Handwritten Digits Classification Competition

MNIST is a handwritten digits image data set created by Yann LeCun. Every digit is represented by a 28 x 28 pixel image. It's become a standard data set for testing classifiers on simple image input. A neural network is a strong model for image classification tasks. There's a long-term hosted competition on Kaggle using this data set. This tutorial shows how to use MXNet to compete in this challenge.

Loading the Data

First, let's download the data from Kaggle and put it in the data/ folder in your working directory.

Now we can read it in R and convert it to matrices:

   require(mxnet)

   ## Loading required package: mxnet
   ## Loading required package: methods

   train <- read.csv('data/train.csv', header=TRUE)
   test <- read.csv('data/test.csv', header=TRUE)
   train <- data.matrix(train)
   test <- data.matrix(test)

   train.x <- train[,-1]
   train.y <- train[,1]

Every image is represented as a single row in train/test. The greyscale of each image falls in the range [0, 255]. Linearly transform it into [0,1] by using the following command:

   train.x <- t(train.x/255)
   test <- t(test/255)

Transpose the input matrix to npixel x nexamples, which is the major format for columns accepted by MXNet (and the convention of R).

In the label section, the number of each digit is fairly evenly distributed:

   table(train.y)

   ## train.y
   ##    0    1    2    3    4    5    6    7    8    9
   ## 4132 4684 4177 4351 4072 3795 4137 4401 4063 4188

Configuring the Network

Now that we have the data, let's configure the structure of our network:

   data <- mx.symbol.Variable("data")
   fc1 <- mx.symbol.FullyConnected(data, name="fc1", num_hidden=128)
   act1 <- mx.symbol.Activation(fc1, name="relu1", act_type="relu")
   fc2 <- mx.symbol.FullyConnected(act1, name="fc2", num_hidden=64)
   act2 <- mx.symbol.Activation(fc2, name="relu2", act_type="relu")
   fc3 <- mx.symbol.FullyConnected(act2, name="fc3", num_hidden=10)
   softmax <- mx.symbol.SoftmaxOutput(fc3, name="sm")

1. In mxnet, we use the data type symbol to configure the network. data <- mx.symbol.Variable("data") uses data to represent the input data, i.e., the input layer.
2. We set the first hidden layer with fc1 <- mx.symbol.FullyConnected(data, name="fc1", num_hidden=128). This layer has data as the input, its name, and the number of hidden neurons.
3. Activation is set with act1 <- mx.symbol.Activation(fc1, name="relu1", act_type="relu"). The activation function takes the output from the first hidden layer, fc1.
4. The second hidden layer takes the result from act1 as input, with its name as "fc2" and the number of hidden neurons as 64.
5. The second activation is almost the same as act1, except we have a different input source and name.
6. This generates the output layer. Because there are only 10 digits, we set the number of neurons to 10.
7. Finally, we set the activation to softmax to get a probabilistic prediction.

Training

We are almost ready for the training process. Before we start the computation, let's decide which device to use:

   devices <- mx.cpu()

We assign CPU to mxnet. Now, you can run the following command to train the neural network! Note that mx.set.seed is the function that controls the random process in mxnet:

   mx.set.seed(0)
   model <- mx.model.FeedForward.create(softmax, X=train.x, y=train.y,
                                        ctx=devices, num.round=10, array.batch.size=100,
                                        learning.rate=0.07, momentum=0.9,  eval.metric=mx.metric.accuracy,
                                        initializer=mx.init.uniform(0.07),
                                           epoch.end.callback=mx.callback.log.train.metric(100))

