I’ve always known that, in theory, to create a PyTorch binary classification prediction model, you can just pretend the problem is a multi-class classification problem. Bottom line: the multi-class approach works but has no advantage over the standard binary approach.
For a PyTorch multi-class classification problem with three or more classes to predict (for example, the political leaning of a person, conservative, moderate, or liberal, based on their age, income, and so on), the standard PyTorch approach is to use zero-based integer ordinal encoding of the target variable, n output nodes, where n is the number of classes, log-softmax output activation, and the NLLLoss loss function (negative log-likelihood).
Note: For a multi-class classification problem, you can also use one-hot target encoding, n output nodes, softmax output activation, and MSELoss (mean squared error loss), but this approach is rare.
For a PyTorch binary classification problem (for example, predict a person’s sex, M or F) the standard PyTorch approach is to use 0-1 encoding of the target variable (which are converted to 0.0 or 1.0 when read into memory), 1 output node, logistic sigmoid output activation (unfortunately, carelessly just named sigmoid() in PyTorch), and the BCELoss function (binary cross entropy).
Note: For a binary classification problem, you can also use 0-1 encoding (converted to 0.0 or 1.0), 1 output node, logistic sigmoid activation, and the MSELoss function — in other words, exactly like the standard binary classification approach but with MSELoss instead of BCELoss, but this appraoach is rare.
So, for a PyTorch binary classification even though I knew that in theory, you can just pretend the problem is a multi-class problem with 2 classes, I have never seen this approach implemented. So, just for fun, I decided to do so.
The goal of my demo is to predict the sex of a person (male = 0, female = 1) based on age, income, state of residence (Michigan, Nebraska, Oklahoma), and political leaning (conservative, moderate, liberal). The synthetic data looks like:
1, 0.24, 1, 0, 0, 0.2950, 0, 0, 1 0, 0.39, 0, 0, 1, 0.5120, 0, 1, 0 1, 0.63, 0, 1, 0, 0.7580, 1, 0, 0 0, 0.36, 1, 0, 0, 0.4450, 0, 1, 0 . . .
The fields are sex, age (divided by 100), State (one-hot encoded), income (divided by 100,000), and political leaning (one-hot encoded). There are just 200 training items and 40 test items.
My neural network has 2 output nodes, uses log-softmax output activation, and NLLLoss — in other words, a two-class multi-class classification problem.
The output of my demo is:
People gender using PyTorch with NLLLoss Creating People train and test Datasets Creating 8-(10-10)-2 binary NN classifier Loss function: NLLLoss() Optimizer: SGD Learn rate: 0.010 Batch size: 10 Max epochs: 500 Starting training epoch = 0 loss = 14.7784 epoch = 100 loss = 13.6010 epoch = 200 loss = 13.2755 epoch = 300 loss = 12.5100 epoch = 400 loss = 10.4068 Done Metrics for train data: accuracy = 0.8900 precision = 0.8684 recall = 0.9340 F1 = 0.9000 Metrics for test data: accuracy = 0.8000 precision = 0.6364 recall = 1.0000 F1 = 0.7778 Saving trained model state_dict Setting age = 30 Oklahoma $40,000 moderate Raw computed output: [[-0.5832 -0.8167]] Prediction = male End People binary classification NLLLoss demo
The results of the multi-class approach were a bit different from the results of the standard binary approach, but were comparable (with such small datasets, it’s difficult to make comparisons).
Anyway, good fun.
In real life, one of the best predictors of a person’s sex is their job occupation. According to the Internet, occupations that have nearly 100% women include cheerleaders, burlesque dancers (with or without clarinets), and Hooter’s restaurant waitresses. I think it’s a good thing that those occupations have nearly 100% women.
Demo code. Note: I recently upgraded my PyTorch from 2.2.1 to 2.3.1 and had to use the –ignore-installed switch when using pip install.
