Random projection algorithm pseudo code

Random Projection Algorithm: Pseudocode

Introduction

The Random Projection Algorithm is a dimensionality reduction technique that aims to reduce the number of features in a dataset while preserving its essential structure. It achieves this by projecting the data onto a lower-dimensional subspace, using a randomly generated projection matrix. This process often reduces the computational cost of downstream tasks, like clustering or classification.

Algorithm Pseudocode

# Generate a random projection matrix
R = random_matrix(d, k)

# Project the data onto the lower-dimensional subspace
D' = D * R

# Return the projected data
return D'

Code Explanation

• random_matrix(d, k): This function generates a random matrix with dimensions (d x k) where d is the original number of features and k is the desired number of features after projection. The specific distribution used for random number generation can vary depending on the application, but common choices include Gaussian or uniform distributions.
• D * R: This matrix multiplication performs the projection. Each row in the data matrix D is multiplied by the random projection matrix R, effectively transforming the original features into a new set of k features.

Example

Consider a data matrix D with 10 samples and 5 features:

D = [[1, 2, 3, 4, 5],
     [2, 3, 4, 5, 6],
     [3, 4, 5, 6, 7],
     [4, 5, 6, 7, 8],
     [5, 6, 7, 8, 9],
     [6, 7, 8, 9, 10],
     [7, 8, 9, 10, 11],
     [8, 9, 10, 11, 12],
     [9, 10, 11, 12, 13],
     [10, 11, 12, 13, 14]]

We want to reduce the dimensionality to 3 features using random projection. A possible random projection matrix R could be:

R = [[0.2, 0.5, 0.1],
     [0.3, 0.4, 0.6],
     [0.7, 0.1, 0.2],
     [0.9, 0.3, 0.4],
     [0.1, 0.6, 0.5]]

Multiplying D by R gives the projected data matrix D’:

D' = [[2.9, 2.8, 2.6],
     [3.8, 3.6, 3.5],
     [4.7, 4.4, 4.4],
     [5.6, 5.2, 5.3],
     [6.5, 6.0, 6.2],
     [7.4, 6.8, 7.1],
     [8.3, 7.6, 8.0],
     [9.2, 8.4, 8.9],
     [10.1, 9.2, 9.8],
     [11.0, 10.0, 10.7]]

Conclusion

The Random Projection Algorithm provides a simple and efficient way to reduce the dimensionality of data. The choice of the random projection matrix and the number of features to retain depend on the specific application and the desired level of data preservation.