How to use sklearn's IncrementalPCA partial_fi

Question

I've got a rather large dataset that I would like to decompose but is too big to load into memory. Researching my options, it seems that sklearn's IncrementalPCA is a good choice, but I can't quite figure out how to make it work.

I can load in the data just fine:

f = h5py.File('my_big_data.h5')
features = f['data']

And from this example, it seems I need to decide what size chunks I want to read from it:

num_rows = data.shape[0]     # total number of rows in data
chunk_size = 10              # how many rows at a time to feed ipca

Then I can create my IncrementalPCA, stream the data chunk-by-chunk, and partially fit it (also from the example above):

ipca = IncrementalPCA(n_components=2)
for i in range(0, num_rows//chunk_size):
    ipca.partial_fit(features[i*chunk_size : (i+1)*chunk_size])

This all goes without error, but I'm not sure what to do next. How do I actually do the dimension reduction and get a new numpy array I can manipulate further and save?

EDIT
The code above was for testing on a smaller subset of my data – as @ImanolLuengo correctly points out, it would be way better to use a larger number of dimensions and chunk size in the final code.

Answer 1

As you well guessed the fitting is done properly, although I would suggest increasing the chunk_size to 100 or 1000 (or even higher, depending on the shape of your data).

What you have to do now to transform it, is actually transforming it:

out = my_new_features_dataset # shape N x 2
for i in range(0, num_rows//chunk_size):
    out[i*chunk_size:(i+1) * chunk_size] = ipca.transform(features[i*chunk_size : (i+1)*chunk_size])

And thats should give you your new transformed features. If you still have too many samples to fit in memory, I would suggest using out as another hdf5 dataset.

Also, I would argue that reducing a huge dataset to 2 components is probably not a very good idea. But is hard to say without knowing the shape of your features. I would suggest reducing them to sqrt(features.shape[1]), as it is a decent heuristic, or pro tip: use ipca.explained_variance_ratio_ to determine the best amount of features for your affordable information loss threshold.

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Edit: as for the explained_variance_ratio_, it returns a vector of dimension n_components (the n_components that you pass as parameter to IPCA) where each value i inicates the percentage of the variance of your original data explained by the i-th new component.

You can follow the procedure in this answer to extract how much information is preserved by the first n components:

>>> print(ipca.explained_variance_ratio_.cumsum())
[ 0.32047581  0.59549787  0.80178824  0.932976    1.        ]

Note: numbers are ficticius taken from the answer above assuming that you have reduced IPCA to 5 components. The i-th number indicates how much of the original data is explained by the first [0, i] components, as it is the cummulative sum of the explained variance ratio.

Thus, what is usually done, is to fit your PCA to the same number of components than your original data:

ipca = IncrementalPCA(n_components=features.shape[1])

Then, after training on your whole data (with iteration + partial_fit) you can plot explaine_variance_ratio_.cumsum() and choose how much data you want to lose. Or do it automatically:

k = np.argmax(ipca.explained_variance_ratio_.cumsum() > 0.9)

The above will return the first index on the cumcum array where the value is > 0.9, this is, indicating the number of PCA components that preserve at least 90% of the original data.

Then you can tweek the transformation to reflect it:

cs = chunk_size
out = my_new_features_dataset # shape N x k
for i in range(0, num_rows//chunk_size):
    out[i*cs:(i+1)*cs] = ipca.transform(features[i*cs:(i+1)*cs])[:, :k]

NOTE the slicing to :k to just select only the first k components while ignoring the rest.