def dimension_reduction():
X = PPMI_matrix()
word_list = list()
vecdict_list = list()
for word, vector in sorted(X.items()):
word_list.append(word)
vecdict_list.append(dict(vector))
Dic2Vec = DictVectorizer(sparse=True)
vector_list = Dic2Vec.fit_transform(vecdict_list)
X_svd = svds(vector_list, 300)
X_pca = np.dot(X_svd[0], np.diag(X_svd[1]))
word_matrix = dict()
for word, vector in zip(word_list, X_pca):
word_matrix[word] = vector
return word_matrix
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