Subtracting the mean of each row of a matrix is a common data preprocessing technique used in various machine learning applications. This technique involves subtracting the mean of each row from each element of the corresponding row in a matrix. The resulting matrix will have a zero mean for each row, which can be useful for normalization or standardization purposes. Here are a few ways through which you can do this:
1. Using "NumPy vectorization":
 The code first creates a 3x3 matrix called
arr
with random integer values between0
and9
.  It then calculates the mean of each row using
np.mean()
withaxis=1
to sum over each row.  After which, it subtracts the row means from each element in the row using NumPy vectorization by adding a new axis to
row_means
with[:, np.newaxis]
.  The resulting array is printed to the console.
2. Using "np.apply_along_axis()" function:
 This code generates a 3x3 matrix of random integers between
0
and10
using the NumPyrandom.randint()
function.  Then, it subtracts the mean of each row of the matrix using the
apply_along_axis()
function with alambda
function that calculates the mean of each row and subtracts it from the elements of that row.  Finally, it prints the resulting matrix with the mean of each row subtracted.

In terms of efficiency, the first method is likely to be more efficient because it uses NumPy’s builtin broadcasting to subtract the row means from each element in the array, which is a vectorized operation that can be performed quickly.

The second method involves applying the
lambda
function to each row individually, which can be slower for larger arrays. 
However, the advantage of the second method is that it is more concise and potentially easier to read, especially for people who are familiar with the
apply_along_axis()
function. 
Additionally, the second method can be more flexible than the first method because it allows for more complex functions to be applied to each row, not just the mean subtraction.