├── .gitignore ├── DINA_new.py ├── DINA_new_bak.py ├── DINA_old.py ├── Multi.py ├── README.md ├── Test.py ├── csvFile └── FrcSub_sg_DINA.csv └── math2015 ├── Example.txt ├── FrcSub ├── data.csv ├── data.txt ├── problemdesc.txt ├── q.csv ├── q.txt └── qnames.txt ├── Math1 ├── data.csv ├── data.txt ├── problemdesc.txt ├── q.csv ├── q.txt ├── qnames.txt └── rawdata.txt ├── Math2 ├── data.csv ├── data.txt ├── problemdesc.txt ├── q.csv ├── q.txt ├── qnames.txt └── rawdata.txt ├── ReadMe.txt ├── TermsOfUse.txt └── math2015.rar /.gitignore: -------------------------------------------------------------------------------- 1 | .idea/ -------------------------------------------------------------------------------- /DINA_new.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pandas as pd 3 | import time 4 | import math 5 | from multiprocessing import Pool 6 | from sklearn.model_selection import KFold 7 | 8 | ''' 9 | use math2015 data,including FrcSub,Math1,Math2 10 | training data use 80% of total data 11 | ''' 12 | 13 | def EStep(IL,sg,n,r,k,i): 14 | base = 2**(k-2) 15 | for l in range(i*base,(i+1)*base): 16 | # student number 17 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 18 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 19 | IL[:, l] = lll.prod(axis=1) 20 | return IL 21 | 22 | def MStep(IL,n,r,k,i): 23 | base = 2**(k-2) 24 | ni,nj=n.shape 25 | IR = np.zeros((4, nj)) 26 | n1 = np.ones(n.shape) 27 | for l in range(i*base,(i+1)*base): 28 | IR[0] += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 29 | IR[1] += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 30 | IR[2] += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 31 | IR[3] += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 32 | return IR 33 | def trainDINAModel(n,Q): 34 | startTime = time.time() 35 | print('*************staring train DINA model*************') 36 | ni, nj = n.shape 37 | Qi, Qj = Q.shape 38 | 39 | #crate K matrix，indict k skill could get how many vector 40 | K = np.mat(np.zeros((Qj, 2 ** Qj), dtype=int)) 41 | for j in range(2 ** Qj): 42 | l = list(bin(j).replace('0b', '')) 43 | for i in range(len(l)): 44 | K[Qj - len(l) + i, j] = l[i] 45 | std = np.sum(Q, axis=1) 46 | r = (Q * K == std) * 1 47 | sg = 0.01 * np.ones((nj, 2)) 48 | 49 | continueSG = True 50 | kk =1 51 | lastLX = 1 52 | # count iteration times 53 | # student*pattern = student* problem problem*skill skill*pattern 54 | while continueSG == True: 55 | # E step，calculate likelihood matrix 56 | IL = np.zeros((ni, 2 ** Qj)) 57 | IR = np.zeros((4, nj)) 58 | # skill pattern number 59 | if multi==True: 60 | print('multi 4 processes') 61 | with Pool(processes=4) as pool: 62 | multiple_results = [pool.apply_async(EStep, (IL, sg, n, r, Qj, i)) for i in range(4)] 63 | for item in ([res.get(timeout=1000) for res in multiple_results]): 64 | IL += item 65 | 66 | sumIL = IL.sum(axis=1) 67 | LX = np.sum([i for i in map(math.log2, sumIL)]) 68 | print('LX', LX) 69 | 70 | IL = (IL.T / sumIL).T * aPrior 71 | 72 | multiple_results = [pool.apply_async(MStep, (IL, n, r, Qj, i)) for i in range(4)] 73 | for item in ([res.get(timeout=1000) for res in multiple_results]): 74 | IR += item 75 | else: 76 | print('single process') 77 | for l in range(2 ** Qj): 78 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 79 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 80 | IL[:, l] = lll.prod(axis=1) 81 | sumIL = IL.sum(axis=1) 82 | LX = np.sum([i for i in map(math.log2, sumIL)]) 83 | print('LX', LX) 84 | IL = (IL.T / sumIL).T* aPrior 85 | n1 = np.ones(n.shape) 86 | for l in range(2 ** Qj): 87 | IR[0] += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 88 | IR[1] += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 89 | IR[2] += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 90 | IR[3] += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 91 | if abs(LX-lastLX) ni: 133 | istop = ni 134 | I0 = np.zeros(nj) 135 | R0 = np.zeros(nj) 136 | I1 = np.zeros(nj) 137 | R1 = np.zeros(nj) 138 | n1 = np.ones(n.shape) 139 | for l in range(2 ** Qj): 140 | I1 += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 141 | R1 += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 142 | I0 += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 143 | R0 += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 144 | if (abs(R0 / I0 - sg[:, 1]) < threshold).any() and (abs((I1 - R1) / I1 - sg[:, 0]) < threshold).any(): 145 | continueSG = False 146 | sg[:, 1] = R0 / I0 147 | sg[:, 0] = (I1 - R1) / I1 148 | print(sg) 149 | print('[%s] time [%s] students [%s] problems'%(kk,ni,ni)) 150 | kk += 1 151 | endTime = time.time() 152 | print('IDINA model cost time: [%.3f] s'%(endTime-startTime)) 153 | return sg,r 154 | 155 | def continuously(IL): 156 | ni,nj = IL.shape 157 | Qj = (int)(math.log2(nj)) 158 | continuous = np.ones((ni, Qj)) 159 | denominator = np.sum(IL, axis=1) 160 | for j in range(Qj): 161 | molecule = np.zeros(ni) 162 | for l in range(nj): 163 | ll = list(bin(l).replace('0b', '')) 164 | if j < len(ll) and ll[len(ll) - j - 1] == '1': 165 | molecule += IL[:, l] 166 | continuous[:, Qj - 1 - j] = molecule / denominator 167 | return continuous 168 | 169 | def discrete(continuous): 170 | ni,k = continuous.shape 171 | a = np.zeros(ni,dtype=int) 172 | for i in range(ni): 173 | for ki in range(k): 174 | if continuous[i][ki]>0.5: 175 | a[i] += 2**(k-ki-1) 176 | return a 177 | 178 | def predictDINA(n,Q,sg,r): 179 | startTime = time.time() 180 | print('---------------predicting---------------') 181 | ni, nj = n.shape 182 | Qi, Qj = Q.shape 183 | IL = np.zeros((ni, 2**Qj)) 184 | if multi == True: 185 | print('multi 4 processes') 186 | with Pool(processes=4) as pool: 187 | multiple_results = [pool.apply_async(EStep, (IL, sg, n, r, Qj, i)) for i in range(4)] 188 | for item in ([res.get(timeout=1000) for res in multiple_results]): 189 | IL += item 190 | else: 191 | for l in range(2 ** Qj): 192 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 193 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 194 | IL[:, l] = lll.prod(axis=1) 195 | # choose most big probability in the IL matrix for every student 196 | a = IL.argmax(axis=1) 197 | unique, counts = np.unique(a, return_counts=True) 198 | aPrior[unique] = counts/len(a) 199 | K = np.mat(np.zeros((Qj, 2 ** Qj), dtype=int)) 200 | for j in range(2 ** Qj): 201 | l = list(bin(j).replace('0b', '')) 202 | for i in range(len(l)): 203 | K[Qj - len(l) + i, j] = l[i] 204 | std = np.sum(Q, axis=1) 205 | r = (Q * K == std) * 1 206 | i, j = n.shape 207 | p = np.sum((r[:,a] == n.T) * 1) / (i * j) 208 | print('total [%s] people, accuracy is [%.3f]'%(ni, p)) 209 | print('predict time [%.3f] s' %(time.time() - startTime)) 210 | return p 211 | 212 | def trainAndPredict(model,dataSet): 213 | print('model:[%s] dataSet:[%s]' %(model,dataSet)) 214 | if dataSet == 'FrcSub': 215 | n = pd.read_csv('math2015/FrcSub/data.csv').values 216 | Q = np.mat(pd.read_csv('math2015/FrcSub/q.csv')) 217 | elif dataSet == 'Math1': 218 | n = pd.read_csv('math2015/Math1/data.csv').values 219 | Q = np.mat(pd.read_csv('math2015/Math1/q.csv').head(15).values) 220 | elif dataSet == 'Math2': 221 | n = pd.read_csv('math2015/Math2/data.csv').head(5000).values 222 | Q = np.mat(pd.read_csv('math2015/Math2/q.csv').head(16).values) 223 | else: 224 | print('dataSet not exist!') 225 | exit(0) 226 | 227 | #n cross verify 228 | n_splits = 10 229 | KF = KFold(n_splits=n_splits,shuffle=True) 230 | precision = 0 231 | for train_index, test_index in KF.split(n): 232 | X_train, X_test = n[train_index], n[test_index] 233 | if model == 'DINA': 234 | sg,r = trainDINAModel(X_train,Q) 235 | else: 236 | sg,r = trainIDINAModel(X_train,Q) 237 | precision += predictDINA(X_test, Q, sg, r) 238 | print('average precision: %.3f' %(precision/n_splits)) 239 | 240 | def main(): 241 | startTime = time.time() 242 | global multi,threshold,aPrior 243 | threshold = 50000 244 | multi = False 245 | aPrior = np.ones(2 ** 8) / 10 ** 8 246 | dataSet = ('FrcSub', 'Math1', 'Math2') 247 | model = ('DINA','IDINA') 248 | trainAndPredict(model[0], dataSet[0]) 249 | print('total cost time:[%.3f] s' %(time.time()-startTime)) 250 | 251 | if __name__ == "__main__": 252 | main() 253 | -------------------------------------------------------------------------------- /DINA_new_bak.