A list of puns related to "Gram matrix"
The only strain of shrooms I've ever taken is Penis Envy. I've read that it's a lot stronger than most strains. At one point in my last deep trip, I was literally convinced we were in The Matrix. I kid you not, I thought aliens had taken over the earth years ago, and that we were currently stuck in a simulation. I was extremely paranoid for like the whole 10 minutes that part of the trip lasted. Anyone experience something similar?
Hey :)
So Lately I have read some of the surprisingly many papers on style transfer (and some of it's applications). (Some stuff I read are: Gatys original, Johnson speed-up, AdaIN, demystifying style transfer etc..)
I have read the Gram matrix captures the second order statistics of the feature (act as a correlation matrix), and that the instance norm captures (?) first order statistics.
I'm trying to grasp the connections between them, what will the gram matrix of the generated image Features would look like after the AdaIN operations compared to the style feature's gram matrix? Is there a way to change the feature map of the generated image to directly match the style's gram matrix?
Hey all.
Equation (14.10) in the book "Machine Learning, A Probabilistic Perspective" by Kevin Murphy says that the Gram matrix K can be split as
K = U^(T)AU
where every column of U is the eigenvector of K and A is a diagonal matrix of eigenvalues. However, I believe Spectral Decomposition says that
K = UAU^(T)
and the above equations are not the same. If that's really the case, then the further derivation of the Mercer's kernel becomes moot. Please correct me if I'm wrong.
Thank you!
I'm not quite understanding this explanation. As I follow, it doesn't seem like this "transpose trick" will give me the same number of principal components as doing standard PCA (getting the eigenvectors of the covariance matrix). If our data matrix, A, is an mxn matrix, then (A^T)A is going to give us an mxm matrix. In this explanation, it is said that we should get the eigenvectors of the mxm "inner product" matrix. But won't that leave us with at most m eigenvectors? Say we make some new matrix, V, that has those m eigenvectors as the columns, making V an mxm matrix. Then (A^T)V is going to yield us a matrix of size nxm. But these dimensions don't match with the matrix made from packing the eigenvectors of the covariance matrix (AA^T) into the columns, as that would give us a matrix of size (presumably) nxn. So how is this equivalent? Where are my other eigenvectors?
EDIT: I've noticed that, when I implement this "Gram Matrix trick" (I'm trying to calculate eigenfaces in python and use them to reconstruct approximations of the original face), this method does actually give me good eigenvectors (sort of), although not as many. The weird thing is, though, is that some of these eigenvectors (seemingly at random) are inverted (i.e. scaled by -1) when compared to the eigenvectors of the covariance matrix with the highest eigenvalues. Would be nice to get some sort of explanation as to why that is as well, if you've got any idea.
https://preview.redd.it/swzjzvwpwuq51.png?width=694&format=png&auto=webp&s=2b764371bcb303d9e3f69b032f646988a02ae330
So I woke up at 6 at ate and nothing, took the shrooms before going to the cinema, they were kicking when i was in the bike and i had a lil fight with my gf so the first 30 minutes were bad shit but then i calmed myself. My friends and gf were already there, i told em nothing at first then i told to my big homie that i ate some shrooms. Had a very introspective trip with some visuals. Crazy shit it was 8k for me.
Can anyone explain me what is Gram Matrix in 3D and higher? I saw gram matrix in Neural Style Transfer.
The code given by Tensorflow website is
def gram_matrix(input_tensor):
result = tf.linalg.einsum('bijc,bijd->bcd', input_tensor, input_tensor) Β input_shape = tf.shape(input_tensor) Β num_locations = tf.cast(input_shape[1]*input_shape[2], tf.float32)
return result/(num_locations)
So the first line of result is for batch dot product. 'b' means the batch images. i,j,c are the dimensions of every image of the batch and i,j,d are the dimensions of its transpose or what? I read that gram matrix is the dot product of the image and its transpose. So each image activation map could be of shape 114*114*64, say there are 40 batch so, it would be 40*114*114*64 in which b = 40, i = 114, j= 114, c = 64. what value should b,i,j,d hold ? Can anyone clear my doubt regarding this please? Explain the equation of einsum used above and gram matrix please.
The distance between the gram matrices of the style image and input image is used as the style loss in Neural Transfer.
The gram matrix is a correlation of filters among themselves.
In CNN, it is said that a filter picks up certain shapes and features such as circles , and then eyes etc.
A correlation among these would include which images have lots of these features.
Wouldn't this be a good indiciator of the contents of the images as opposed to the style?
I don't get the intution as to why this was a considered a good indicator of style similarity among images.
Thank you.
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I know it's sensible because it discards spatial information about the image, but it seems like there's something special about the gram matrix which captures a picture's artistic fingerprint. Does this trick apply in more general settings?
I'm using Scikit-Learn for text classification in Python. My classifier is currently making false predictions for everything (I was fooled for a while because it reported "75% accuracy" when 75% of the labels were false), so I'm trying to figure out what's wrong.
Currently, I'm doing SVC(kernel='precomputed') and computing the Gram matrix manually before passing it to fit() and predict(). The entry $G_{ij}$ of the Gram matrix is the kernel $K(d_i, d_j)$, where K denotes the kernel function and d_i is the ith document.
For my kernel function, the Gram matrix entries are not normalized, i.e. some are greater than 1. Do I need to apply kernel normalization
$$ K'(d_i, d_j) = \frac{K(d_i, d_j)}{\sqrt{K(d_i, d_i) \times K(d_j, d_j)}} $$
to get it between 0 and 1? Or do SVMs not care?
I have to find q1, q2, and q3 for the matrix [1, 1] [2, -1] [-2, 4]. I used the gram schmidt algorithm twice to get q1 and q2 smoothly they are 1/3[1,2,-2] and 1/3[2, 1, 2] I checked the back of the book those are right. For q3 I have no idea what vector I apply to gram schmidt so I more or less cheated at took q1xq2 which is probably not what I was supposed to do. How could I have used gram schmidt to find q3?
I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.
Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.
Do your worst!
I'm surprised it hasn't decade.
For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.
I said "hey look, an escaPEA"
No one near me but it didn't half make me laugh for a good hour or so!
Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies π
It really does, I swear!
Theyβre on standbi
https://preview.redd.it/9fszcied1lp41.png?width=948&format=png&auto=webp&s=75f7ca35dd578413ce6987e5dad93e46b57ee0eb
https://preview.redd.it/mplksqza1lp41.png?width=923&format=png&auto=webp&s=41892535835d4434ca2183c75a49a1312f8f9435
Is my solution correct?
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