# Initializing Cluster centroids for 3D arrays

In the lab test for K-means clustering, the code imported an image which we experimented our trained model on. The image is a 128 x 128 x 3 matrix. However, the code reshaped the dimension to 128*128 x 3 making it a 2D array. It is with this 2D array that we randomly initialize cluster centroids and complete the algorithm.

However, if I don’t want to reshape the matrix from 3D to 2D, how do I initialize the centroids? Do I just select a random number of points from the 3D matrix just as I would do with 2D matrix?

To illustrate:

Imagine I have a 720 x 1280 x 3 matrix of an image which I am not willing to change to a 2D matrix, assuming that I want to use K = 4 cluster centroids,

1. Do I just select 4 random points from the 720 examples meaning each centroid would have a dimension of 1280 x 3?

Or

1. I will have to first select 4 random points then for each selected point which would have 1280 x 3 elements, I will select 1 example from the 1280 leaving me with a centroid of 1 x 3 vector? I will then repeat the selection for the other 3 of the initial 4 random points?

Which implementation is right?

Or to put it better, what would the dimension of the cluster centroids of 720 x 1280 x 3 matrix be

In K-means clustering, the cluster centroids are typically represented as points in the same feature space as the data points that you are trying to cluster. In the case of an image, each pixel can be thought of as a data point with three features (red, green, and blue values).

In the case of a 720 x 1280 x 3 matrix, you could select 4 random points from the 720 x 1280 x 3 matrix and use these as the initial cluster centroids. Each centroid would have a dimension of 1 x 1280 x 3, representing the color values of a single pixel in the image.

Alternatively, you could select 4 random points from the 720 x 1280 x 3 matrix, and for each selected point, select 1 example from the 1280, so each centroid would have a dimension of 1 x 3. This is also a valid method but it would be reducing the dimension of the data.

The key thing to remember is that the cluster centroids should be represented in the same feature space as the data points, and that the specific implementation of how to select the initial cluster centroids will depend on the problem and the specific requirements of the application.

In general, the first approach is more common, where you select random pixels and use the RGB values of the pixel as the centroid’s coordinates. The second approach, where you select a random subset of pixels and use the average of the RGB values as the centroid’s coordinates is less common, as it discards information from the data.

Hope so you got the answer

Regards: