# Colors with tensors

Finally, my implementation of color descriptor in TensorFlow!

Two weeks ago I had a post about color meanings . Today I want to go through an implementation of color descriptor. Basically, the resulted machinery will take a color (in HSV form) and produces a suitable description. This is a reimplementation of this work.

These descriptions are learned from the Munroe’s color survey preprocessed in RUGSTK (with very little modification which you can see here)

WARNING! You will see lots of preprocessing here! :D

## Preprocessing

After downloading the dataset (comes with LUX code), place it in your working folder. Then, you can start your code by adding the package path in python paths:

The first step is to create our dictionary of vocabularies in the corpus. In order to get all possible descriptions in LUX, we extract all keys from a training handle. Keys are the complete description, or textual part of the corpus. In next step, we just need to parse them into chunks of words.

Notice that I also put empty string and a start and end tokens in my vocabulary.
Now, that our vocabulary is ready, we can create an encoder which makes vector representation of these words.
The easiest way to encode vocabulary is one-hot encoding. Basically, the assumption of one-hot representations is that no word in vocabulary shares any feature with other words.
In other word, we have a feature space in size of the vocabulary, represents each symbol with a binary vector with `1`

in its corresponding dimension and `0`

in others, {0: absent, 1: present}.

It can also be interpreted as a vector representation for discrete probability distribution.

\[P(w_i\ |\ w_i) = \left[\begin{array} {c} 0 \\ 0 \\ ... \\ 1 \\ ... \\ 0 \\ 0 \end{array}\right]\begin{array} {l} 1 \\ 2 \\ ... \\ i \\ ... \\ d-1 \\ d \end{array} \forall\ w_i \in VOC\ (vocabulary)\ \forall\ i \in \{1, ..., d\}\ (index\ of\ words)\]The number of dimensions \(d\) is equal to the size of our vocabulary \(d=\|VOC\|\). We can also represent the the vocabulary with an identity matrix.

\[I_{d \times d} = \left[\begin{array} {cccccc} 1 & 0 & ... & 0 & ... & 0 \\ 0 & 1 & ... & 0 & ... & 0 \\ ... & ... & ... & ... & ... & ... \\ 0 & 0 & ... & 1 &... & 0 \\ ... & ... & ... & ... & ... & ... \\ 0 & 0 & ... & 0 & ... & 1 \end{array}\right]\begin{array} {l} 1 \\ 2 \\ ... \\ i \\ ... \\ d \end{array}\]I am using the one-hot encoder in scikit-learn, however, you can invent your own version:

This function might be useful later, in order to convert a string into a sequence of vector representations:

This is the inverse of the function, which we will need in future:

In next section, we will read features and prepare them for our neural nets.

## Prepare the dataset

The challenge in this stage is to understand the input data, output data and how you want read it while you don’t blowdown your memory.

Ok, here it is what I want to do: I want to create two arrays in parallel, `X_train`

as input, and `Y_train`

as output.
They consist of samples from datapoint, each sample has a sequence of description words, the input starts with start tag ‘~~' and output ends with end tag '~~’:

For example:

The only thing we need to do is to convert them in to vectors instead of taking them as strings. In addition to this, each word-vector in input, according to the decoder model, needs to be concatenated with color feature vector.

This is almost all of the story. I will talk about the test and development in future.

One missing piece is reading from memory! the training input is a 3-dimensional color code and a sequence of word-vectors are in size of the vocabulary. The length of sequence is fixed and we just pad it with zeros when the description is shorter than maximum length. Let’s do a simple math:

(3-d color = float x 3) x (max_sequence_length = 3) x (vocabulary size = float x 337) x (number of samples = 1.5 million) =>
16*3*3*16*337*1500000 / (1024*1024*1024) = 1 tera bytes

Conclusion: we need a way to read mini-batches from file in a size which fits our memory.

## TensorFlow

The simplest line of code: import the library.

As I mentioned in one of my previous posts, you can see TensorFlow in two phases of programming. First, you create a graph of tensors and their flow in network with operations. Then, you run a session which there you can feed data.

