FashionMNIST Image Classification

This repository comprises the noteboook MLP_Tutorial.ipynb, embedding a tutorial template that belongs originally to TensorFlow, alongside additional contents with relevant elaborations. The template roughly corresponds to Section I. Basic classification in the notebook. It showcases the assembly and training of an image classifier via tensorflow.keras based on the Fashion MNIST dataset, which embeds 70,000 low resolution (28 x 28 pixel) images of clothing articles from 10 categories, as per this sample (each category takes three rows).

The classifier is a multi-layer perceptron (MLP) model, with one hidden layer comprising 144 neurons and relu activation function. Consistently with the category levels, the output layer consists of 10 neurons with softmax activation. The default GlorotUniform initialiser has been fed a RANDOM_SEED to ensure reproducibility of results. For reference, the summary of the MLP model is shown below.

The additional elaborations in the notebook are mostly located from Section II. Post-processing onwards, regarding the following aspects, succinctly presented here:

• Weight interpretation
• Handling of a blank input
• Weight evolution over training

Weight interpretation

It is of interest to retrieve the trained weights associated to the hidden layer (i.e. model.layers[1]) to assess if they can be visually interpreted. This can be achieved via the method get_weights() and some convenient reshaping. Illustratively, gathering all weights associated to the first neuron in the hidden layer and rearranging as a (28 x 28) array leads to the following representation:

There is no salient interpretation, but it was expected that a number of neurons would learn a pattern that would not necessarily be intuitive. If the same process is repeated iteratively over all neurons in the hidden layer, the following array of arrays is retrieved:

Amongst the 144 neurons, there are some patterns that are intuitive (to a human observer) indeed, as shown below.

Note that neuron 129 seems to have learned patterns pointing to two categories simultaneously (possibly Sneaker and Shirt).

Formally, the weights associated to the output layer (model.layers[2]) can be treated in the same manner. When doing so, each set of weights transforms into a (12 x 12) array.

In this case, there is no intuitive interpretation for these weights.

Handling of a blank input

It also bears interest to inspect what is the output of the trained MLP when passing a blank image as input (i.e. an array np.ones((28,28)) as the one below, recalling that the pixel values have been normalised).

Under such circumstances, the model prediction is distinctly Bag:

As a double check, the forward propagation can be replicated manually by executing the following steps:

1. retrieve the weight (model.layers[1].get_weights()[0]) and bias (model.layers[1].get_weights()[1]) coefficients of the hidden layer and perform the appropriate array operations with the blank input.

2. apply the relu activation function on the previous result to obtain the hidden feature values.

3. calculate the 'raw' output values by operating on the previous hidden feature values and the weight and bias coefficients of the output layer.

4. apply the softmax activation function on the previous result.

These steps lead to exactly the same array of predictions as the one resulting from feeding a blank input to model.predict(), as expected. When rearranging the hidden feature values from step 2 above as a (12 x 12) array, the following is obtained:

There is no intuitive visual meaning. By inspection (though this can be corroborated programmatically with ease), the neuron with the largest value after activation is neuron number 33 which, upon review of the corresponding weight distribution in the weight interpretation further above, does not convey intuitive meaning either.

Also, and leaving the bias coefficients aside, only 30 of the 144 neurons in the hidden layer contribute to the Bag neuron when feeding in a blank input (i.e. multiplying the hidden feature values by the output weights and subsetting by the Bag neuron leads to only 30 non-zero values). The fact that Bag is predicted from a blank is seemengly a serendipitous byproduct of the parameter values learned at training.

Weight evolution over training

By defining a pair of convenient functions to retrieve the weight distribution after each epoch during training, it is possible the track the evolution of the weight coefficients, and possibly enable visual inspection of the weight array to check if any patterns emerge during training (in this case defined by n_epochs=15). Illustratively, doing this for the first neuron of the hidden layer returns:

Interestingly, the weight distribution of this neuron adopts an intuitive shape early on (resemblance to class Coat or Shirt at epoch 4) but then becomes rather 'abstract' again. It is suggested that this could be interpreted as another sign of overfitting, though more thorough research would be needed to confirm this.