How to create a kernel matrix from a pandas dataframe?

Question

I have a pandas dataframe in which the rows are the observations (data points) and the columns are the features. I want to create a kernel matrix from this dataframe using a Gaussian kernel. Therefore I need to calculate the kernel function for every combination of data points (rows). How to do that in an efficient way in python without using a for loop?

I tried with for loop, but is extremely inefficient. I think I should probably use the broadcasting feature of numpy, but I don't know how to use it.

Answer 1

Okay first you will need to calculate squared length of each row with numpy, to do that convert your database into NumPy array then compute the squared norm of each row like this

squared_norm = np.sum(X**2, axis=1)

squared_norm X**2 squares each element in the array X. np.sum(..., axis=1) sums these squared values along the rows (axis=1). Each element in squared_norm is the sum of squares of the features for a corresponding row in X.

then you compute the squared Euclidian distance matrix

distance_matrix = squared_norm[:, np.newaxis] + squared_norm - 2 * np.dot(X, X.T)

squared_norm[:, np.newaxis] reshapes squared_norm to be a column vector. squared_norm (a row vector due to broadcasting) and squared_norm[:, np.newaxis] (a column vector) are added together. This addition applies broadcasting, resulting in a matrix where each element (i, j) is the sum of the squared norms of row i and row j. np.dot(X, X.T) computes the matrix product of X with its transpose, which gives a matrix of dot products between all pairs of rows in X.

You will need to define Gaussian kernel parameter (sigma)

sigma = 1.0  # Adjust this based on your data

Apply the Gaussian kernel

kernel_matrix = np.exp(-distance_matrix / (2 * sigma**2))

This approach is efficient and leverages NumPy's capabilities for vectorized operations, making it suitable for handling large datasets without the need for explicit Python loops. You can find additional informations here LINK LINK-2 LINK-3