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pandas as pd 3 | import time 4 | import math 5 | from multiprocessing import Pool 6 | from sklearn.model_selection import KFold 7 | 8 | ''' 9 | use math2015 data,including FrcSub,Math1,Math2 10 | training data use 80% of total data 11 | ''' 12 | 13 | multi = True 14 | # sg threshold 15 | threshold = 50000 16 | 17 | def EStep(IL,sg,n,r,k,i): 18 | base = 2**(k-2) 19 | for l in range(i*base,(i+1)*base): 20 | # student number 21 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 22 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 23 | IL[:, l] = lll.prod(axis=1) 24 | return IL 25 | 26 | def MStep(IL,n,r,k,i): 27 | base = 2**(k-2) 28 | ni,nj=n.shape 29 | IR = np.zeros((4, nj)) 30 | n1 = np.ones(n.shape) 31 | for l in range(i*base,(i+1)*base): 32 | IR[0] += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 33 | IR[1] += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 34 | IR[2] += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 35 | IR[3] += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 36 | return IR 37 | def trainDINAModel(n,Q): 38 | startTime = time.time() 39 | print('*************staring train DINA model*************') 40 | ni, nj = n.shape 41 | Qi, Qj = Q.shape 42 | 43 | 44 | k = 2 45 | chunkSize = math.floor(Qj/k) 46 | k0 = 0 47 | k1 = (int)(Qj/k) 48 | #crate K matrix，indict k skill could get how many vector 49 | K0 = np.mat(np.zeros((chunkSize, 2 ** chunkSize), dtype=int)) 50 | for j in range(2 ** chunkSize): 51 | l = list(bin(j).replace('0b', '')) 52 | for i in range(len(l)): 53 | K0[chunkSize - len(l) + i, j] = l[i] 54 | # K1 = np.mat(np.zeros((6, 2 ** 6), dtype=int)) 55 | # for j in range(2 ** 6): 56 | # l = list(bin(j).replace('0b', '')) 57 | # for i in range(len(l)): 58 | # K1[6 - len(l) + i, j] = l[i] 59 | K1 = K0 60 | Q0 = Q[:,:k1] 61 | Q1 = Q[:,k1:] 62 | #r matrix indicate l skill vector whether could do right j problem 63 | std0 = np.sum(Q0, axis=1) 64 | r0 = (Q0 * K0 == std0) * 1 65 | std1 = np.sum(Q1, axis=1) 66 | r1 = (Q1 * K1 == std1) * 1 67 | 68 | 69 | # sg[i][0] indicate slip，sg[i][1] indicate guess 70 | sg = 0.01 * np.ones((nj, 2)) 71 | continueSG = True 72 | kk =1 73 | lastLX = 1 74 | # count iteration times 75 | # student*pattern = student* problem problem*skill skill*pattern 76 | while continueSG == True: 77 | # E step，calculate likelihood matrix 78 | 79 | IL = np.zeros((ni, 2 ** k1)) 80 | IL1 = np.zeros((ni, 2 ** k1)) 81 | # skill pattern number 82 | if multi==True: 83 | print('multi 4 processes') 84 | with Pool(processes=4) as pool: 85 | multiple_results = [pool.apply_async(EStep, (IL, sg, n, r0, k1, i)) for i in range(4)] 86 | for item in ([res.get(timeout=1000) for res in multiple_results]): 87 | IL += item 88 | sumIL =IL.sum(axis=1) 89 | LX = np.sum([i for i in map(math.log2, sumIL)]) 90 | print('LX',LX) 91 | IL = (IL.T / sumIL).T 92 | IR = np.zeros((4, nj)) 93 | multiple_results = [pool.apply_async(MStep, (IL, n, r0, k1, i)) for i in range(4)] 94 | for item in ([res.get(timeout=1000) for res in multiple_results]): 95 | IR += item 96 | 97 | multiple_results1 = [pool.apply_async(EStep, (IL1, sg, n, r1, k1, i)) for i in range(4)] 98 | for item in ([res.get(timeout=1000) for res in multiple_results1]): 99 | IL1 += item 100 | sumIL1 = IL1.sum(axis=1) 101 | LX1 = np.sum([i for i in map(math.log2, sumIL1)]) 102 | IL1 = (IL1.T / sumIL1).T 103 | print('LX1 ',LX1) 104 | IR1 = np.zeros((4, nj)) 105 | multiple_results1 = [pool.apply_async(MStep, (IL1, n, r1, k1, i)) for i in range(4)] 106 | for item in ([res.get(timeout=1000) for res in multiple_results1]): 107 | IR1 += item 108 | IR = (IR+IR1)/2 109 | if abs((LX+LX1)/2-lastLX) ni: 151 | istop = ni 152 | I0 = np.zeros(nj) 153 | R0 = np.zeros(nj) 154 | I1 = np.zeros(nj) 155 | R1 = np.zeros(nj) 156 | n1 = np.ones(n.shape) 157 | for l in range(2 ** Qj): 158 | I1 += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 159 | R1 += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 160 | I0 += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 161 | R0 += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 162 | if (abs(R0 / I0 - sg[:, 1]) < threshold).any() and (abs((I1 - R1) / I1 - sg[:, 0]) < threshold).any(): 163 | continueSG = False 164 | sg[:, 1] = R0 / I0 165 | sg[:, 0] = (I1 - R1) / I1 166 | print(sg) 167 | print('[%s] time [%s] students [%s] problems'%(kk,ni,ni)) 168 | kk += 1 169 | endTime = time.time() 170 | print('IDINA model cost time: [%.3f] s'%(endTime-startTime)) 171 | return sg,r 172 | 173 | def continuously(IL): 174 | ni,nj = IL.shape 175 | Qj = (int)(math.log2(nj)) 176 | continuous = np.ones((ni, Qj)) 177 | denominator = np.sum(IL, axis=1) 178 | for j in range(Qj): 179 | molecule = np.zeros(ni) 180 | for l in range(nj): 181 | ll = list(bin(l).replace('0b', '')) 182 | if j < len(ll) and ll[len(ll) - j - 1] == '1': 183 | molecule += IL[:, l] 184 | continuous[:, Qj - 1 - j] = molecule / denominator 185 | return continuous 186 | 187 | def discrete(continuous): 188 | ni,k = continuous.shape 189 | a = np.zeros(ni,dtype=int) 190 | for i in range(ni): 191 | for ki in range(k): 192 | if continuous[i][ki]>0.5: 193 | a[i] += 2**(k-ki-1) 194 | return a 195 | 196 | def predictDINA(n,Q,sg,r0,r1): 197 | startTime = time.time() 198 | print('---------------predicting---------------') 199 | ni, nj = n.shape 200 | Qi, Qj = Q.shape 201 | k = Qj 202 | k1 = (int)(k / 2) 203 | k2 = k-k1 204 | IL = np.zeros((ni, 2**k1)) 205 | IL1 = np.zeros((ni, 2**k2)) 206 | if multi == True: 207 | print('multi 4 processes') 208 | with Pool(processes=4) as pool: 209 | multiple_results = [pool.apply_async(EStep, (IL, sg, n, r0, k1, i)) for i in range(4)] 210 | for item in ([res.get(timeout=1000) for res in multiple_results]): 211 | IL += item 212 | multiple_results = [pool.apply_async(EStep, (IL1, sg, n, r1, k2, i)) for i in range(4)] 213 | for item in ([res.get(timeout=1000) for res in multiple_results]): 214 | IL1 += item 215 | # choose most big probability in the IL matrix for every student 216 | a = IL.argmax(axis=1) 217 | a1 = IL1.argmax(axis=1) 218 | a2 = a*2**k2+a1 219 | K = np.mat(np.zeros((k, 2 ** k), dtype=int)) 220 | for j in range(2 ** k): 221 | l = list(bin(j).replace('0b', '')) 222 | for i in range(len(l)): 223 | K[k - len(l) + i, j] = l[i] 224 | std = np.sum(Q, axis=1) 225 | r = (Q * K == std) * 1 226 | i, j = n.shape 227 | p = np.sum((r[:,a2] == n.T) * 1) / (i * j) 228 | print('total [%s] people, accuracy is [%.3f]'%(ni, p)) 229 | print('predict time [%.3f] s' %(time.time() - startTime)) 230 | return p 231 | 232 | def trainAndPredict(model,dataSet): 233 | print('model:[%s] dataSet:[%s]' %(model,dataSet)) 234 | if dataSet == 'FrcSub': 235 | n = pd.read_csv('math2015/FrcSub/data.csv').values 236 | Q = np.mat(pd.read_csv('math2015/FrcSub/q.csv')) 237 | elif dataSet == 'Math1': 238 | n = pd.read_csv('math2015/Math1/data.csv').values 239 | Q = np.mat(pd.read_csv('math2015/Math1/q.csv').head(15).values) 240 | elif dataSet == 'Math2': 241 | n = pd.read_csv('math2015/Math2/data.csv').head(5000).values 242 | Q = np.mat(pd.read_csv('math2015/Math2/q.csv').head(16).values) 243 | else: 244 | print('dataSet not exist!') 245 | exit(0) 246 | 247 | #n cross verify 248 | n_splits = 1 249 | KF = KFold(n_splits=n_splits,shuffle=True) 250 | precision = 0 251 | for train_index, test_index in KF.split(n): 252 | X_train, X_test = n[train_index], n[test_index] 253 | if model == 'DINA': 254 | sg,r0,r1 = trainDINAModel(X_train,Q) 255 | else: 256 | sg,r = trainIDINAModel(X_train,Q) 257 | precision += predictDINA(X_test, Q, sg, r0,r1) 258 | print('average precision: %.3f' %(precision/n_splits)) 259 | 260 | def main(): 261 | startTime = time.time() 262 | dataSet = ('FrcSub', 'Math1', 'Math2') 263 | model = ('DINA','IDINA') 264 | trainAndPredict(model[0], dataSet[0]) 265 | print('total cost time:[%.3f] s' %(time.time()-startTime)) 266 | 267 | if __name__ == "__main__": 268 | main() 269 | -------------------------------------------------------------------------------- /DINA_old.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pandas as pd 3 | import time 4 | import math 5 | from multiprocessing import Pool 6 | from sklearn.model_selection import KFold 7 | ''' 8 | 使用公开数据集，math2015中的FrcSub 9 | 将data和q矩阵文件txt转为了csv的格式方便读取 10 | ''' 11 | 12 | # 用来测试少量的数据，减少计算等待时间 13 | multi = False 14 | # sg迭代的阈值 15 | threshold = 50000 16 | 17 | 18 | ''' 19 | 拿训练集数据，80%的学生 20 | 计算每道题目的s失误率和g猜测率 21 | ''' 22 | 23 | def EStep(IL,sg,n,r,k,i): 24 | base = 2**(k-2) 25 | for l in range(i*base,(i+1)*base): 26 | # 学生的数量 27 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 28 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 29 | IL[:, l] = lll.prod(axis=1) 30 | return IL 31 | 32 | def MStep(IL,n,r,k,i): 33 | base = 2**(k-2) 34 | ni,nj=n.shape 35 | IR = np.zeros((4, nj)) 36 | n1 = np.ones(n.shape) 37 | for l in range(i*base,(i+1)*base): 38 | IR[0] += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 39 | IR[1] += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 40 | IR[2] += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 41 | IR[3] += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 42 | return IR 43 | def trainDINAModel(n,Q): 44 | startTime = time.time() 45 | print('开始训练DINA模型') 46 | ni, nj = n.shape 47 | Qi, k = Q.shape 48 | # 计算每道题目的s失误率和g猜测率 49 | sg = np.zeros((nj, 2)) 50 | 51 | #构造K矩阵，表示k个技能可以组成的技能模式矩阵 52 | K = np.mat(np.zeros((k, 2 ** k), dtype=int)) 53 | for j in range(2 ** k): 54 | l = list(bin(j).replace('0b', '')) 55 | for i in range(len(l)): 56 | K[k - len(l) + i, j] = l[i] 57 | #r矩阵表示理论上j这道题目对于l这个模式能否做对 58 | std = np.sum(Q, axis=1) 59 | r = (Q * K == std) * 1 60 | 61 | 62 | # 初始化每道题目的s失误率和g猜测率， 63 | # sg[i][0]表示第i道题目的s失误率，sg[i][1]表示第i道题目的g猜测率 64 | for i in range(nj): 65 | sg[i][0] = 0.2 66 | sg[i][1] = 0.2 67 | 68 | continueSG = True 69 | kk =1 70 | lastLX = 1 71 | # 计算s和g迭代的次数 72 | # 学生*模式数 = 学生* 题目数 题目数*技能 技能*模式数 73 | while continueSG == True: 74 | # E步，求似然矩阵 75 | IL = np.zeros((ni, 2 ** k)) 76 | # 技能模式的数量 77 | if multi==True: 78 | print('multi 4 processes') 79 | with Pool(processes=4) as pool: 80 | multiple_results = [pool.apply_async(EStep, (IL, sg, n, r, k, i)) for i in range(4)] 81 | for item in ([res.get(timeout=1000) for res in multiple_results]): 82 | IL += item 83 | sumIL =IL.sum(axis=1) 84 | LX = np.sum([i for i in map(math.log2, sumIL)]) 85 | print('LX') 86 | print(LX) 87 | IL = (IL.T / sumIL).T 88 | IR = np.zeros((4, nj)) 89 | multiple_results = [pool.apply_async(MStep, (IL, n, r, k, i)) for i in range(4)] 90 | for item in ([res.get(timeout=1000) for res in multiple_results]): 91 | IR += item 92 | else: 93 | print('single process') 94 | for l in range(2 ** k): 95 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 96 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 97 | IL[:,l] = lll.prod(axis=1) 98 | sumIL = IL.sum(axis=1) 99 | LX = np.sum([i for i in map(math.log2, sumIL)]) 100 | print('LX') 101 | print(LX) 102 | IL = (IL.T / sumIL).T 103 | #IR中的 0 1 2 3 分别表示 IO RO I1 R1 104 | IR = np.zeros((4,nj)) 105 | n1 = np.ones(n.shape) 106 | for l in range(2 ** k): 107 | IR[0] += np.sum(((1-r.A[:,l])* n1).T*IL[:,l],axis=1) 108 | IR[1] += np.sum(((1-r.A[:,l])* n).T*IL[:,l],axis=1) 109 | IR[2] += np.sum((r.A[:,l]* n1).T*IL[:,l],axis=1) 110 | IR[3] += np.sum((r.A[:,l]* n).T*IL[:,l],axis=1) 111 | #针对每一道题目，根据I0,R0,I1,R1，来更新s和g，更新后的sg，又重新计算似然函数矩阵IL 112 | # if (abs(IR[1] / IR[0] - sg[:,1]) ni: 176 | istop = ni 177 | 178 | # M步，求s，g 179 | # 根据这四个参数来更新迭代s和g 180 | I0 = np.zeros(nj) 181 | R0 = np.zeros(nj) 182 | I1 = np.zeros(nj) 183 | R1 = np.zeros(nj) 184 | # l表示每一种技能模式 185 | n1 = np.ones(n.shape) 186 | for l in range(2 ** Qj): 187 | I1 += np.sum((r.A[:, l] * n1).T * IL[:, l], axis=1) 188 | R1 += np.sum((r.A[:, l] * n).T * IL[:, l], axis=1) 189 | I0 += np.sum(((1 - r.A[:, l]) * n1).T * IL[:, l], axis=1) 190 | R0 += np.sum(((1 - r.A[:, l]) * n).T * IL[:, l], axis=1) 191 | # 针对每一道题目，根据I0,R0,I1,R1，来更新s和g，更新后的sg，又重新计算似然函数矩阵IL 192 | if (abs(R0 / I0 - sg[:, 1]) < threshold).any() and (abs((I1 - R1) / I1 - sg[:, 0]) < threshold).any(): 193 | continueSG = False 194 | sg[:, 1] = R0 / I0 195 | sg[:, 0] = (I1 - R1) / I1 196 | print(sg) 197 | print(str(kk) + "次迭代，" + str(ni) + "个学生，" + str(nj) + "道题目的失误率和猜测率") 198 | kk += 1 199 | endTime = time.time() 200 | print('IDINA模型训练消耗时间：'+str(int(endTime-startTime))+'秒') 201 | return sg,r 202 | 203 | def continuously(IL): 204 | ni,nj = IL.shape 205 | Qj = (int)(math.log2(nj)) 206 | continuous = np.ones((ni, Qj)) 207 | denominator = np.sum(IL, axis=1) 208 | for j in range(Qj): 209 | molecule = np.zeros(ni) 210 | for l in range(nj): 211 | ll = list(bin(l).replace('0b', '')) 212 | if j < len(ll) and ll[len(ll) - j - 1] == '1': 213 | molecule += IL[:, l] 214 | continuous[:, Qj - 1 - j] = molecule / denominator 215 | return continuous 216 | def discrete(continuous): 217 | ni,k = continuous.shape 218 | a = np.zeros(ni,dtype=int) 219 | for i in range(ni): 220 | for ki in range(k): 221 | if continuous[i][ki]>0.5: 222 | a[i] += 2**(k-ki-1) 223 | return a 224 | def predictDINA(n,Q,sg,r,K): 225 | startTime = time.time() 226 | print('预测开始') 227 | 228 | ni, nj = n.shape 229 | Qi, Qj = Q.shape 230 | # 预测的每个学生的技能向量 231 | IL = np.zeros((ni, 2 ** Qj)) 232 | k = Qj 233 | 234 | if multi == True: 235 | print('预测 multi 4 processes') 236 | with Pool(processes=4) as pool: 237 | multiple_results = [pool.apply_async(EStep, (IL, sg, n, r, k, i)) for i in range(4)] 238 | for item in ([res.get(timeout=1000) for res in multiple_results]): 239 | IL += item 240 | else: 241 | for l in range(2 ** Qj): 242 | # 学生的数量 243 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 244 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 245 | IL[:, l] = lll.prod(axis=1) 246 | # 只需要在上面的IL中，针对每一个学生，寻找他在所有l模式中，似然函数最大的那一项l 247 | a = IL.argmax(axis=1) 248 | 249 | # a2 = discrete(continuously(IL)) 250 | 251 | # print('连续化向量') 252 | # print(continuous) 253 | # 计算准确率 254 | 255 | i, j = n.shape 256 | print('总共有' + str(ni) + '个人，a准确率为：') 257 | # print(K) 258 | pd.DataFrame(K[:,a].T).to_csv("math2_skill_2500.csv",index=False) 259 | p1 = np.sum((r[:, a] == n.T) * 1) / (i * j) 260 | print(p1) 261 | # print('总共有' + str(ni) + '个人，a2准确率为：') 262 | # p1 = np.sum((r[:, a2] == n.T) * 1) / (i * j) 263 | # print(p1) 264 | print('预测消耗时间：' + str(int(time.time()) - int(startTime)) + '秒') 265 | print('-----------------------------------------------') 266 | return p1 267 | 268 | 269 | def testPredict(model,dataSet): 270 | print('dataSet is',dataSet) 271 | if dataSet == 'FrcSub': 272 | n = pd.read_csv('math2015/FrcSub/data.csv').values 273 | Q = np.mat(pd.read_csv('math2015/FrcSub/q.csv')) 274 | elif dataSet == 'Math1': 275 | n = pd.read_csv('math2015/Math1/data.csv').values 276 | Q = np.mat(pd.read_csv('math2015/Math1/q.csv').head(15).values) 277 | elif dataSet == 'Math2': 278 | n = pd.read_csv('math2015/Math2/data.csv').head(2500).values 279 | Q = np.mat(pd.read_csv('math2015/Math2/q.csv').head(16).values) 280 | else: 281 | print('no dataSet exist!') 282 | exit(0) 283 | KF = KFold(n_splits=5,shuffle=True) 284 | precision = 0 285 | sg,r,K = trainDINAModel(n, Q) 286 | pd.DataFrame(sg).to_csv("csvFile/%s_sg_%s.csv" %(dataSet,model), index=False) 287 | predictDINA(n, Q, sg, r,K) 288 | # for train_index, test_index in KF.split(n): 289 | # X_train, X_test = n[train_index], n[test_index] 290 | # if model == 'DINA': 291 | # sg,r = trainDINAModel(X_train,Q) 292 | # else: 293 | # sg,r = trainIDINAModel(X_train,Q) 294 | # precision += predictDINA(X_test, Q, sg, r) 295 | 296 | print('准确率平均值') 297 | print(precision/5) 298 | 299 | def main(): 300 | print('main starting') 301 | startTime = time.time() 302 | dataSet = ['FrcSub', 'Math1', 'Math2'] 303 | testPredict('DINA', dataSet[0]) 304 | print('总时间:', time.time() - startTime) 305 | if __name__ == "__main__": 306 | main() 307 | 308 | 309 | -------------------------------------------------------------------------------- /Multi.py: -------------------------------------------------------------------------------- 1 | from multiprocessing import Pool 2 | import os 3 | import numpy as np 4 | import pandas as pd 5 | import time 6 | def EStep(IL,sg,n,r,k,i): 7 | print(os.getpid()) 8 | base = 2**(k-1) 9 | for l in range(i*base,(i+1)*base): 10 | # 学生的数量 11 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 12 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 13 | IL[:, l] = lll.prod(axis=1) 14 | return IL 15 | 16 | def single(n,Q): 17 | s, k = Q.shape 18 | ni, nj = n.shape 19 | IL = np.zeros((ni, 2 ** k)) 20 | K = np.mat(np.zeros((k, 2 ** k), dtype=int)) 21 | for j in range(2 ** k): 22 | l = list(bin(j).replace('0b', '')) 23 | for i in range(len(l)): 24 | K[k - len(l) + i, j] = l[i] 25 | std = np.sum(Q, axis=1) 26 | r = (Q * K == std) * 1 27 | sg = np.zeros((s, 2)) 28 | for i in range(s): 29 | sg[i][0] = 0.01 30 | sg[i][1] = 0.01 31 | for l in range(2**k): 32 | # 学生的数量 33 | lll = ((1 - sg[:, 0]) ** n * sg[:, 0] ** (1 - n)) ** r.T.A[l] * (sg[:, 1] ** n * ( 34 | 1 - sg[:, 1]) ** (1 - n)) ** (1 - r.T.A[l]) 35 | IL[:, l] = lll.prod(axis=1) 36 | return IL 37 | 38 | def multi(n,Q,nThreads): 39 | with Pool(processes=nThreads) as pool: 40 | s,k = Q.shape 41 | ni,nj = n.shape 42 | IL = np.zeros((ni, 2 ** k)) 43 | K = np.mat(np.zeros((k, 2 ** k), dtype=int)) 44 | for j in range(2 ** k): 45 | l = list(bin(j).replace('0b', '')) 46 | for i in range(len(l)): 47 | K[k - len(l) + i, j] = l[i] 48 | std = np.sum(Q, axis=1) 49 | r = (Q * K == std) * 1 50 | sg = np.zeros((s, 2)) 51 | for i in range(s): 52 | sg[i][0] = 0.01 53 | sg[i][1] = 0.01 54 | multiple_results = [pool.apply_async(EStep, (IL,sg,n,r,k,i)) for i in range(nThreads)] 55 | for item in ([res.get(timeout=10000) for res in multiple_results]): 56 | IL += item 57 | return IL 58 | 59 | if __name__ == '__main__': 60 | # start 4 worker processes 61 | n = pd.read_csv('math2015/Math2/data.csv').sample(frac=0.8).values 62 | Q = np.mat(pd.read_csv('math2015/Math2/q.csv').head(16).values) 63 | startTime = time.time() 64 | nThreads = 2 65 | IL1 = multi(n,Q,nThreads) 66 | # IL2 = single(n,Q) 67 | endTime = time.time() 68 | print(endTime-startTime) -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 实验数据来源： 2 | http://staff.ustc.edu.cn/%7Eqiliuql/data/math2015.rar. 3 | 数据集已经添加在math2015这个文件夹下面，里面包含3个数据集，FrcSub是经典数据集，分数减法的计算，Math1、Math2是某市部分高中生的数学考试记录。数据集具体详情见里面的说明文档。 4 | 5 | 6 | 7 | 8 | 9 | -------------------------------------------------------------------------------- /Test.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import math 3 | -------------------------------------------------------------------------------- /csvFile/FrcSub_sg_DINA.csv: -------------------------------------------------------------------------------- 1 | 0,1 2 | 0.0500751477642406,0.20204299345953247 3 | 0.04090985530663209,0.09697096101289357 4 | 0.10832008482476176,0.04272709381147803 5 | 0.0723751563780848,0.28187760597949546 6 | 0.08824525825138924,0.3255193444223228 7 | 0.049784578105030786,0.2546278267885612 8 | 0.13791931748823766,0.0836098075189171 9 | 0.14032327871203593,0.36052686918139487 10 | 0.22076255495318858,0.1981055460804273 11 | 0.14285254564689367,0.07247452115166438 12 | 0.06859774356279418,0.08863646526399602 13 | 0.04415688882392043,0.36993434307733375 14 | 0.2906516350052832,0.029015340815632045 15 | 0.04629269852609254,0.24614642685093122 16 | 0.12280033561808981,0.1204165889146962 17 | 0.07949469574489457,0.23457382743517202 18 | 0.1262836790648701,0.061603941604512935 19 | 0.06959067657994059,0.19493245556900834 20 | 0.11170099628474658,0.0718919370981354 21 | 0.09878690425418525,0.07807709245208035 22 | -------------------------------------------------------------------------------- /math2015/Example.txt: -------------------------------------------------------------------------------- 1 | Here two examples about the datasets we use are given as follows: 2 | 3 | 1. FrcSub dataset. 4 | a. "problemdesc.txt" can tell us that all the problems are objective and the full score of each problem is 1; 5 | b. From Line 1 of "data.txt", we can find that the first examinee gives correct response on Problem 4,7,8,10,11,12,14,15,16,18,19,20 and wrong response on the rest problems; 6 | c. From Line 1 of "q.txt", we can find that the first problem requires skill 4,6,7; 7 | d. From "qnames.txt", we can find that specifically the skills the first problem requires are "Find a common denominator", "Column borrow to subtract the second numerator from the first" and "Subtract numerators". 8 | 9 | 2. Math1 dataset. 10 | a. "problemdesc.txt" can tell us that Problem 1 to 15 are objective and their full scores are 4 while Problem 16 to 20 are subjective and the full scores of them are 6,8,8,9,9; 11 | b. From Line 1 of "rawdata.txt", we can find that the raw scores of the first examinee on Problem 1 and 16 are 4 and 5, respectively; 12 | c. In the experiments, we normalize raw scores into a value in [0,1] by dividing the full score of each problem. From Line 1 of "data.txt", we can find that the normalized scores of the first examinee on Problem 1 and 16 are 1 and 0.8333, respectively; 13 | d. The usage of "q.txt" and "qnames.txt" is the same as described above in FrcSub dataset. -------------------------------------------------------------------------------- /math2015/FrcSub/data.csv: -------------------------------------------------------------------------------- 1 | 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 2 | 0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,0,1,1,1 3 | 0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 4 | 0,1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0 5 | 1,1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1 6 | 0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0 7 | 0,0,0,0,0,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0 8 | 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 9 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 10 | 0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0 11 | 0,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0 12 | 1,1,1,0,1,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0 13 | 1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,0,1,0,0 14 | 1,0,0,0,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1 15 | 0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0 16 | 0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0 17 | 0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1 18 | 0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0 19 | 0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0 20 | 0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0 21 | 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 22 | 1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0 23 | 1,1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1 24 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 25 | 0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,1,1,1,0,1 26 | 