Compute Fermat distance for the MNIST data set

This notebook computes the fermat distance between the images in the MNIST data set. We are reading the data set from https://www.kaggle.com/oddrationale/mnist-in-csv#mnist_train.csv

Contents:

1- Preprocessing data
2- Computing Fermat distance
3- Visualization using t-sne

1- Preprocessing data

import random
import numpy as np
from scipy.spatial import distance_matrix
import matplotlib.pyplot as plt
from sklearn.manifold import TSNE

from fermat import Fermat

Reading mnist data from https://www.kaggle.com/oddrationale/mnist-in-csv#mnist_train.csv

labels = []
data = []
with open('../data/mnist_train.csv', 'r') as f:
    for l in f.readlines():
        row = l[:-1].split(',')
        labels.append(row[0])
        data.append([float(x)/255 for x in row[1:]])

2- Computing Fermat distance

# we only consider a sample of data points
test_size = 1000 

# compute euclidean distances between data points
distances = distance_matrix(data[:test_size], data[:test_size])

# Initialize the fermat model
# The distances would be computed used the aprox method and the euclidean distances as input
f = Fermat(alpha = 4, path_method='L', k=30, landmarks=30)


# fit the Fermat model
f.fit(np.matrix(distances))

3- Visualization

def plot_figure(data,S,s_labels, xlabel):
    plt.figure(figsize=(20, 10))
    plt.xlabel(xlabel, fontsize='large')
    for digit in range(10):
        xs = [data[i, 0] for i in range(S) if s_labels[i] == str(digit)]
        ys = [data[i, 1] for i in range(S) if s_labels[i] == str(digit)]
        plt.plot(xs, ys, 'o', label=str(digit))
    plt.legend(numpoints=1)

tsne = TSNE(n_components=2, perplexity=60, n_iter=1000)

T-sne on the euclidean distance

tsne_euclidean = tsne.fit_transform(distances)

plot_figure(tsne_euclidean, test_size, labels[:test_size], "TSNE on euclidean distance")

T-sne on the Fermat distance

tsne_fermat = tsne.fit_transform(f.get_distances())

plot_figure(tsne_fermat, test_size, labels[:test_size], "TSNE on Fermat distance")