# people_gender_nllloss.py
# binary classification using NLLLoss
# PyTorch 2.3.1-CPU Anaconda3-2023.09-0 Python 3.11.5
# Windows 10/11
# classical approach : 0.0/1.0, sigmoid, MSELoss
# std binary approach : ordinal to 0.0/1.0, sigmoid, BCELoss
# multi-class approach : ordinal, log_softmax, NLLLoss
import numpy as np
import torch as T
device = T.device('cpu') # apply to Tensor or Module
class PeopleDataset(T.utils.data.Dataset):
# sex age state income politics
# 0, 0.27, 0, 1, 0, 0.7610, 0, 0, 1
# 1, 0.19, 0, 0, 1, 0.6550, 1, 0, 0
# sex: 0 = male, 1 = female
# state: michigan, nebraska, oklahoma
# politics: conservative, moderate, liberal
def __init__(self, src_file):
all_data = np.loadtxt(src_file, usecols=range(0,9),
delimiter=",", comments="#", dtype=np.float32)
self.x_data = T.tensor(all_data[:,1:9],
dtype=T.float32).to(device)
self.y_data = T.tensor(all_data[:,0],
dtype=T.int64).to(device) # 1D
def __len__(self):
return len(self.x_data)
def __getitem__(self, idx):
preds = self.x_data[idx] # idx row, all 8 cols
sex = self.y_data[idx]
return preds, sex # as a Tuple
# ---------------------------------------------------------
class Net(T.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hid1 = T.nn.Linear(8, 10) # 8-(10-10)-2
self.hid2 = T.nn.Linear(10, 10)
self.oupt = T.nn.Linear(10, 2)
# explicit init
T.nn.init.xavier_uniform_(self.hid1.weight)
T.nn.init.zeros_(self.hid1.bias)
T.nn.init.xavier_uniform_(self.hid2.weight)
T.nn.init.zeros_(self.hid2.bias)
T.nn.init.xavier_uniform_(self.oupt.weight)
T.nn.init.zeros_(self.oupt.bias)
def forward(self, x):
z = T.tanh(self.hid1(x))
z = T.tanh(self.hid2(z))
# z = T.sigmoid(self.oupt(z)) # for BCELoss()
z = T.log_softmax(self.oupt(z), dim=1) # NLLLoss()
return z
# ---------------------------------------------------------
def metrics(model, ds):
# assumes model.eval()
# item-by-item version
tp = 0; tn = 0; fp = 0; fn = 0
# TP = true positive : correct predict for positive class
# TN = true negative : correct predict for negative class
# FP = false positive : wrong predicted as positive
# FN = false negative : wrong predicted as negative
# But because designation of positive class and negative
# class are arbitrary, these definitions are arbitrary.
for i in range(len(ds)):
X = ds[i][0].reshape(1,-1) # make it a batch
y = ds[i][1].reshape(1) # 0 or 1
with T.no_grad():
oupt = model(X) # log-softmax logits form