1,1,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0 27 | 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 28 | 0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0 29 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 30 | 0,0,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0 31 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 32 | 1,0,0,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,0 33 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 34 | 1,1,1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1 35 | 0,0,0,1,0,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1 36 | 1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,0,1,1,1 37 | 1,1,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0 38 | 0,0,0,1,0,0,0,1,0,0,0,1,0,1,1,1,1,0,0,1 39 | 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0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1 148 | 1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0 149 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 150 | 0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1 151 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 152 | 1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,0,1,1 153 | 1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 154 | 1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1 155 | 1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1 156 | 0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1 157 | 1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1 158 | 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0 159 | 0,0,0,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1 160 | 0,1,1,1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0 161 | 1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1 162 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,0,1 163 | 1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1 164 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1 165 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0 166 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 167 | 0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 168 | 0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0 169 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 170 | 1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1 171 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 172 | 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,1 173 | 0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1 174 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 175 | 0,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,1,1,0,0 176 | 0,0,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0 177 | 0,0,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1 178 | 0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,1,1,0,1 179 | 0,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0 180 | 0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,0 181 | 1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 182 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 183 | 1,1,1,1,1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0 184 | 1,1,1,1,0,1,1,1,1,0,1,0,0,1,0,1,1,0,0,0 185 | 1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 186 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1 187 | 1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0 188 | 1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0 189 | 0,0,0,0,0,1,0,1,0,0,1,1,0,1,0,0,0,0,0,0 190 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 191 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 192 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1 193 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 194 | 1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1 195 | 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,1,1,0,1 196 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0 197 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 198 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1 199 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 200 | 1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 201 | 1,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0 202 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 203 | 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1 204 | 1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1 205 | 1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 206 | 0,0,0,1,0,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0 207 | 0,0,0,0,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1 208 | 1,1,1,1,0,1,0,1,0,0,1,1,1,1,1,1,0,1,0,1 209 | 1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0 210 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1 211 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 212 | 0,0,0,1,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0 213 | 0,1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0 214 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 215 | 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 216 | 1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0 217 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 218 | 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 219 | 1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 220 | 1,1,1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0 221 | 1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,1 222 | 0,0,0,1,0,1,1,1,0,0,1,1,0,1,1,1,1,1,0,0 223 | 1,1,1,0,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,0 224 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 225 | 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 226 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1 227 | 0,0,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0,0,0,0 228 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 229 | 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0 230 | 1,1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1 231 | 1,1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0 232 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 233 | 1,1,1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0 234 | 0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 235 | 0,1,0,1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1 236 | 1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0 237 | 1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0 238 | 1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0 239 | 1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 240 | 0,0,0,1,0,0,0,0,0,1,1,1,0,1,0,0,1,1,0,1 241 | 1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0 242 | 1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,0,1 243 | 1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,0 244 | 1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1 245 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 246 | 1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1 247 | 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 248 | 1,1,0,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,1,1 249 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1 250 | 0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0 251 | 0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,0,0,0 252 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 253 | 1,1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0 254 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0 255 | 1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,1 256 | 1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1,0,0 257 | 1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1 258 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 259 | 1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,1 260 | 1,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1 261 | 