. will be zero P( X Ci) n P( xk k 1 Ci) Ex. Suppose a dataset with 1000 tuples, income=low (0), income= medium (990), and income = high (10) Use Laplacian correction (or Laplacian estimator) Adding 1 to each case Prob(income = low) = 1/1003 Prob(income = medium) = 991/1003 Prob(income = high) = 11/1003 The corrected prob. estimates are close to their uncorrected counterparts 32

33 Naïve Bayes Classifier: Comments Advantages Easy to implement Good results obtained in most of the cases Disadvantages Assumption: class conditional independence, therefore loss of accuracy Practically, dependencies exist among variables, e.g.: Hospitals Patients Profile: age, family history, etc. Symptoms: fever, cough etc., Disease: lung cancer, diabetes, etc. Dependencies among these cannot be modeled by Naïve Bayes Classifier How to deal with these dependencies? Bayesian Belief Networks 33

34 3 Neural Network 34

35 Neural Network Neural Network adalah suatu model yang dibuat untuk meniru fungsi belajar yang dimiliki otak manusia atau jaringan dari sekelompok unit pemroses kecil yang dimodelkan berdasarkan jaringan saraf manusia 35

36 Neural Network Model Perceptron adalah model jaringan yang terdiri dari beberapa unit masukan (ditambah dengan sebuah bias), dan memiliki sebuah unit keluaran Fungsi aktivasi bukan hanya merupakan fungsi biner (0,1) melainkan bipolar (1,0,-1) Untuk suatu harga threshold ѳ yang ditentukan: 1 Jika net > ѳ F (net) = 0 Jika ѳ net ѳ -1 Jika net < - ѳ 36

37 Fungsi Aktivasi Macam fungsi aktivasi yang dipakai untuk mengaktifkan net di berbagai jenis neural network: 1. Aktivasi linear, Rumus: y = sign(v) = v 2. Aktivasi step, Rumus: 3. Aktivasi sigmoid biner, Rumus: 4. Aktivasi sigmoid bipolar, Rumus: 37

38 Tahapan Algoritma Perceptron 1. Inisialisasi semua bobot dan bias (umumnya wi = b = 0) 2. Selama ada elemen vektor masukan yang respon unit keluarannya tidak sama dengan target, lakukan: 2.1 Set aktivasi unit masukan xi = Si (i = 1,...,n) 2.2 Hitung respon unit keluaran: net = + b 1 Jika net > ѳ F (net) = 0 Jika ѳ net ѳ -1 Jika net < - ѳ 2.3 Perbaiki bobot pola yang mengadung kesalahan menurut persamaan: wi (baru) = wi (lama) + w (i = 1,...,n) dengan w = α t xi b (baru) = b(lama) + b dengan b = α t Dimana: α = Laju pembelajaran (Learning rate) yang ditentukan ѳ = Threshold yang ditentukan t = Target 2.4 Ulangi iterasi sampai perubahan bobot ( wn = 0) tidak ada Semakin besar α, semakin sedikit iterasi. Namun, α terlalu besar akan merusak pola yang sudah benar sehingga pemahaman menjadi lambat. 38

39 Studi Kasus Diketahui sebuah dataset kelulusan berdasarkan IPK untuk program S1: Status IPK Semester Lulus Tidak Lulus Tidak Lulus Tidak lulus Jika ada mahasiswa IPK 2.85 dan masih semester 1, maka masuk ke dalam manakah status tersebut? 39

40 1: Inisialisasi Bobot Inisialisasi Bobot dan bias awal: b = 0 dan bias = 1 t X1 X2 1 2, ,7 6 40

41 2.1: Set aktivasi unit masukan Treshold (batasan), θ = 0, yang artinya : 1 Jika net > 0 F (net) = 0 Jika net = 0-1 Jika net < 0 41

42 Hitung Respon dan Perbaiki Bobot Hitung Response Keluaran iterasi 1 Perbaiki bobot pola yang mengandung kesalahan MASUKAN TARGET y= PERUBAHAN BOBOT BOBOT BARU X1 X2 1 t NET f(net) W1 W2 b W1 W2 b INISIALISASI , , , ,

43 2.4 Ulangi iterasi sampai perubahan bobot ( wn = 0) tidak ada (Iterasi 2) Hitung Response Keluaran iterasi 2 Perbaiki bobot pola yang mengandung kesalahan MASUKAN TARGET y= PERUBAHAN BOBOT BOBOT BARU X1 X2 1 t NET f(net) W1 W2 b W1 W2 b INISIALISASI , , , ,

44 2.4 Ulangi iterasi sampai perubahan bobot ( wn = 0) tidak ada... (Iterasi 5) Hitung Response Keluaran iterasi 3 Perbaiki bobot pola yang mengandung kesalahan MASUKAN TARGET y= PERUBAHAN BOBOT BOBOT BARU X1 X2 1 t NET f(net) W1 W2 b W1 W2 b INISIALISASI , , , , Semua pola f(net) = target, maka jaringan sudah mengenal semua pola dan iterasi dihentikan. Untuk data IPK memiliki pola 3.2 x - 5 y + 1 = 0 dapat dihitung prediksinya menggunakan bobot yang terakhir didapat: net = X1*W1 + X2*W2 + b = 3,2 * 2,85-5*1 +1 = 5,12 f(net)=1 (Lulus) 44

45 Latihan Lakukan eksperimen untuk mengumpulkan dataset yang memiliki 4-5 atribut dan analisis dengan Naïve Bayes dan neural network pada dataset tersebut 45

46 4 Model Evaluation and Selection 46

47 Model Evaluation and Selection Evaluation metrics: How can we measure accuracy? Other metrics to consider? Use validation test set of class-labeled tuples instead of training set when assessing accuracy Methods for estimating a classifier s accuracy: Holdout method, random subsampling Cross-validation Bootstrap Comparing classifiers: Confidence intervals Cost-benefit analysis and ROC Curves 47

48 Evaluating Classifier Accuracy: Holdout & Cross-Validation Methods Holdout method Given data is randomly partitioned into two independent sets Training set (e.g., 2/3) for model construction Test set (e.g., 1/3) for accuracy estimation Random sampling: a variation of holdout Repeat holdout k times, accuracy = avg. of the accuracies obtained Cross-validation (k-fold, where k = 10 is most popular) Randomly partition the data into k mutually exclusive subsets, each approximately equal size At i-th iteration, use D i as test set and others as training set Leave-one-out: k folds where k = # of tuples, for small sized data *Stratified cross-validation*: folds are stratified so that class dist. in each fold is approx. the same as that in the initial data 48

49 Evaluating Classifier Accuracy: Bootstrap Bootstrap Works well with small data sets Samples the given training tuples uniformly with replacement, i.e., each time a tuple is selected, it is equally likely to be selected again and readded to the training set Several bootstrap methods, and a common one is.632 boostrap 1. A data set with d tuples is sampled d times, with replacement, resulting in a training set of d samples 2. The data tuples that did not make it into the training set end up forming the test set. About 63.2% of the original data end up in the bootstrap, and the remaining 36.8% form the test set (since (1 1/d) d e -1 = 0.368) 3. Repeat the sampling procedure k times, overall accuracy of the model: 49

50 Estimating Confidence Intervals: Classifier Models M 1 vs. M 2 Suppose we have two classifiers, M 1 and M 2, which one is better? Use 10-fold cross-validation to obtain and These mean error rates are just estimates of error on the true population of future data cases What if the difference between the two error rates is just attributed to chance? Use a test of statistical significance Obtain confidence limits for our error estimates 50

51 Estimating Confidence Intervals: Null Hypothesis 1. Perform 10-fold cross-validation 2. Assume samples follow a t distribution with k 1 degrees of freedom (here, k=10) 3. Use t-test (or Student s t-test) 4. Null Hypothesis: M 1 & M 2 are the same 5. If we can reject null hypothesis, then 1. we conclude that the difference between M 1 & M 2 is statistically significant 2. Chose model with lower error rate 51

52 Estimating Confidence Intervals: t-test If only 1 test set available: pairwise comparison For i th round of 10-fold cross-validation, the same cross partitioning is used to obtain err(m 1 ) i and err(m 2 ) i Average over 10 rounds to get t-test computes t-statistic with k-1 degrees of freedom: where If two test sets available: use non-paired t-test where where k 1 & k 2 are # of cross-validation samples used for M 1 & M 2, resp. 52

53 Estimating Confidence Intervals: Table for t-distribution Symmetric Significance level, e.g., sig = 0.05 or 5% means M 1 & M 2 are significantly different for 95% of population Confidence limit, z = sig/2 53

54 Estimating Confidence Intervals: Statistical Significance Are M 1 & M 2 significantly different? 1. Compute t. Select significance level (e.g. sig = 5%) 2. Consult table for t-distribution: Find t value corresponding to k-1 degrees of freedom (here, 9) 3. t-distribution is symmetric: typically upper % points of distribution shown look up value for confidence limit z=sig/2 (here, 0.025) 4. If t > z or t < -z, then t value lies in rejection region: 1. Reject null hypothesis that mean error rates of M 1 & M 2 are same 2. Conclude: statistically significant difference between M 1 & M 2 5. Otherwise, conclude that any difference is chance 54

55 Model Selection: ROC Curves ROC (Receiver Operating Characteristics) curves: for visual comparison of classification models Originated from signal detection theory Shows the trade-off between the true positive rate and the false positive rate The area under the ROC curve is a measure of the accuracy of the model Rank the test tuples in decreasing order: the one that is most likely to belong to the positive class appears at the top of the list The closer to the diagonal line (i.e., the closer the area is to 0.5), the less accurate is the model 55 Vertical axis represents the true positive rate Horizontal axis rep. the false positive rate The plot also shows a diagonal line A model with perfect accuracy will have an area of 1.0

56 Issues Affecting Model Selection Accuracy classifier accuracy: predicting class label Speed time to construct the model (training time) time to use the model (classification/prediction time) Robustness: handling noise and missing values Scalability: efficiency in disk-resident databases Interpretability understanding and insight provided by the model Other measures, e.g., goodness of rules, such as decision tree size or compactness of classification rules 56