pred_y = T.argmax(oupt).item() # 0 or 1
act_y = y.item() # 0 or 1
if act_y == 1 and pred_y == 1: # TP
tp += 1
elif act_y == 0 and pred_y == 0: # TN
tn += 1
elif act_y == 0 and pred_y == 1: # FP
fp += 1
elif act_y == 1 and pred_y == 0: # FN
fn += 1
N = tp + fp + tn + fn
if N != len(ds):
print("FATAL LOGIC ERROR in metrics()")
accuracy = (tp + tn) / (N * 1.0)
precision = (1.0 * tp) / (tp + fp) # tp + fp != 0
recall = (1.0 * tp) / (tp + fn) # tp + fn != 0
f1 = 2.0 / ((1.0 / precision) + (1.0 / recall))
return (accuracy, precision, recall, f1) # as a Tuple
# -----------------------------------------------------------
def main():
# 0. get started
print("\nPeople gender using PyTorch with NLLLoss ")
T.manual_seed(1)
np.random.seed(1)
# 1. create Dataset and DataLoader objects
print("\nCreating People train and test Datasets ")
train_file = ".\\Data\\people_train.txt"
test_file = ".\\Data\\people_test.txt"
train_ds = PeopleDataset(train_file) # 200 rows
test_ds = PeopleDataset(test_file) # 40 rows
bat_size = 10
train_ldr = T.utils.data.DataLoader(train_ds,
batch_size=bat_size, shuffle=True)
# 2. create neural network
print("\nCreating 8-(10-10)-2 binary NN classifier \n")
net = Net().to(device)
net.train() # set training mode
# 3. train network
lrn_rate = 0.01
# loss_func = T.nn.BCELoss() # binary cross entropy
# loss_func = T.nn.MSELoss()
loss_func = T.nn.NLLLoss() # expects log-softmax values
optimizer = T.optim.SGD(net.parameters(),
lr=lrn_rate)
max_epochs = 500
ep_log_interval = 100
print("Loss function: " + str(loss_func))
print("Optimizer: " + str(optimizer.__class__.__name__))
print("Learn rate: " + "%0.3f" % lrn_rate)
print("Batch size: " + str(bat_size))
print("Max epochs: " + str(max_epochs))
print("\nStarting training")
for epoch in range(0, max_epochs):
epoch_loss = 0.0 # for one full epoch
for (batch_idx, batch) in enumerate(train_ldr):
X = batch[0]
Y = batch[1]
oupt = net(X) # log-softmax values
loss_val = loss_func(oupt, Y) # a tensor
epoch_loss += loss_val.item() # accumulate
optimizer.zero_grad() # reset all gradients
loss_val.backward() # compute new gradients
optimizer.step() # update all weights
if epoch % ep_log_interval == 0:
print("epoch = %4d loss = %8.4f" % \
(epoch, epoch_loss))
print("Done ")
# ---------------------------------------------------------
# 4. evaluate model
net.eval()
metrics_train = metrics(net, train_ds)