1,0,0,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1 262 | 0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0 263 | 0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1 264 | 0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0 265 | 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0 266 | 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0 267 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1 268 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 269 | 1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0 270 | 1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,1,1,0 271 | 1,1,1,1,1,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1 272 | 0,0,0,0,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0 273 | 1,1,0,1,0,0,0,1,1,1,1,1,1,1,0,1,0,1,0,1 274 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0 275 | 1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0 276 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 277 | 1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0 278 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0 279 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 280 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 281 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 282 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1 283 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 284 | 0,0,0,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1 285 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1 286 | 0,1,1,0,0,0,1,1,1,1,1,0,1,1,1,0,1,0,1,1 287 | 1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 288 | 0,1,1,1,1,1,1,0,0,1,1,1,0,1,1,1,1,1,1,0 289 | 1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1 290 | 1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,1,1,0,1 291 | 1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1 292 | 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 293 | 1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0 294 | 0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0 295 | 0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 296 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1 297 | 0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0 298 | 0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0 299 | 0,0,0,0,0,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1 300 | 0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0 301 | 1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1 302 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 303 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1 304 | 1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,0,1,0,0 305 | 1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0 306 | 1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1 307 | 1,1,1,0,1,1,0,0,1,1,0,1,1,1,1,1,1,0,0,1 308 | 1,1,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0 309 | 1,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0 310 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 311 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0 312 | 1,1,1,0,1,1,1,1,1,0,0,1,0,1,1,1,0,0,0,0 313 | 0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 314 | 1,1,1,1,0,1,0,1,1,0,1,1,1,1,1,1,1,1,0,0 315 | 0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0 316 | 1,1,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1 317 | 1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0 318 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0 319 | 1,1,1,1,1,1,1,1,0,0,0,1,0,1,1,1,1,1,1,0 320 | 1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,0,1,1,1,1 321 | 0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 322 | 1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0 323 | 1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,1,1 324 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 325 | 1,1,1,1,0,1,0,1,0,0,1,1,1,1,1,1,1,1,0,1 326 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1 327 | 0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0 328 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 329 | 1,1,1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1 330 | 1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0,0 331 | 1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0 332 | 0,1,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0 333 | 1,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0 334 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 335 | 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 336 | 1,1,1,1,1,1,0,1,0,0,1,1,0,1,0,1,1,1,1,1 337 | 1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,1,0,0 338 | 0,0,0,0,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0 339 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0 340 | 1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0 341 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 342 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 343 | 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 344 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 345 | 1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1 346 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 347 | 1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1 348 | 0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0 349 | 1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0 350 | 1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0 351 | 1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,0 352 | 1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 353 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 354 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 355 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 356 | 1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0 357 | 1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1 358 | 1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0 359 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 360 | 1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1 361 | 1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0 362 | 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0 363 | 1,1,1,1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,1,0 364 | 1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1 365 | 0,0,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0 366 | 1,1,0,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1 367 | 1,1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0 368 | 0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 369 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0 370 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0 371 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 372 | 1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0 373 | 0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 374 | 0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0 375 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,1 376 | 1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1 377 | 1,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,1 378 | 0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 379 | 1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0 380 | 1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0 381 | 1,0,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0 382 | 1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0,0 383 | 0,1,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 384 | 1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1 385 | 1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,0 386 | 1,1,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1,1,1,1 387 | 1,1,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0 388 | 0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 389 | 1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0 