57 5 Techniques to Improve Classification Accuracy: Ensemble Methods 57

58 Ensemble Methods: Increasing the Accuracy Ensemble methods Use a combination of models to increase accuracy Combine a series of k learned models, M1, M2,, Mk, with the aim of creating an improved model M* Popular ensemble methods Bagging: averaging the prediction over a collection of classifiers Boosting: weighted vote with a collection of classifiers Ensemble: combining a set of heterogeneous classifiers 58

59 Bagging: Boostrap Aggregation Analogy: Diagnosis based on multiple doctors majority vote Training Given a set D of d tuples, at each iteration i, a training set D i of d tuples is sampled with replacement from D (i.e., bootstrap) A classifier model M i is learned for each training set D i Classification: classify an unknown sample X Each classifier M i returns its class prediction The bagged classifier M* counts the votes and assigns the class with the most votes to X Prediction: can be applied to the prediction of continuous values by taking the average value of each prediction for a given test tuple Accuracy Often significantly better than a single classifier derived from D For noise data: not considerably worse, more robust Proved improved accuracy in prediction 59

60 Boosting Analogy: Consult several doctors, based on a combination of weighted diagnoses weight assigned based on the previous diagnosis accuracy How boosting works? 1. Weights are assigned to each training tuple 2. A series of k classifiers is iteratively learned 3. After a classifier M i is learned, the weights are updated to allow the subsequent classifier, M i+1, to pay more attention to the training tuples that were misclassified by M i 4. The final M* combines the votes of each individual classifier, where the weight of each classifier's vote is a function of its accuracy Boosting algorithm can be extended for numeric prediction Comparing with bagging: Boosting tends to have greater accuracy, but it also risks overfitting the model to misclassified data 60

61 Adaboost (Freund and Schapire, 1997) 1. Given a set of d class-labeled tuples, (X 1, y 1 ),, (X d, y d ) 2. Initially, all the weights of tuples are set the same (1/d) 3. Generate k classifiers in k rounds. At round i, 1. Tuples from D are sampled (with replacement) to form a training set D i of the same size 2. Each tuple s chance of being selected is based on its weight 3. A classification model M i is derived from D i 4. Its error rate is calculated using D i as a test set 5. If a tuple is misclassified, its weight is increased, o.w. it is decreased 4. Error rate: err(x j ) is the misclassification error of tuple X j. Classifier M i error rate is the sum of the weights of the misclassified tuples: d ( i j j j error M ) w err ( X ) 5. The weight of classifier M i s vote is 61 1 error ( M i ) log error ( M ) i

62 Random Forest (Breiman 2001) Random Forest: Each classifier in the ensemble is a decision tree classifier and is generated using a random selection of attributes at each node to determine the split During classification, each tree votes and the most popular class is returned Two Methods to construct Random Forest: 1. Forest-RI (random input selection): Randomly select, at each node, F attributes as candidates for the split at the node. The CART methodology is used to grow the trees to maximum size 2. Forest-RC (random linear combinations): Creates new attributes (or features) that are a linear combination of the existing attributes (reduces the correlation between individual classifiers) Comparable in accuracy to Adaboost, but more robust to errors and outliers Insensitive to the number of attributes selected for consideration at each split, and faster than bagging or boosting 62

63 Classification of Class-Imbalanced Data Sets Class-imbalance problem: Rare positive example but numerous negative ones, e.g., medical diagnosis, fraud, oilspill, fault, etc. Traditional methods assume a balanced distribution of classes and equal error costs: not suitable for classimbalanced data Typical methods for imbalance data in 2-class classification: 1. Oversampling: re-sampling of data from positive class 2. Under-sampling: randomly eliminate tuples from negative class 3. Threshold-moving: moves the decision threshold, t, so that the rare class tuples are easier to classify, and hence, less chance of costly false negative errors 4. Ensemble techniques: Ensemble multiple classifiers introduced above Still difficult for class imbalance problem on multiclass tasks 63

64 Rangkuman Classification is a form of data analysis that extracts models describing important data classes Effective and scalable methods have been developed for decision tree induction, Naive Bayesian classification, rule-based classification, and many other classification methods Evaluation metrics include: accuracy, sensitivity, specificity, precision, recall, F measure, and Fß measure Stratified k-fold cross-validation is recommended for accuracy estimation. Bagging and boosting can be used to increase overall accuracy by learning and combining a series of individual models 64

65 Rangkuman Significance tests and ROC curves are useful for model selection. There have been numerous comparisons of the different classification methods; the matter remains a research topic No single method has been found to be superior over all others for all data sets Issues such as accuracy, training time, robustness, scalability, and interpretability must be considered and can involve trade-offs, further complicating the quest for an overall superior method 65

66 TERIMA KASIH 66

67 Credit Romi Satria Wahono Jong Jek Siang Jaringan syaraf tiruan dan pemrogramannya menggunakan matlab, ANDI Offset. 67