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import numpy as np
from dataclasses import dataclass
from sklearn.decomposition import PCA
@dataclass
class ItemProjection:
P: np.ndarray # [k, d]
mean: np.ndarray # [d]
@classmethod
def from_pca(cls, embeddings: np.ndarray, k: int) -> "ItemProjection":
"""
embeddings: [M, d]
"""
mean = embeddings.mean(axis=0)
centered = embeddings - mean
# Ensure k is not larger than min(n_samples, n_features)
n_samples, n_features = embeddings.shape
actual_k = min(k, n_samples, n_features)
pca = PCA(n_components=actual_k)
pca.fit(centered)
# pca.components_: [k, d]
P = pca.components_ # Each row is a principal component vector
# If we had to reduce k, we might want to pad P or handle it?
# For now, let's assume we get what we asked for or less if data is small.
# But for the system we want fixed k.
# If actual_k < k, we should pad with zeros to match expected dimension.
if actual_k < k:
padding = np.zeros((k - actual_k, n_features), dtype=P.dtype)
P = np.vstack([P, padding])
return cls(P=P, mean=mean)
def transform_embeddings(self, E: np.ndarray) -> np.ndarray:
"""
E: [N, d] -> [N, k]
"""
return (E - self.mean) @ self.P.T
def transform_vector(self, e: np.ndarray) -> np.ndarray:
"""
e: [d] -> [k]
"""
return self.P @ (e - self.mean)
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