390 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 391 | 0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0 392 | 0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0 393 | 0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0,0 394 | 0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,1,0,0,0,0 395 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 396 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 397 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 398 | 0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 399 | 1,1,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 400 | 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 401 | 0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 402 | 1,1,1,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0 403 | 1,1,1,1,1,1,0,1,1,1,1,0,1,1,0,1,0,1,0,1 404 | 1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,1,1,1,1,1 405 | 0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0 406 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1 407 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 408 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0 409 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 410 | 1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,1,0 411 | 1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1 412 | 1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0,0 413 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 414 | 1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 415 | 0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0 416 | 0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 417 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0 418 | 0,0,0,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0,0,0 419 | 0,0,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0 420 | 1,1,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 421 | 0,0,0,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0 422 | 0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 423 | 1,1,1,1,0,1,0,0,1,0,1,1,1,1,1,1,1,1,1,0 424 | 0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 425 | 0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 426 | 0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 427 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 428 | 0,1,0,0,1,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0 429 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1 430 | 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1 431 | 0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 432 | 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 433 | 1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1 434 | 1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1 435 | 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1 436 | 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0 437 | 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 438 | 0,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0 439 | 1,1,1,0,0,1,1,1,1,0,0,1,0,1,1,1,0,0,0,0 440 | 1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1 441 | 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0 0 0 0 0 0 530 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 531 | 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 532 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 533 | 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 534 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 535 | 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 536 | 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 537 | -------------------------------------------------------------------------------- /math2015/FrcSub/problemdesc.txt: -------------------------------------------------------------------------------- 1 | No. Type Full Score 2 | 1 Obj 1 3 | 2 Obj 1 4 | 3 Obj 1 5 | 4 Obj 1 6 | 5 Obj 1 7 | 6 Obj 1 8 | 7 Obj 1 9 | 8 Obj 1 10 | 9 Obj 1 11 | 10 Obj 1 12 | 11 Obj 1 13 | 12 Obj 1 14 | 13 Obj 1 15 | 14 Obj 1 16 | 15 Obj 1 17 | 16 Obj 1 18 | 17 Obj 1 19 | 18 Obj 1 20 | 19 Obj 1 21 | 20 Obj 1 22 | -------------------------------------------------------------------------------- /math2015/FrcSub/q.csv: -------------------------------------------------------------------------------- 1 | 1,2,3,4,5,6,7,8 2 | 0,0,0,1,0,1,1,0 3 | 0,0,0,1,0,0,1,0 4 | 0,0,0,1,0,0,1,0 5 | 0,1,1,0,1,0,1,0 6 | 0,1,0,1,0,0,1,1 7 | 0,0,0,0,0,0,1,0 8 | 1,1,0,0,0,0,1,0 9 | 0,0,0,0,0,0,1,0 10 | 0,1,0,0,0,0,0,0 11 | 0,1,0,0,1,0,1,1 12 | 0,1,0,0,1,0,1,0 13 | 0,0,0,0,0,0,1,1 14 | 0,1,0,1,1,0,1,0 15 | 0,1,0,0,0,0,1,0 16 | 1,0,0,0,0,0,1,0 17 | 0,1,0,0,0,0,1,0 18 | 0,1,0,0,1,0,1,0 19 | 0,1,0,0,1,1,1,0 20 | 1,1,1,0,1,0,1,0 21 | 0,1,1,0,1,0,1,0 22 | -------------------------------------------------------------------------------- /math2015/FrcSub/q.txt: -------------------------------------------------------------------------------- 1 | 0 0 0 1 0 1 1 0 2 | 0 0 0 1 0 0 1 0 3 | 0 0 0 1 0 0 1 0 4 | 0 1 1 0 1 0 1 0 5 | 0 1 0 1 0 0 1 1 6 | 0 0 0 0 0 0 1 0 7 | 1 1 0 0 0 0 1 0 8 | 0 0 0 0 0 0 1 0 9 | 0 1 0 0 0 0 0 0 10 | 0 1 0 0 1 0 1 1 11 | 0 1 0 0 1 0 1 0 12 | 0 0 0 0 0 0 1 1 13 | 0 1 0 1 1 0 1 0 14 | 0 1 0 0 0 0 1 0 15 | 1 0 0 0 0 0 1 0 16 | 0 1 0 0 0 0 1 0 17 | 0 1 0 0 1 0 1 0 18 | 0 1 0 0 1 1 1 0 19 | 1 1 1 0 1 0 1 0 20 | 0 1 1 0 1 0 1 0 21 | -------------------------------------------------------------------------------- /math2015/FrcSub/qnames.txt: -------------------------------------------------------------------------------- 1 | No. Skill Names 2 | 1 Convert a whole number to a fraction, 3 | 2 Separate a whole number from a fraction, 4 | 3 Simplify before subtracting, 5 | 4 Find a common denominator, 6 | 5 Borrow from whole number part, 7 | 6 Column borrow to subtract the second numerator from the first, 8 | 7 Subtract numerators, 9 | 8 Reduce answers to simplest form. 10 | -------------------------------------------------------------------------------- /math2015/Math1/problemdesc.txt: -------------------------------------------------------------------------------- 1 | No. Type Full Score 2 | 1 Obj 4 3 | 2 Obj 4 4 | 3 Obj 4 5 | 4 Obj 4 6 | 5 Obj 4 7 | 6 Obj 4 8 | 7 Obj 4 9 | 8 Obj 4 10 | 9 Obj 4 11 | 10 Obj 4 12 | 11 Obj 4 13 | 12 Obj 4 14 | 13 Obj 4 15 | 14 Obj 4 16 | 15 Obj 4 17 | 16 Sub 6 18 | 17 Sub 8 19 | 18 Sub 8 20 | 19 Sub 9 21 | 20 Sub 9 22 | -------------------------------------------------------------------------------- /math2015/Math1/q.csv: -------------------------------------------------------------------------------- 1 | 1,2,3,4,5,6,7,8,9,10,11 2 | 1,1,0,0,0,0,0,0,0,1,1 3 | 0,0,1,0,0,0,0,1,0,0,0 4 | 0,0,1,0,0,0,0,0,0,0,1 5 | 0,0,0,0,1,0,0,0,0,1,1 6 | 0,0,0,0,0,1,0,1,0,0,0 7 | 0,0,0,0,0,0,1,1,0,1,0 8 | 0,0,0,0,0,1,0,0,1,0,1 9 | 0,0,0,0,1,0,0,0,0,1,1 10 | 0,0,1,0,0,0,0,1,0,0,1 11 | 1,0,1,0,0,1,1,1,0,1,1 12 | 0,0,0,1,0,0,0,0,0,0,1 13 | 0,0,0,0,0,1,0,1,0,0,1 14 | 0,0,1,0,0,0,0,0,0,0,1 15 | 0,0,0,0,1,0,0,0,0,1,1 16 | 0,0,0,0,0,1,1,1,1,1,1 17 | 1,0,0,0,0,0,0,1,0,1,1 18 | 0,0,0,0,1,0,0,0,0,1,1 19 | 0,0,1,0,0,0,0,0,0,1,1 20 | 0,0,0,0,0,1,1,1,0,1,1 21 | 0,0,1,0,0,0,0,1,0,1,1 22 | -------------------------------------------------------------------------------- /math2015/Math1/q.txt: -------------------------------------------------------------------------------- 1 | 1 1 0 0 0 0 0 0 0 1 1 2 | 0 0 1 0 0 0 0 1 0 0 0 3 | 0 0 1 0 0 0 0 0 0 0 1 4 | 0 0 0 0 1 0 0 0 0 1 1 5 | 0 0 0 0 0 1 0 1 0 0 0 6 | 0 0 0 0 0 0 1 1 0 1 0 7 | 0 0 0 0 0 1 0 0 1 0 1 8 | 0 0 0 0 1 0 0 0 0 1 1 9 | 0 0 1 0 0 0 0 1 0 0 1 10 | 1 0 1 0 0 1 1 1 0 1 1 11 | 0 0 0 1 0 0 0 0 0 0 1 12 | 0 0 0 0 0 1 0 1 0 0 1 13 | 0 0 1 0 0 0 0 0 0 0 1 14 | 0 0 0 0 1 0 0 0 0 1 1 15 | 0 0 0 0 0 1 1 1 1 1 1 16 | 1 0 0 0 0 0 0 1 0 1 1 17 | 0 0 0 0 1 0 0 0 0 1 1 18 | 0 0 1 0 0 0 0 0 0 1 1 19 | 0 0 0 0 0 1 1 1 0 1 1 20 | 0 0 1 