   ## Start training with 1 devices
   ## Batch [100] Train-accuracy=0.6563
   ## Batch [200] Train-accuracy=0.777999999999999
   ## Batch [300] Train-accuracy=0.827466666666665
   ## Batch [400] Train-accuracy=0.855499999999999
   ## [1] Train-accuracy=0.859832935560859
   ## Batch [100] Train-accuracy=0.9529
   ## Batch [200] Train-accuracy=0.953049999999999
   ## Batch [300] Train-accuracy=0.955866666666666
   ## Batch [400] Train-accuracy=0.957525000000001
   ## [2] Train-accuracy=0.958309523809525
   ## Batch [100] Train-accuracy=0.968
   ## Batch [200] Train-accuracy=0.9677
   ## Batch [300] Train-accuracy=0.9696
   ## Batch [400] Train-accuracy=0.970650000000002
   ## [3] Train-accuracy=0.970809523809526
   ## Batch [100] Train-accuracy=0.973
   ## Batch [200] Train-accuracy=0.974249999999999
   ## Batch [300] Train-accuracy=0.976
   ## Batch [400] Train-accuracy=0.977100000000003
   ## [4] Train-accuracy=0.977452380952384
   ## Batch [100] Train-accuracy=0.9834
   ## Batch [200] Train-accuracy=0.981949999999999
   ## Batch [300] Train-accuracy=0.981900000000001
   ## Batch [400] Train-accuracy=0.982600000000003
   ## [5] Train-accuracy=0.983000000000003
   ## Batch [100] Train-accuracy=0.983399999999999
   ## Batch [200] Train-accuracy=0.98405
   ## Batch [300] Train-accuracy=0.985000000000001
   ## Batch [400] Train-accuracy=0.985725000000003
   ## [6] Train-accuracy=0.985952380952384
   ## Batch [100] Train-accuracy=0.988999999999999
   ## Batch [200] Train-accuracy=0.9876
   ## Batch [300] Train-accuracy=0.988100000000001
   ## Batch [400] Train-accuracy=0.988750000000003
   ## [7] Train-accuracy=0.988880952380955
   ## Batch [100] Train-accuracy=0.991999999999999
   ## Batch [200] Train-accuracy=0.9912
   ## Batch [300] Train-accuracy=0.990066666666668
   ## Batch [400] Train-accuracy=0.990275000000003
   ## [8] Train-accuracy=0.990452380952384
   ## Batch [100] Train-accuracy=0.9937
   ## Batch [200] Train-accuracy=0.99235
   ## Batch [300] Train-accuracy=0.991966666666668
   ## Batch [400] Train-accuracy=0.991425000000003
   ## [9] Train-accuracy=0.991500000000003
   ## Batch [100] Train-accuracy=0.9942
   ## Batch [200] Train-accuracy=0.99245
   ## Batch [300] Train-accuracy=0.992433333333334
   ## Batch [400] Train-accuracy=0.992275000000002
   ## [10] Train-accuracy=0.992380952380955

Making a Prediction and Submitting to the Competition

To make a prediction, type:

   preds <- predict(model, test)
   dim(preds)

   ## [1]    10 28000

It is a matrix with 28000 rows and 10 cols, containing the desired classification probabilities from the output layer. To extract the maximum label for each row, use max.col:

   pred.label <- max.col(t(preds)) - 1
   table(pred.label)

   ## pred.label
   ##    0    1    2    3    4    5    6    7    8    9
   ## 2818 3195 2744 2767 2683 2596 2798 2790 2784 2825

With a little extra effort to modify the .csv format, our submission is ready for the competition!

   submission <- data.frame(ImageId=1:ncol(test), Label=pred.label)
   write.csv(submission, file='submission.csv', row.names=FALSE,  quote=FALSE)

LeNet

Now let's use a new network structure: LeNet. It has been proposed by Yann LeCun for recognizing handwritten digits. We'll demonstrate how to construct and train a LeNet in mxnet.

First, we construct the network:

# input
data <- mx.symbol.Variable('data')
# first conv
conv1 <- mx.symbol.Convolution(data=data, kernel=c(5,5), num_filter=20)
tanh1 <- mx.symbol.Activation(data=conv1, act_type="tanh")
pool1 <- mx.symbol.Pooling(data=tanh1, pool_type="max",
                          kernel=c(2,2), stride=c(2,2))
# second conv
conv2 <- mx.symbol.Convolution(data=pool1, kernel=c(5,5), num_filter=50)
tanh2 <- mx.symbol.Activation(data=conv2, act_type="tanh")
pool2 <- mx.symbol.Pooling(data=tanh2, pool_type="max",
                          kernel=c(2,2), stride=c(2,2))
# first fullc
flatten <- mx.symbol.Flatten(data=pool2)
fc1 <- mx.symbol.FullyConnected(data=flatten, num_hidden=500)
tanh3 <- mx.symbol.Activation(data=fc1, act_type="tanh")
# second fullc
fc2 <- mx.symbol.FullyConnected(data=tanh3, num_hidden=10)
# loss
lenet <- mx.symbol.SoftmaxOutput(data=fc2)

