In this assignment, we are expected to implement multiple dimensionality reduction algorithms with and without using a weighting function and compare the results. To be able to compare the results, we need to calculate correlation between human judgements and word similarities. Also, we need to apply statistical significance test between the correlations to prove the experimental result.

I used pre-generated matrix file to load the corpus. After that, I applied the PPMI (Positive Pointwise Mutual Information) weighting to it. I used both SVD and NMF dimensionality reduction algorithms to reduce the dimensions of the matrix.

I implemented combinations of algorithms as follows:

• NMF with raw occurrence matrix
• NMF with PPMI weighted matrix
• SVD with raw occurrence matrix
• SVD with PPMI weighted matrix

You can see the correlation results on the below figure, which clearly shows that; using PPMI weighting gives better results with dimensionality reduction on the given corpus. We cannot sure about the difference between NMF and SVD only by looking at the correlations, because they are close to each other. Thus, we have to apply a statistical significance test on the correlations to find out whether the difference between them occurred randomly or not.

I used Z-Test as a statistical significance test. First, I applied z-transformation on correlations by taking inverse tangent (arctan(x)) of them. Then I applied the below formula to find z-value. After finding the z-value, I looked up the z-table to find the corresponding p-value for it.

You can see the z-test results on the below figure.

2.1. PPMI or Co-occurrence Counts?

The first and second rows show the comparison between raw co-occurrence matrix and PPMI weighted version of it. The both p-values are less than 0.05, which is our level of significance value. Thus, we can say that the difference between the correlations are statistically significant and we cannot randomly achieve these results with using raw co-occurrence counts. In other words, there is a significant difference between raw co-occurrence counts and PPMI for our samples.

2.2. SVD or NMF?

The third and fourth rows show the comparison between SVD and NMF dimensionality reduction algorithms. The both p-values are higher 0.05. Thus, we can say that the difference between the correlations are not statistically significant and we can randomly achieve these results with using any of two algorithms. In other words, there is no significant difference between SVD and NMF for our samples.

Python version: Python 3.6.5

To install the requirements use the following command: pip3 install -r requirements.pip

To run the code use the following command: python3 src/main.py