Questions tagged [principal-component-analysis]
For questions related to principal component analysis (PCA), which is commonly used in machine learning for dimensionality reduction.
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Dimensionality Reduction of a matrix preserving number of rows
Let A ($d \times k $) be a matrix such that k < d. How to reduce the dimension of the matrix A to another lower dimension matrix B ($d \times l$ ) such that $l < k$. Note that, while reducing ...
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What is $D_i$ in "Common Principal Components Analysis"?
The following is from Ethem Alpaydin, "Introduction to Machine Learning", Fourth Edition, MIT Press, 2020, page 129.
Here, $C$ is the orthogonal matrix found from the sample covariance of ...
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What is $D_i$ in "Common Principal Components Analysis"?
The following is from Ethem Alpaydin, "Introduction to Machine Learning", Fourth Edition, MIT Press, 2020, page 129.
Here, $C$ is the orthogonal matrix found from the sample covariance of ...
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Are the dimensions in embedding vectors ordered (similar to PCA)?
I am getting started with the vector embeddings. I have a general question about the embedding vectors generated by popular algorithms.
In PCA, usually, there is an implicit order of importance in the ...
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Fast feature elimination in python on GPU
I have a dataset with millions of samples and tens of thousands of features. Most of these features are highly correlated with each other. However, eliminating features based on a correlation ...
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Is there a way to select the subset of most important features using PCA?
Is there a way to select the most important features using PCA? I am not looking for the principal components with the highest scores but a subset of the original features.
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How do I select the number of neurons for each layer in an auto-encoder for dimensionality reduction?
I am trying to apply an auto-encoder for dimensionality reduction. I wonder how it will be applied on a large dataset.
I have tried this code below. I have total of 8 features in my data and I want to ...
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Under what circumstances is a fully connected layer similar to PCA?
I am reading this paper on image retrieval where the goal is to train a network that produces highly discriminative descriptors (aka embeddings) for input images. If you are familiar with facial ...
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Why does PCA of the vertices of a hexagon result in principal components of equal length?
I do PCA on the data points placed in the corners of a hexagon, and get the following principal components:
The PCA variance is $0.6$ and is the same for each component. Why is that? Shouldn't it be ...
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Why Autoencoder Weights Are Not Always Tied
To me, tying weights in an autoencoder makes sense if we think of the auto encoder as doing PCA. Why in any situation would it make sense to not tie the weights? If we don't tie the weights, would it ...
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When using PCA for dimensionality reduction of the feature vectors to speed up learning, how do I know that I'm not letting the model overfit?
I'm following Andrew Ng's course for Machine Learning and I just don't quite understand the following.
Using PCA to speed up learning
Using PCA to reduce the number of features, thus lowering the ...
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Estimating dimensions to reduce input image size to in CNNs
Considering input images to a CNN that have a large dimension (e.g. 256X256), what are some possible methods to estimate the exact dimensions (e.g. 16X16 or 32X32) to which it can be condensed in the ...
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Is the 3d convolution associative given that it can be represented as matrix multiplication?
I'm trying to understand if a 3D convolution of the sort performed in a convolutional layer of a CNN is associative. Specifically, is the following true:
$$
X \otimes(W \cdot Q)=(X \otimes W) \cdot Q,
...
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Unable to meet desired mean squared error
I wish to get MSE < 0.5 on test data (https://easyupload.io/zr7xf3) which is 20% of given data chosen randomly. But I am reaching 0.73 using both plain Ridge Regression as well as a neural network ...
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How does PCA work when we reduce the original space to 2 or higher-dimensional space?
How does PCA work when we reduce the original space to a 2 or higher-dimensional space? I understand the case when we reduce the dimensionality to $1$, but not this case.
$$\begin{array}{ll} \text{...
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Looking for the proper algorithm to compress many lowres images of nearby locations
I have an optimization problem that I'm looking for the right algorithm to solve.
What I have: A large set of low-res 360 images that were taken on a regular grid within a certain area. each of these ...
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Is it theoretically possible (or impossible) that principal component analysis worsens the performance of the model?
In case I had a prediction model and decided to add a PCA step prior to the model, is it theoretically possible/impossible that the number of output dimensions that is better for all tests may perform ...
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Multiple-dimension scaling (MDS) objective for MDS and PCA
The following is the MDS Objective.
Let's think of a senario where I apply MDS with/from the solution I obtained from PCA. Then I calculate the objective function on the initial PCA solution and MDS ...
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What are examples of approaches to dimensionality reduction of feature vectors?
Given a pre-trained CNN model, I extract feature vector of images in reference and query dataset with several thousands of elements.
I would like to apply some augmentation techniques to reduce the ...
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What is the difference between principal component analysis and singular value decomposition in image processing?
What is the difference between principal component analysis and singular value decomposition in image processing? Which one performs better, and why?
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Do the eigenvectors represent the original features?
I've got a test dataset with 4 features and the PCA produces a set of 4 eigenvectors, e.g.,
...
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Why does PCA work well while the total variance retained is small?
I'm learning machine learning by looking through other people's kernel on Kaggle, specifically this Mushroom Classification kernel.
The author first applied PCA to the transformed indicator matrix. He ...
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How to perform PCA in the validation/test set?
I was using PCA on my whole dataset (and, after that, I would split it into training, validation, and test datasets). However, after a little bit of research, I found out that this is the wrong way to ...
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