print("\nMetrics for train data: ")
print("accuracy = %0.4f " % metrics_train[0])
print("precision = %0.4f " % metrics_train[1])
print("recall = %0.4f " % metrics_train[2])
print("F1 = %0.4f " % metrics_train[3])
metrics_test = metrics(net, test_ds)
print("\nMetrics for test data: ")
print("accuracy = %0.4f " % metrics_test[0])
print("precision = %0.4f " % metrics_test[1])
print("recall = %0.4f " % metrics_test[2])
print("F1 = %0.4f " % metrics_test[3])
# 5. save model
print("\nSaving trained model state_dict ")
net.eval()
# path = ".\\Models\\people_gender_model.pt"
# T.save(net.state_dict(), path)
# 6. make a prediction
print("\nSetting age = 30 Oklahoma $40,000 moderate ")
inpt = np.array([[0.30, 0,0,1, 0.4000, 0,1,0]],
dtype=np.float32)
inpt = T.tensor(inpt, dtype=T.float32).to(device)
net.eval()
with T.no_grad():
oupt = net(inpt) # pair of log_soft logits
print("Raw computed output: ", end="")
np.set_printoptions(precision=4, suppress=True)
print(oupt.numpy())
pred_y = T.argmax(oupt).item() # 0 or 1
if pred_y == 0:
print("Prediction = male")
else:
print("Prediction = female")
print("\nEnd People binary classification NLLLoss demo ")
if __name__== "__main__":
main()
Training data:
# people_train.txt # sex (0 = male, 1 = female) - dependent variable # age, state (michigan, nebraska, oklahoma), income, # politics type (conservative, moderate, liberal) # 1, 0.24, 1, 0, 0, 0.2950, 0, 0, 1 0, 0.39, 0, 0, 1, 0.5120, 0, 1, 0 1, 0.63, 0, 1, 0, 0.7580, 1, 0, 0 0, 0.36, 1, 0, 0, 0.4450, 0, 1, 0 1, 0.27, 0, 1, 0, 0.2860, 0, 0, 1 1, 0.50, 0, 1, 0, 0.5650, 0, 1, 0 1, 0.50, 0, 0, 1, 0.5500, 0, 1, 0 0, 0.19, 0, 0, 1, 0.3270, 1, 0, 0 1, 0.22, 0, 1, 0, 0.2770, 0, 1, 0 0, 0.39, 0, 0, 1, 0.4710, 0, 0, 1 1, 0.34, 1, 0, 0, 0.3940, 0, 1, 0 0, 0.22, 1, 0, 0, 0.3350, 1, 0, 0 1, 0.35, 0, 0, 1, 0.3520, 0, 0, 1 0, 0.33, 0, 1, 0, 0.4640, 0, 1, 0 1, 0.45, 0, 1, 0, 0.5410, 0, 1, 0 1, 0.42, 0, 1, 0, 0.5070, 0, 1, 0 0, 0.33, 0, 1, 0, 0.4680, 0, 1, 0 1, 0.25, 0, 0, 1, 0.3000, 0, 1, 0 0, 0.31, 0, 1, 0, 0.4640, 1, 0, 0 1, 0.27, 1, 0, 0, 0.3250, 0, 0, 1 1, 0.48, 1, 0, 0, 0.5400, 0, 1, 0 0, 0.64, 0, 1, 0, 0.7130, 0, 0, 1 1, 0.61, 0, 1, 0, 0.7240, 1, 0, 0 1, 0.54, 0, 0, 1, 0.6100, 1, 0, 0 1, 0.29, 1, 0, 0, 0.3630, 1, 0, 0 1, 0.50, 0, 0, 1, 0.5500, 0, 1, 0 1, 0.55, 0, 0, 1, 0.6250, 1, 0, 0 1, 0.40, 1, 0, 0, 0.5240, 1, 0, 0 1, 0.22, 1, 0, 0, 0.2360, 0, 0, 1 1, 0.68, 0, 1, 0, 0.7840, 1, 0, 0 0, 0.60, 1, 0, 0, 0.7170, 0, 0, 1 0, 0.34, 0, 0, 1, 0.4650, 0, 1, 0 0, 0.25, 0, 0, 1, 0.3710, 1, 0, 0 0, 0.31, 0, 1, 0, 0.4890, 0, 1, 0 1, 0.43, 0, 0, 1, 0.4800, 0, 1, 0 1, 0.58, 0, 1, 0, 0.6540, 0, 0, 1 0, 0.55, 0, 1, 0, 0.6070, 0, 0, 1 0, 0.43, 0, 1, 0, 0.5110, 0, 1, 0 0, 0.43, 0, 0, 1, 0.5320, 0, 1, 0 0, 0.21, 1, 0, 0, 0.3720, 1, 0, 0 1, 0.55, 0, 0, 1, 0.6460, 1, 0, 0 1, 0.64, 0, 1, 0, 0.7480, 1, 0, 0 0, 0.41, 1, 0, 0, 0.5880, 0, 1, 0 1, 0.64, 0, 0, 1, 0.7270, 1, 0, 0 0, 0.56, 0, 0, 1, 0.6660, 0, 0, 1 1, 0.31, 0, 0, 1, 0.3600, 0, 1, 0 0, 0.65, 0, 0, 1, 0.7010, 0, 0, 1 1, 0.55, 0, 0, 1, 0.6430, 1, 0, 0 0, 0.25, 1, 0, 0, 0.4030, 1, 0, 0 1, 0.46, 0, 0, 1, 0.5100, 0, 1, 0 0, 0.36, 1, 0, 0, 0.5350, 1, 0, 0 1, 0.52, 0, 1, 0, 0.5810, 0, 1, 0 1, 0.61, 0, 0, 1, 0.6790, 1, 0, 0 1, 0.57, 0, 0, 1, 0.6570, 1, 0, 0 0, 0.46, 0, 1, 0, 0.5260, 0, 1, 0 0, 0.62, 1, 0, 0, 0.6680, 0, 0, 1 1, 0.55, 0, 0, 1, 0.6270, 1, 0, 0 0, 0.22, 0, 0, 1, 0.2770, 0, 1, 0 0, 0.50, 1, 0, 0, 0.6290, 1, 0, 0 0, 0.32, 0, 1, 0, 0.4180, 0, 1, 0 0, 0.21, 0, 0, 1, 0.3560, 1, 0, 0 1, 0.44, 0, 1, 0, 0.5200, 0, 1, 0 1, 0.46, 0, 1, 0, 0.5170, 0, 1, 0 1, 0.62, 0, 1, 0, 0.6970, 1, 0, 0 1, 0.57, 0, 1, 0, 0.6640, 1, 0, 0 0, 0.67, 0, 0, 1, 0.7580, 0, 0, 1 1, 0.29, 1, 0, 0, 0.3430, 0, 0, 1 1, 0.53, 1, 0, 0, 0.6010, 1, 0, 0 0, 0.44, 1, 0, 0, 0.5480, 0, 1, 0 1, 0.46, 0, 1, 0, 0.5230, 0, 1, 0 0, 0.20, 0, 1, 0, 0.3010, 0, 1, 0 0, 0.38, 1, 0, 0, 0.5350, 0, 1, 0 1, 0.50, 0, 1, 0, 0.5860, 0, 1, 0 1, 0.33, 0, 1, 0, 0.4250, 0, 1, 0 0, 0.33, 0, 1, 0, 0.3930, 0, 1, 0 1, 0.26, 0, 1, 0, 0.4040, 1, 0, 0 1, 0.58, 1, 0, 0, 0.7070, 1, 0, 0 1, 0.43, 0, 0, 1, 0.4800, 0, 1, 0 0, 0.46, 1, 0, 0, 0.6440, 1, 0, 0 1, 0.60, 1, 0, 0, 0.7170, 1, 0, 0 0, 0.42, 1, 0, 0, 0.4890, 0, 1, 0 0, 0.56, 0, 0, 1, 0.5640, 0, 0, 1 0, 0.62, 0, 1, 0, 0.6630, 0, 0, 1 0, 0.50, 1, 0, 0, 0.6480, 0, 1, 0 1, 0.47, 0, 0, 1, 0.5200, 0, 1, 0 0, 0.67, 0, 1, 0, 0.8040, 0, 0, 1 0, 0.40, 0, 0, 1, 0.5040, 0, 1, 0 1, 0.42, 0, 1, 0, 0.4840, 0, 1, 0 1, 0.64, 1, 0, 0, 0.7200, 1, 0, 0 0, 0.47, 1, 0, 0, 0.5870, 0, 0, 1 1, 0.45, 0, 1, 0, 0.5280, 0, 1, 0 0, 0.25, 0, 0, 1, 0.4090, 1, 0, 0 1, 0.38, 1, 0, 0, 0.4840, 1, 0, 0 1, 0.55, 0, 0, 1, 0.6000, 0, 1, 0 0, 0.44, 1, 0, 0, 0.6060, 0, 1, 0 1, 0.33, 1, 0, 0, 0.4100, 0, 1, 0 1, 0.34, 0, 0, 1, 0.3900, 0, 1, 0 1, 0.27, 0, 1, 0, 0.3370, 0, 0, 1 1, 0.32, 0, 1, 0, 0.4070, 0, 1, 0 1, 0.42, 0, 0, 1, 0.4700, 0, 1, 0 0, 0.24, 0, 0, 1, 0.4030, 1, 0, 0 1, 0.42, 0, 1, 0, 0.5030, 0, 1, 0 1, 0.25, 0, 0, 1, 0.2800, 0, 0, 1 1, 0.51, 0, 1, 0, 0.5800, 0, 1, 0 0, 0.55, 0, 1, 0, 0.6350, 0, 0, 1 1, 0.44, 1, 0, 0, 0.4780, 0, 0, 1 0, 0.18, 1, 0, 0, 0.3980, 1, 0, 0 0, 0.67, 0, 1, 0, 0.7160, 0, 0, 1 1, 0.45, 0, 0, 1, 0.5000, 0, 1, 0 1, 0.48, 1, 0, 0, 0.5580, 0, 1, 0 0, 0.25, 0, 1, 0, 0.3900, 0, 1, 0 0, 0.67, 1, 0, 0, 0.7830, 0, 1, 0 1, 0.37, 0, 0, 1, 0.4200, 0, 1, 0 0, 0.32, 1, 0, 0, 0.4270, 0, 1, 0 1, 0.48, 1, 0, 0, 0.5700, 0, 1, 0 0, 0.66, 0, 0, 1, 0.7500, 0, 0, 1 1, 0.61, 1, 0, 0, 0.7000, 1, 0, 0 0, 0.58, 0, 0, 1, 0.6890, 0, 1, 0 1, 0.19, 1, 0, 0, 0.2400, 0, 0, 1 1, 0.38, 0, 0, 1, 0.4300, 0, 1, 0 0, 0.27, 1, 0, 0, 0.3640, 0, 1, 0 1, 0.42, 1, 0, 0, 0.4800, 0, 1, 0 1, 0.60, 1, 0, 0, 0.7130, 1, 0, 0 0, 0.27, 0, 0, 1, 0.3480, 1, 0, 0 1, 0.29, 0, 1, 0, 0.3710, 1, 0, 0 0, 0.43, 1, 0, 0, 0.5670, 0, 1, 0 1, 0.48, 1, 0, 0, 0.5670, 0, 1, 0 1, 0.27, 0, 0, 1, 0.2940, 0, 0, 1 0, 0.44, 1, 0, 0, 0.5520, 1, 0, 0 1, 0.23, 0, 1, 0, 0.2630, 0, 0, 1 0, 0.36, 0, 1, 0, 0.5300, 0, 0, 1 1, 0.64, 0, 0, 1, 0.7250, 1, 0, 0 1, 0.29, 0, 0, 1, 0.3000, 0, 0, 1 0, 0.33, 1, 0, 0, 0.4930, 0, 1, 0 0, 0.66, 0, 1, 0, 0.7500, 0, 0, 1 0, 0.21, 0, 0, 1, 0.3430, 1, 0, 0 1, 0.27, 1, 0, 0, 0.3270, 0, 0, 1 1, 0.29, 1, 0, 0, 0.3180, 0, 0, 1 0, 0.31, 1, 0, 0, 0.4860, 0, 1, 0 1, 0.36, 0, 0, 1, 0.4100, 0, 1, 0 1, 0.49, 0, 1, 0, 0.5570, 0, 1, 0 0, 0.28, 1, 0, 0, 0.3840, 1, 0, 0 0, 0.43, 0, 0, 1, 0.5660, 0, 1, 0 0, 0.46, 0, 1, 0, 0.5880, 0, 1, 0 1, 0.57, 1, 0, 0, 0.6980, 1, 0, 0 0, 0.52, 0, 0, 1, 0.5940, 0, 1, 0 0, 0.31, 0, 0, 1, 0.4350, 0, 1, 0 0, 0.55, 1, 0, 0, 0.6200, 0, 0, 1 1, 0.50, 1, 0, 0, 0.5640, 0, 1, 0 1, 0.48, 0, 1, 0, 0.5590, 0, 1, 0 0, 0.22, 0, 0, 1, 0.3450, 1, 0, 0 1, 0.59, 0, 0, 1, 0.6670, 1, 0, 0 1, 0.34, 1, 0, 0, 0.4280, 0, 0, 1 0, 0.64, 1, 0, 0, 0.7720, 0, 0, 1 1, 0.29, 0, 0, 1, 0.3350, 0, 0, 1 0, 0.34, 0, 1, 0, 0.4320, 0, 1, 0 0, 0.61, 1, 0, 0, 0.7500, 0, 0, 1 1, 0.64, 0, 0, 1, 0.7110, 1, 0, 0 0, 0.29, 1, 0, 0, 0.4130, 1, 0, 0 1, 0.63, 0, 1, 0, 0.7060, 1, 0, 0 0, 0.29, 0, 1, 0, 0.4000, 1, 0, 0 0, 0.51, 1, 0, 0, 0.6270, 0, 1, 0 0, 0.24, 0, 0, 1, 0.3770, 1, 0, 0 1, 0.48, 0, 1, 0, 0.5750, 0, 1, 0 1, 0.18, 1, 0, 0, 0.2740, 1, 0, 0 1, 0.18, 1, 0, 0, 0.2030, 0, 0, 1 1, 0.33, 0, 1, 0, 0.3820, 0, 0, 1 0, 0.20, 0, 0, 1, 0.3480, 1, 0, 0 1, 0.29, 0, 0, 1, 0.3300, 0, 0, 1 0, 0.44, 0, 0, 1, 0.6300, 1, 0, 0 0, 0.65, 0, 0, 1, 0.8180, 1, 0, 0 0, 0.56, 1, 