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Ricardo Cruz February 2016
### TensorFlow for binary classification

I am trying to adapt this MNIST example to binary classification.

But when changing my `NLABELS`

from `NLABELS=2`

to `NLABELS=1`

, the loss function always returns 0 (and accuracy 1).

```
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
# Import data
mnist = input_data.read_data_sets('data', one_hot=True)
NLABELS = 2
sess = tf.InteractiveSession()
# Create the model
x = tf.placeholder(tf.float32, [None, 784], name='x-input')
W = tf.Variable(tf.zeros([784, NLABELS]), name='weights')
b = tf.Variable(tf.zeros([NLABELS], name='bias'))
y = tf.nn.softmax(tf.matmul(x, W) + b)
# Add summary ops to collect data
_ = tf.histogram_summary('weights', W)
_ = tf.histogram_summary('biases', b)
_ = tf.histogram_summary('y', y)
# Define loss and optimizer
y_ = tf.placeholder(tf.float32, [None, NLABELS], name='y-input')
# More name scopes will clean up the graph representation
with tf.name_scope('cross_entropy'):
cross_entropy = -tf.reduce_mean(y_ * tf.log(y))
_ = tf.scalar_summary('cross entropy', cross_entropy)
with tf.name_scope('train'):
train_step = tf.train.GradientDescentOptimizer(10.).minimize(cross_entropy)
with tf.name_scope('test'):
correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
_ = tf.scalar_summary('accuracy', accuracy)
# Merge all the summaries and write them out to /tmp/mnist_logs
merged = tf.merge_all_summaries()
writer = tf.train.SummaryWriter('logs', sess.graph_def)
tf.initialize_all_variables().run()
# Train the model, and feed in test data and record summaries every 10 steps
for i in range(1000):
if i % 10 == 0: # Record summary data
```

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```### Answers

mrry February 2016
The original MNIST example uses a one-hot encoding to represent the labels in the data: this means that if there are `NLABELS = 10`

classes (as in MNIST), the target output is `[1 0 0 0 0 0 0 0 0 0]`

for class 0, `[0 1 0 0 0 0 0 0 0 0]`

for class 1, etc. The `tf.nn.softmax()`

operator converts the logits computed by `tf.matmul(x, W) + b`

into a probability distribution across the different output classes, which is then compared to the fed-in value for `y_`

.

If `NLABELS = 1`

, this acts as if there were only a single class, and the `tf.nn.softmax()`

op would compute a probability of `1.0`

for that class, leading to a cross-entropy of `0.0`

, since `tf.log(1.0)`

is `0.0`

for all of the examples.

There are (at least) two approaches you could try for binary classification:

The simplest would be to set `NLABELS = 2`

for the two possible classes, and encode your training data as `[1 0]`

for label 0 and `[1 0]`

for label 1. This answer has a suggestion for how to do that.

You could keep the labels as integers `0`

and `1`

and use`tf.nn.sparse_softmax_cross_entropy_with_logits()`

, as suggested in this answer.

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```#### Post Status

Asked in February 2016

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