Sample points in a circle are not uniformly distributed.

[kwonoh]

Hi,

Thank you for sharing the code.

In the original implementation, I found that the function generateZ in MNIST_SlicedWassersteinAutoEncoder_Circle.ipynb does not generate sample points in a circle uniformly.
The generated sample points are more dense at the center of a circle. This can affect the resulting latent space.

I made an issue in the original implementation repository.

For this PyTorch implementation, It can be easily fixed by applying sqrt on random radius samples from a uniform distribution in rand_cirlce2d.

def rand_cirlce2d(batch_size):
    """ This function generates 2D samples from a filled-circle distribution in a 2-dimensional space.
        Args:
            batch_size (int): number of batch samples
        Return:
            torch.Tensor: tensor of size (batch_size, 2)
    """
    # r = np.random.uniform(size=(batch_size)) # before
    r = np.sqrt(np.random.uniform(size=(batch_size))) # after
    theta = 2 * np.pi * np.random.uniform(size=(batch_size))
    x = r * np.cos(theta)
    y = r * np.sin(theta)
    z = np.array([x, y]).T
    return torch.from_numpy(z).type(torch.FloatTensor)

Here is an related article: Generate a random point within a circle (uniformly)

Best,
Oh-Hyun

[eifuentes]

thanks @kwonoh , the stack overflow link was very informative. i'll re-run the experiment with your suggested changes!