0 0 0 0 1 0 1 1 21 | -------------------------------------------------------------------------------- /math2015/Math1/qnames.txt: -------------------------------------------------------------------------------- 1 | No. Skill Names 2 | 1 Set, 3 | 2 Inequality, 4 | 3 Trigonometric function, 5 | 4 Logarithm versus exponential, 6 | 5 Plane vector, 7 | 6 Property of function, 8 | 7 Image of function, 9 | 8 Spatial imagination, 10 | 9 Abstract summarization, 11 | 10 Reasoning and demonstration, 12 | 11 Calculation. -------------------------------------------------------------------------------- /math2015/Math2/problemdesc.txt: -------------------------------------------------------------------------------- 1 | No. Type Full Score 2 | 1 Obj 3 3 | 2 Obj 3 4 | 3 Obj 3 5 | 4 Obj 3 6 | 5 Obj 3 7 | 6 Obj 3 8 | 7 Obj 3 9 | 8 Obj 3 10 | 9 Obj 3 11 | 10 Obj 3 12 | 11 Obj 3 13 | 12 Obj 3 14 | 13 Obj 4 15 | 14 Obj 4 16 | 15 Obj 4 17 | 16 Obj 4 18 | 17 Sub 12 19 | 18 Sub 12 20 | 19 Sub 12 21 | 20 Sub 12 22 | 23 | -------------------------------------------------------------------------------- /math2015/Math2/q.csv: -------------------------------------------------------------------------------- 1 | 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 2 | 1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0 3 | 0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0 4 | 0,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0 5 | 0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0 6 | 0,0,0,0,1,0,0,0,0,0,0,1,0,1,1,0 7 | 0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,1 8 | 0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1 9 | 0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,0 10 | 0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0 11 | 0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0 12 | 0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0 13 | 0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,1 14 | 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0 15 | 1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0 16 | 0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0 17 | 0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0 18 | 1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0 19 | 0,0,0,0,1,0,0,0,0,0,1,1,0,1,1,0 20 | 0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0 21 | 0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0 22 | -------------------------------------------------------------------------------- /math2015/Math2/q.txt: -------------------------------------------------------------------------------- 1 | 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 2 | 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 | 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 4 | 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 5 | 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 6 | 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 7 | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 8 | 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 9 | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 10 | 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 11 | 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 12 | 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 13 | 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 14 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 15 | 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 16 | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 17 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 18 | 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 19 | 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 20 | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 21 | -------------------------------------------------------------------------------- /math2015/Math2/qnames.txt: -------------------------------------------------------------------------------- 1 | No. Skill Names 2 | 1 Property of inequality, 3 | 2 Methods of data sampling, 4 | 3 Geometric progression, 5 | 4 Function versus equation, 6 | 5 Solving triangle, 7 | 6 Principles of data analysis, 8 | 7 Classical probability theory, 9 | 8 Linear programming, 10 | 9 Definitions of algorithm, 11 | 10 Algorithm logic, 12 | 11 Arithmetic progression, 13 | 12 Spatial imagination, 14 | 13 Abstract summarization, 15 | 14 Reasoning and demonstration, 16 | 15 Calculation, 17 | 16 Data handling. -------------------------------------------------------------------------------- /math2015/ReadMe.txt: -------------------------------------------------------------------------------- 1 | 1. There are three directories in the current folder, and each directory contains a piece of data used in our paper as follows: 2 | FrcSub-----------------The public dataset, widely used in cognitive modelling (e.g., [Tatsuoka, 1984; Junker and Sijtsma, 2001; DeCarlo, 2010]), is made up of test responses (right or wrong, coded to 1 or 0) of examinees on Fraction-Substraction problems. 3 | Math1&Math2------------The private datasets we used include two final math examination results (scores of each examinee on each problem) of a high school. 4 | 5 | 2. There are four files in each directory as follows: 6 | data.txt---------------The responses or normalized scores (which are scaled in range [0,1] by dividing full scores of each problem) of each examinee on each problems, and a row denotes an examinee while a column stands for a problem. 7 | qnames.txt-------------The detailed names or meanings of related specific skill. 8 | q.txt------------------The indicator matrix of relationship between problems and skills, which derives from experienced education experts. And a row represents a problem while a column for a skill. E.g., problem i requires skill k if entry(i, k) equals to 1 and vice versa. 9 | problemdesc.txt--------The description of each problem, including the problem type (objective or subjective) and full scores of each problem (set to 1 for all the problems in FrcSub dataset). 10 | 11 | 3. Besides, there is one more file in Math1 and Math2 directories. 12 | rawdata.txt------------The raw unnormalized scores of the Math1 and Math2 datasets. 13 | 14 | 4. For better understanding, we give two examples of how to use the datasets in the file "Example.txt" in the current folder. 15 | 16 | 5. And if you intend to use the two private datasets (called Math dataset) for any exploratory analysis, please refer to the Terms of Use, which is decribed in the file "TermsOfUse.txt" in detail. 17 | 18 | -------------------------------------------------------------------------------- /math2015/TermsOfUse.txt: -------------------------------------------------------------------------------- 1 | By using the Math dataset, you agree to the following terms of use: 2 | 3 | 1. Data is for research purposes, not commercial purposes. 4 | 5 | 2. You will not make any attempts to de-anonymize the data. 6 | 7 | 3. Please include the following reference in your publication: 8 | Runze Wu, Qi Liu, Yuping Liu, Enhong Chen, Yu Su, Zhigang Chen and Guoping Hu. "Cognitive Modelling for Predicting Examinee Performance." In Proceedings of the Twenty-Fourth international joint conference on Artificial Intelligence. AAAI Press, 2015. 9 | or you might also cite our URL in the text of your paper: 10 | For exploratory analysis, I used the Math dataset, available at http://staff.ustc.edu.cn/~qiliuql/data/math2015.rar (Runze, Qi et al., 2015). -------------------------------------------------------------------------------- /math2015/math2015.rar: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/inzhengda/DINA/516167b43eb695631ee98620798bb7c7225089a5/math2015/math2015.rar --------------------------------------------------------------------------------