lvdmaaten.github.io | Website of Laurens van der Maaten

It looks like you're doing dimensionality reduction on both the training and testing data separately. During training, you're supposed to remember the principal scores or basis vectors of the examples during training. Remember that you are finding a new representation of your data with a new set of orthogonal axes based on the training data. During testing, you repeat the exact same procedure as you did with the training data as you are representing the data with respect to these basis vectors. Therefore, you use the basis vectors for the training data to reduce your data down. You are only getting a 2408 x 2408 matrix because you are performing PCA on the test examples as it is impossible to produce basis vectors beyond the rank of the matrix in question (i.e. 2408).

Retain your basis vectors from the training stage and when it's time to perform classification in the testing stage, you must use the same basis vectors from the training stage. Remember that in PCA, you must centre your data by performing mean subtraction prior to the dimensionality reduction. To do this, in your code we note that the basis vectors are stored in mapping.M and the associated mean vector is stored in mapping.mean. When it comes to the testing stage, make sure you mean subtract your test data with the mapping.mean from the training stage:

The main reason for t-SNE being slower than PCA is that no analytical solution exists for the criterion that is being optimised. Instead, a solution must be approximated through gradient descend iterations.

In practice, this means lots of for loops. Not in the least the main iteration for-loop in line 129, that runs up to max_iter=1000 times. Additionally, the x2p function iterates over all data points with a for loop.

The reference implementation is optimised for readability, not for computational speed. The authors link to an optimised Torch implementation as well, which should speed up the computation a lot. If you want to stay in pure Python, I recommend the implementation in Scikit-Learn, which should also be a lot faster.