### Graph of tensors and operations

Most of the things that you write in TensorFlow like `tf.something`

are nodes of a graph. I like to make it simple and straight forward. Well, I don’t know the best practice, but if it works and it’s readable it is enough. So, first trick is to always reset the graph before writing anything in graph. This makes sure that you are not problem free in interactive mode:

Before starting, let me give you a bigger picture. The plan is to define the graph with its flow of information. At heart of this graph, there will be a chain of LSTM cells. The setup will be similar to Graves (2013) text prediction:

\begin{equation} P(x_{t+1} = k|y_t) = softmax(y_t) \end{equation}

Read it like this: the \(k_{th}\) dimension of the output vector (from softmax) in step \(t\) indicates the probability of the next word been the \(k_{th}\) word in vocabulary. In other words, recurrent neural language model. If you want to know more about LSTM or if you think you need to see its visualization I suggest this post by Christopher Olah.

Ok! We can start with creating placeholders for data which will be fed in the graph (input and output):

Let me go though the details. placeholder, creates an input feed for the graph. It defines the type and shape of the tensor here. Tensors are high dimensional vectors and matrixes. In this code, I defined a placeholder called `X`

and `Y`

with type float32, and a 3D shape dimensions. Notice that the matrix is not 3D, the shape of dimension of the matrix comes with 3 numbers, The first number is not defined, which means arbitrary size, and other two size indicates the two other sizes of dimensions.

The first number in shape means that we can send any number of batch samples. The second number defines a fixed length of sequence and third number is the size of the feature-vector in each time-step of the sequence. (the input vectors has both color features and word features)

Now we need to define a chain of RNN and plug the sequence input and sequence out put in it. The chain of LSTM must be made out of one cell (in this setup dimensions of output vectors from each cell will be 20).

Where the `tf.nn.rnn_cell.LSTMCell`

instantiates the cell, and `tf.nn.dynamic_rnn`

creates a chain of these cells `lstm_cell`

in size of the input tensors `X`

.

All these outputs from chain, should go though a fully connected network which translates outputs into logits of predictable categories. A fully connected network is just a weight matrix and a bias vector. We just need to be careful about its size, type:

Maybe now we are in the complicated part of the process. Because we need to take the output of each cell and multiply it with weights then add the bias. I want to remind you that tensors are not like numpy arrays, they don’t any data in them. They are like concept which we can create an operations to process them. In order to separately get each output out of chain of cell, we cannot call use their index like arrays. Instead we have to apply an operation like `tf.gather`

which chose a tensor in a list of tensors. Since the shape of `output`

shows the batches first, we cannot use gather, unless we transpose the outputs on and reshape it to a list of sequence out puts instead of list of batches. This easy:

Now logit predictions for each time space output can make use `tf.gather`

:

Let me remind you, that these predictions are stepwise outputs which represent probability function of possible outcome of the chain conditioned with previous inputs.

Now it’s time to define the loss function and the trainer which will update all parameters based on the loss. So, again, each prediction logits with a softmax function will become a probability distribution predicting the class of the target output. During the training where we have the correct answer, we want to improve this distribution toward the right answer. Basically, we want the this distribution be more similar to a distribution which only the correct category wins the prediction. Based on this intuition, the cross-entropy distance is our loss function:

With loss, we only need to choose a right stochastic gradient descent technique. In this case, I have AdamOptimizer. (The original paper has a different model)

And finally, I have another tensor which will represent the error rates after each prediction:

Using argmax gives us the index of the correct answer from Y and we are comparing it with argmax in prediction vectors. This code basically will calculate the average of errors in each cell output.

## Running the session

Feeding the graph of tensors is the final stage. Before doing it, I want to remind that we need to save variables after training otherwise we have to retrain the model each time! (days and weeks of training)

Let’s initialize the variables before flowing the data in our graph:

Now we can train it:

Lots of work, ha?

### The top 10 descriptions

In addition to the learning model. I wanted to have code to show how it works. Then I thought let’s write a beam search which finds top something descriptions and their probability!

Here is the code, I will add more description later. Probably there are better implementations out there, this is just a quick respond.

I will put all codes in my toy projects. :)