Then let's reshape the matrices into arrays:

train.array <- train.x
dim(train.array) <- c(28, 28, 1, ncol(train.x))
test.array <- test
dim(test.array) <- c(28, 28, 1, ncol(test))

We want to compare training speed on different devices, so define the devices:

n.gpu <- 1
device.cpu <- mx.cpu()
device.gpu <- lapply(0:(n.gpu-1), function(i) {
  mx.gpu(i)
})

We can pass a list of devices to ask MXNet to train on multiple GPUs (you can do this for CPUs, but because internal computation of CPUs is already multi-threaded, there is less gain than with using GPUs).

Start by training on the CPU first. Because this takes a bit time, we run it for just one iteration.

   mx.set.seed(0)
   tic <- proc.time()
   model <- mx.model.FeedForward.create(lenet, X=train.array, y=train.y,
                                    ctx=device.cpu, num.round=1, array.batch.size=100,
                                    learning.rate=0.05, momentum=0.9, wd=0.00001,
                                    eval.metric=mx.metric.accuracy,
                                      epoch.end.callback=mx.callback.log.train.metric(100))

   ## Start training with 1 devices
   ## Batch [100] Train-accuracy=0.1066
   ## Batch [200] Train-accuracy=0.16495
   ## Batch [300] Train-accuracy=0.401766666666667
   ## Batch [400] Train-accuracy=0.537675
   ## [1] Train-accuracy=0.557136038186157

   print(proc.time() - tic)

   ##    user  system elapsed
   ## 130.030 204.976  83.821

Train on a GPU:

   mx.set.seed(0)
   tic <- proc.time()
   model <- mx.model.FeedForward.create(lenet, X=train.array, y=train.y,
                                    ctx=device.gpu, num.round=5, array.batch.size=100,
                                    learning.rate=0.05, momentum=0.9, wd=0.00001,
                                    eval.metric=mx.metric.accuracy,
                                      epoch.end.callback=mx.callback.log.train.metric(100))

   ## Start training with 1 devices
   ## Batch [100] Train-accuracy=0.1066
   ## Batch [200] Train-accuracy=0.1596
   ## Batch [300] Train-accuracy=0.3983
   ## Batch [400] Train-accuracy=0.533975
   ## [1] Train-accuracy=0.553532219570405
   ## Batch [100] Train-accuracy=0.958
   ## Batch [200] Train-accuracy=0.96155
   ## Batch [300] Train-accuracy=0.966100000000001
   ## Batch [400] Train-accuracy=0.968550000000003
   ## [2] Train-accuracy=0.969071428571432
   ## Batch [100] Train-accuracy=0.977
   ## Batch [200] Train-accuracy=0.97715
   ## Batch [300] Train-accuracy=0.979566666666668
   ## Batch [400] Train-accuracy=0.980900000000003
   ## [3] Train-accuracy=0.981309523809527
   ## Batch [100] Train-accuracy=0.9853
   ## Batch [200] Train-accuracy=0.985899999999999
   ## Batch [300] Train-accuracy=0.986966666666668
   ## Batch [400] Train-accuracy=0.988150000000002
   ## [4] Train-accuracy=0.988452380952384
   ## Batch [100] Train-accuracy=0.990199999999999
   ## Batch [200] Train-accuracy=0.98995
   ## Batch [300] Train-accuracy=0.990600000000001
   ## Batch [400] Train-accuracy=0.991325000000002
   ## [5] Train-accuracy=0.991523809523812

   print(proc.time() - tic)

   ##    user  system elapsed
   ##   9.288   1.680   6.889

By using a GPU processor, we significantly speed up training! Now, we can submit the result to Kaggle to see the improvement of our ranking!

   preds <- predict(model, test.array)
   pred.label <- max.col(t(preds)) - 1
   submission <- data.frame(ImageId=1:ncol(test), Label=pred.label)
   write.csv(submission, file='submission.csv', row.names=FALSE, quote=FALSE)

Next Steps

• Character Language Model using RNN