# How to apply the ZCA whitening matrix correctly with LinearTransformation **URL:** \ **Category:** Uncategorized\ **Created:** [June 4, 2018, 11:57am UTC](https://discuss.pytorch.org/t/how-to-apply-the-zca-whitening-matrix-correctly-with-lineartransformation/19168 "2018-06-04T11:57:00Z")\ **Posts on this page:** 3\ **Page:** 1
**Author:** ![iAvicenna](https://discuss.pytorch.org/user_avatar/discuss.pytorch.org/iavicenna/32/4870_2.png) [@iAvicenna](https://discuss.pytorch.org/u/iAvicenna)\ **Post date:** [June 4, 2018, 11:57am UTC](https://discuss.pytorch.org/t/how-to-apply-the-zca-whitening-matrix-correctly-with-lineartransformation/19168/1 "2018-06-04T11:57:00Z")
I am trying to apply ZCA whitening matrix to my dataset. The code I use is as follows: ```auto import torchvision import torch import torchvision.transforms as transforms from torchvision import transforms, datasets, models import matplotlib.pyplot as plt import numpy as np def show(i): i = i.reshape((32,32,3)) m,M = i.min(), i.max() plt.imshow((i - m) / (M - m)) plt.show() def computeZCAMAtrix(): #This function computes the ZCA matrix for a set of observables X where #rows are the observations and columns are the variables (M x C x W x H matrix) #C is number of color channels and W x H is width and height of each image root = 'cifar10/' temp= datasets.CIFAR10(root = root, train = True, download = True) #normalize the data to [0 1] range temp.train_data=temp.train_data/255 #compute mean and std and normalize the data to -1 1 range with 1 std mean=(temp.train_data.mean(axis=(0,1,2))) std=(temp.train_data.std(axis=(0,1,2))) temp.train_data=np.multiply(1/std,np.add(temp.train_data,-mean)) #reshape data from M x C x W x H to M x N where N=C x W x H X = temp.train_data X = X.reshape(-1, 3072) # compute the covariance cov = np.cov(X, rowvar=False) # cov is (N, N) # singular value decomposition U,S,V = np.linalg.svd(cov) # U is (N, N), S is (N,1) V is (N,N) # build the ZCA matrix which is (N,N) epsilon = 1e-5 zca_matrix = np.dot(U, np.dot(np.diag(1.0/np.sqrt(S + epsilon)), U.T)) return (torch.from_numpy(zca_matrix).float(), mean, std) #this transformation is used to transform the images to [0,1] range #then normalize to 0 mean and 1 std, and then some #random transformation to boost data variety at each epoch batch_size=4 (Z,mean,std) = computeZCAMAtrix() root = 'cifar10/' transform_train = transforms.Compose( [ transforms.ToTensor(), transforms.LinearTransformation(Z), ]) transform_test = transforms.Compose( [ transforms.ToTensor(), transforms.LinearTransformation(Z), ]) #get the training and test sets training_set = datasets.CIFAR10(root = root, transform = transform_train, train = True, download = True) test_set = datasets.CIFAR10(root = root, transform = transform_test, train = False, download = True) #trying to apply the transformation manually to see the result it produces X = training_set.train_data X = X.reshape(-1, 3072) a=X[1] zca2=np.dot(a,Z) print('printing truck') show2(zca2) training_loader = torch.utils.data.DataLoader(dataset=training_set, batch_size=batch_size, shuffle=False ) test_loader = torch.utils.data.DataLoader(dataset=test_set, batch_size=batch_size, shuffle=False ) classes = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck') # get some random training images dataiter = iter(training_loader) for i, (images, labels) in enumerate(training_loader ,1): a=images[0,:,:,:] b=images[1,:,:,:] c=images[2,:,:,:] d=images[3,:,:,:] #show images #imshow(torchvision.utils.make_grid(images)) print('%5s' % classes[labels[2]]) show(b.numpy()) break ``` As you see I compute the ZCAmatrix and feed it as input (Z) to the dataloading function. However in computation of the ZCA matrix I assume that the data is of the form 50000 x H x W x C. However if I want to apply it as a transformation during dataloading with transforms.LinearTransformation(Z), it seems I need to first convert it to tensor using ToTensor which reorders data as 50000 x C x H x W. Then the application of the ZCA matrix to the data points reorder and flattened this way does not produce what I want it to produce. For instance if I manually apply the transformation to a truck picture of the form H x W x C I get the first picture below where as the LinearTransformation produces the second picture. How can I work around this? it also seems I need to produce the ZCA matrix using 50000 x H x W x C as reordering data the other form and computing the ZCA matrix does not produce correct results as well. ![truck1](https://discuss.pytorch.org/uploads/default/original/2X/3/32bbb51c3daee690ac898f330b13dc0889037667.png) ![truck2](https://discuss.pytorch.org/uploads/default/original/2X/5/50b85d064157180ef8e3f23ab6bf3540f09018c0.png) ---
**Author:** ![SomeOneIntheWorld](https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/s/f6c823/32.png) [@SomeOneIntheWorld](https://discuss.pytorch.org/u/SomeOneIntheWorld)\ **Post date:** [July 3, 2019, 9:43am UTC](https://discuss.pytorch.org/t/how-to-apply-the-zca-whitening-matrix-correctly-with-lineartransformation/19168/2 "2019-07-03T09:43:06Z")
You can find out how to use ZCA in PyTorch [here](https://github.com/semi-supervised-paper/semi-supervised-paper-implementation/blob/e39b61ccab/semi_supervised/core/utils/data_util.py#L150). ---
**Author:** ![BarCodeReader](https://discuss.pytorch.org/user_avatar/discuss.pytorch.org/barcodereader/32/18717_2.png) [@BarCodeReader](https://discuss.pytorch.org/u/BarCodeReader)\ **Post date:** [December 19, 2019, 2:53pm UTC](https://discuss.pytorch.org/t/how-to-apply-the-zca-whitening-matrix-correctly-with-lineartransformation/19168/3 "2019-12-19T14:53:13Z")
how to do this? we apply ZCA on the whole dataset or we apply ZCA on everyt batch? I just feel so confused