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Word Embedding Postprocessing: All but the top
All-but-the-Top: Simple and Effective Postprocessing for Word Representations
Last Updated: Fri 15 Nov 2019 11:47:00 AM CET
**Prior version had serious issues, please excuse any inconveniences.**
import numpy as np
from sklearn.decomposition import PCA
def all_but_the_top(v, D):
:v: word vectors of shape (n_words, n_dimensions)
:D: number of principal components to subtract
# 1. Subtract mean vector
v_tilde = v - np.mean(v, axis=0)
# 2. Compute the first `D` principal components
# on centered embedding vectors
u = PCA(n_components=D).fit(v_tilde).components_ # [D, emb_size]
# Subtract first `D` principal components
# [vocab_size, emb_size] @ [emb_size, D] @ [D, emb_size] -> [vocab_size, emb_size]
return v_tilde - (v @ u.T @ u)
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gojomo commented Nov 15, 2019

Thanks - trying this version (that ends return v - (v_tilde @ u.T @ u)) has the expected behavior in my evaluations!

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lgalke commented Nov 15, 2019

@gojomo I just double checked with the paper itself and it should be v_tilde - (v @ u.T @ u) instead of v - (v_tilde @....

Applying PCA to centered / non-centered versions should not make a difference. The important thing is to subtract the mean from the embeddings to match the paper. v_tilde holds the centered version in this gist so now we return the embeddings - mean - first D principal components.

@s1998: I think this last point is also not considered in your implementation. In line 11 you do not subtract from the centered version. Am I missing something?

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s1998 commented Nov 18, 2019

@lgalke You are correct, it should be mean centered embeddings that I need to subtract from. I'll fix that, thanks.

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