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dimensionality_reduction.py
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import numpy as np
import torch
from torch.optim import Adam
from tqdm import tqdm
from copy import deepcopy
from scipy.stats import ortho_group
class NormalizedSoftmax():
"""
Uses the NormalizedSoftmax loss function to find a good transformation.
Is used for the Oracle baseline.
"""
def __init__(self,
num_components:int=2,
patience:int=100,
learning_rate:float=0.01,
) -> None:
self.num_components = num_components
self.U = None
self.patience = patience
self.lr = learning_rate
self.loss_func = torch.nn.CrossEntropyLoss()
def _loss(self, X:torch.Tensor, labels:torch.Tensor, U:torch.Tensor, P:torch.Tensor) -> torch.Tensor:
# encode
V = X @ U.T
V = V / V.norm(dim=1, keepdim=True)
# decode
P_norm = P / P.norm(dim=1, keepdim=True)
X_hat = V @ P_norm.T
# loss
loss = self.loss_func(X_hat, labels)
return loss
def fit(self, X:torch.Tensor, labels:torch.Tensor) -> None:
# convert to tensor
X = torch.as_tensor(X, dtype=torch.float)
X = X / X.norm(dim=1, keepdim=True)
num_classes = len(set(labels.numpy()))
print(f"Fitting to {num_classes} classes")
best_loss = torch.inf
best_epoch = 0
iteration = 0
U = torch.normal(0, 0.1, (self.num_components, X.shape[1]), requires_grad=True, dtype=torch.float)
P = torch.normal(0, 0.1, (num_classes, self.num_components), requires_grad=True, dtype=torch.float)
optimizer = Adam([U, P], lr=self.lr)
pbar = tqdm()
while True:
pbar.update(1)
iteration += 1
optimizer.zero_grad()
loss = self._loss(X, labels, U, P)
pbar.set_description(f"Loss ({iteration}): {loss.item():.4f}")
if loss.item() < best_loss:
best_loss = loss.item()
best_epoch = iteration
self.U = U.clone().detach()
if iteration - best_epoch >= self.patience:
break
loss.backward()
optimizer.step()
print(f"Finished optimization. Best loss ({best_loss}) achieved after {best_epoch} iterations.")
def transform(self, X:torch.Tensor) -> torch.Tensor:
with torch.no_grad():
X = torch.as_tensor(X, dtype=torch.float)
X = X / X.norm(dim=1, keepdim=True)
V = X @ self.U.T
V = V / V.norm(dim=1, keepdim=True)
return V
def fit_transform(self, X: torch.Tensor, labels:torch.Tensor=None) -> torch.Tensor:
self.fit(X, labels)
return self.transform(X)
class DimRedRecon():
def __init__(self,
num_components:int=2,
patience:int=100,
learning_rate:float=0.01
) -> None:
self.num_components = num_components
self.U = None
self.lamb = 0
self.patience = patience
self.lr = learning_rate
# from https://github.com/pytorch/pytorch/issues/8069#issuecomment-524096597
# avoids gradient instabilities in acos at the edges
def acos_safe(self, x, eps=1e-7):
slope = np.arccos(1-eps) / eps
buf = torch.empty_like(x)
good = abs(x) <= 1-eps
bad = ~good
sign = torch.sign(x[bad])
buf[good] = torch.acos(x[good])
buf[bad] = torch.acos(sign * (1 - eps)) - slope*sign*(abs(x[bad]) - 1 + eps)
return buf
def _loss(self, X: torch.Tensor, U: torch.Tensor) -> torch.Tensor:
# X = X / X.norm(dim=1, keepdim=True)
# encode
V = X @ U.T
V = V / V.norm(dim=1, keepdim=True)
# decode
X_recon = V @ U
X_recon = X_recon / X_recon.norm(dim=1, keepdim=True)
# loss
loss = torch.mean(self.acos_safe(torch.sum(X * X_recon, dim=1))) \
+ self.lamb * torch.sum(torch.square(U @ U.T - torch.eye(self.num_components)))
return loss
def fit(self, X:torch.tensor) -> None:
# convert to tensor
X = torch.as_tensor(X, dtype=torch.float)
X = X / X.norm(dim=1, keepdim=True)
best_loss = torch.inf
best_epoch = 0
epoch = 0
U = torch.normal(0, 0.1, (self.num_components, X.shape[1]), requires_grad=True, dtype=torch.float)
optimizer = Adam([U], lr=self.lr)
pbar = tqdm()
while True:
epoch += 1
pbar.update(1)
optimizer.zero_grad()
loss = self._loss(X, U)
pbar.set_description(f"Loss ({epoch}): {loss.item()}")
if loss.item() < best_loss:
best_loss = loss
best_epoch = epoch
self.U = U.clone().detach()
if epoch - best_epoch >= self.patience:
break
loss.backward()
optimizer.step()
print(f"Finished optimization. Best loss ({best_loss}) achieved after {best_epoch} iterations.")