0, 0, 0.6370, 0, 0, 1 0, 0.52, 0, 0, 1, 0.5840, 0, 1, 0 0, 0.29, 0, 1, 0, 0.4860, 1, 0, 0 0, 0.47, 0, 1, 0, 0.5890, 0, 1, 0 1, 0.68, 1, 0, 0, 0.7260, 0, 0, 1 1, 0.31, 0, 0, 1, 0.3600, 0, 1, 0 1, 0.61, 0, 1, 0, 0.6250, 0, 0, 1 1, 0.19, 0, 1, 0, 0.2150, 0, 0, 1 1, 0.38, 0, 0, 1, 0.4300, 0, 1, 0 0, 0.26, 1, 0, 0, 0.4230, 1, 0, 0 1, 0.61, 0, 1, 0, 0.6740, 1, 0, 0 1, 0.40, 1, 0, 0, 0.4650, 0, 1, 0 0, 0.49, 1, 0, 0, 0.6520, 0, 1, 0 1, 0.56, 1, 0, 0, 0.6750, 1, 0, 0 0, 0.48, 0, 1, 0, 0.6600, 0, 1, 0 1, 0.52, 1, 0, 0, 0.5630, 0, 0, 1 0, 0.18, 1, 0, 0, 0.2980, 1, 0, 0 0, 0.56, 0, 0, 1, 0.5930, 0, 0, 1 0, 0.52, 0, 1, 0, 0.6440, 0, 1, 0 0, 0.18, 0, 1, 0, 0.2860, 0, 1, 0 0, 0.58, 1, 0, 0, 0.6620, 0, 0, 1 0, 0.39, 0, 1, 0, 0.5510, 0, 1, 0 0, 0.46, 1, 0, 0, 0.6290, 0, 1, 0 0, 0.40, 0, 1, 0, 0.4620, 0, 1, 0 0, 0.60, 1, 0, 0, 0.7270, 0, 0, 1 1, 0.36, 0, 1, 0, 0.4070, 0, 0, 1 1, 0.44, 1, 0, 0, 0.5230, 0, 1, 0 1, 0.28, 1, 0, 0, 0.3130, 0, 0, 1 1, 0.54, 0, 0, 1, 0.6260, 1, 0, 0
Test data:
0, 0.51, 1, 0, 0, 0.6120, 0, 1, 0 0, 0.32, 0, 1, 0, 0.4610, 0, 1, 0 1, 0.55, 1, 0, 0, 0.6270, 1, 0, 0 1, 0.25, 0, 0, 1, 0.2620, 0, 0, 1 1, 0.33, 0, 0, 1, 0.3730, 0, 0, 1 0, 0.29, 0, 1, 0, 0.4620, 1, 0, 0 1, 0.65, 1, 0, 0, 0.7270, 1, 0, 0 0, 0.43, 0, 1, 0, 0.5140, 0, 1, 0 0, 0.54, 0, 1, 0, 0.6480, 0, 0, 1 1, 0.61, 0, 1, 0, 0.7270, 1, 0, 0 1, 0.52, 0, 1, 0, 0.6360, 1, 0, 0 1, 0.30, 0, 1, 0, 0.3350, 0, 0, 1 1, 0.29, 1, 0, 0, 0.3140, 0, 0, 1 0, 0.47, 0, 0, 1, 0.5940, 0, 1, 0 1, 0.39, 0, 1, 0, 0.4780, 0, 1, 0 1, 0.47, 0, 0, 1, 0.5200, 0, 1, 0 0, 0.49, 1, 0, 0, 0.5860, 0, 1, 0 0, 0.63, 0, 0, 1, 0.6740, 0, 0, 1 0, 0.30, 1, 0, 0, 0.3920, 1, 0, 0 0, 0.61, 0, 0, 1, 0.6960, 0, 0, 1 0, 0.47, 0, 0, 1, 0.5870, 0, 1, 0 1, 0.30, 0, 0, 1, 0.3450, 0, 0, 1 0, 0.51, 0, 0, 1, 0.5800, 0, 1, 0 0, 0.24, 1, 0, 0, 0.3880, 0, 1, 0 0, 0.49, 1, 0, 0, 0.6450, 0, 1, 0 1, 0.66, 0, 0, 1, 0.7450, 1, 0, 0 0, 0.65, 1, 0, 0, 0.7690, 1, 0, 0 0, 0.46, 0, 1, 0, 0.5800, 1, 0, 0 0, 0.45, 0, 0, 1, 0.5180, 0, 1, 0 0, 0.47, 1, 0, 0, 0.6360, 1, 0, 0 0, 0.29, 1, 0, 0, 0.4480, 1, 0, 0 0, 0.57, 0, 0, 1, 0.6930, 0, 0, 1 0, 0.20, 1, 0, 0, 0.2870, 0, 0, 1 0, 0.35, 1, 0, 0, 0.4340, 0, 1, 0 0, 0.61, 0, 0, 1, 0.6700, 0, 0, 1 0, 0.31, 0, 0, 1, 0.3730, 0, 1, 0 1, 0.18, 1, 0, 0, 0.2080, 0, 0, 1 1, 0.26, 0, 0, 1, 0.2920, 0, 0, 1 0, 0.28, 1, 0, 0, 0.3640, 0, 0, 1 0, 0.59, 0, 0, 1, 0.6940, 0, 0, 1
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