How to use the 'sphereize data' option with PCA in TensorFlow

Question

I have used PCA with the 'Sphereize data' option on the following page successfully: https://projector.tensorflow.org/

I wonder how to run the same computation locally using the TensorFlow API. I found the PCA documentation in the API documentation, but I am not sure if sphereizing the data is available somewhere in the API too?

Answer 1

The "sphereize data" option normalizes the data by shifting each point by the centroid and making unit norm.

Here is the code used in Tensorboard (in typescript):

  normalize() {
    // Compute the centroid of all data points.
    let centroid = vector.centroid(this.points, (a) => a.vector);
    if (centroid == null) {
      throw Error('centroid should not be null');
    }
    // Shift all points by the centroid and make them unit norm.
    for (let id = 0; id < this.points.length; ++id) {
      let dataPoint = this.points[id];
      dataPoint.vector = vector.sub(dataPoint.vector, centroid);
      if (vector.norm2(dataPoint.vector) > 0) {
        // If we take the unit norm of a vector of all 0s, we get a vector of
        // all NaNs. We prevent that with a guard.
        vector.unit(dataPoint.vector);
      }
    }
  }

You can reproduce that normalization using the following python function:

def sphereize_data(x):
    """
    x is a 2D Tensor of shape :(num_vectors, dim_vectors) 
    """
    centroids = tf.reduce_mean(x, axis=0, keepdims=True) 
    return tf.math.div_no_nan((x - centroids), tf.norm(x - centroids, axis=0, keepdims=True))