def transform(self, X:torch.tensor) -> np.array:
# with torch.no_grad():
X = torch.as_tensor(X, dtype=torch.float)
X = X / X.norm(dim=1, keepdim=True)
V = X @ self.U.T
V = V / V.norm(dim=1, keepdim=True)
return V
def fit_transform(self, X: torch.tensor) -> np.array:
self.fit(X)
return self.transform(X)
class LinearAutoencoder():
def __init__(self,
num_components:int=2,
patience:int=100,
learning_rate:float=0.01
) -> None:
self.num_components = num_components
self.patience = patience
self.lr = learning_rate
self.encoder = None
self.decoder = None
def fit(self, X:torch.tensor) -> None:
# convert to tensor
X = torch.as_tensor(X, dtype=torch.float)
best_loss = torch.inf
best_epoch = 0
epoch = 0
encoder = torch.nn.Linear(X.shape[1], self.num_components)
decoder = torch.nn.Linear(self.num_components, X.shape[1])
optimizer = Adam(list(encoder.parameters())+list(decoder.parameters()), lr=self.lr)
pbar = tqdm()
while True:
epoch += 1
pbar.update(1)
optimizer.zero_grad()
# encode
V = encoder(X)
# decode
X_recon = decoder(V)
# loss
loss = torch.sum(torch.square(X - X_recon))
pbar.set_description(f"Loss ({epoch}): {loss.item()}")
if loss.item() < best_loss:
best_loss = loss
best_epoch = epoch
self.encoder = deepcopy(encoder)
self.decoder = deepcopy(decoder)
if epoch - best_epoch >= self.patience:
break
loss.backward()
optimizer.step()
print(f"Finished optimization. Best loss ({best_loss}) achieved after {best_epoch} iterations.")
def transform(self, X:torch.tensor) -> np.array:
X = torch.as_tensor(X, dtype=torch.float)
with torch.no_grad():
V = self.encoder(X)
return V.detach()
def fit_transform(self, X: torch.tensor) -> np.array:
self.fit(X)
return self.transform(X)
class Autoencoder():
def __init__(self,
num_components:int=2,
patience:int=100,
learning_rate:float=0.01
) -> None:
self.num_components = num_components
self.patience = patience
self.lr = learning_rate
self.encoder = None
self.decoder = None
self.hidden_size = 512 # best trade-off between speed and performance
def fit(self, X:torch.tensor) -> None:
# convert to tensor
X = torch.as_tensor(X, dtype=torch.float)
best_loss = torch.inf
best_epoch = 0
epoch = 0
encoder = torch.nn.Sequential(
torch.nn.Linear(X.shape[1], self.hidden_size),
torch.nn.LeakyReLU(),
torch.nn.Linear(self.hidden_size, self.num_components),
)
decoder = torch.nn.Sequential(
torch.nn.Linear(self.num_components, self.hidden_size),
torch.nn.LeakyReLU(),
torch.nn.Linear(self.hidden_size, X.shape[1]),
)
optimizer = Adam(list(encoder.parameters())+list(decoder.parameters()), lr=self.lr, weight_decay=1e-2)
pbar = tqdm()
while True:
epoch += 1
pbar.update(1)
optimizer.zero_grad()
# encode
V = encoder(X)
# decode
X_recon = decoder(V)
# loss
# loss = torch.mean(torch.sqrt(torch.sum(torch.square(X - X_recon), dim=1)))
loss = torch.sum(torch.square(X - X_recon)) # Loss from LAE
pbar.set_description(f"Loss ({epoch}): {loss.item()}")
if loss.item() < best_loss:
best_loss = loss
best_epoch = epoch
self.encoder = deepcopy(encoder)
self.decoder = deepcopy(decoder)
if epoch - best_epoch >= self.patience:
break
loss.backward()
optimizer.step()
print(f"Finished optimization. Best loss ({best_loss}) achieved after {best_epoch} iterations.")
def transform(self, X:torch.tensor) -> np.array:
X = torch.as_tensor(X, dtype=torch.float)
with torch.no_grad():
V = self.encoder(X)
return V.detach()
def fit_transform(self, X: torch.tensor) -> np.array:
self.fit(X)
return self.transform(X)