6
votes
Accepted
Can Principal Component Analysis (PCA) Solve the Cocktail Party Problem?
The Cocktail Party Problem is a Blind Source Separation (BSS) problem.
Given a linear mixture of signals:
$$ \boldsymbol{y} \left[ n \right] = A \boldsymbol{x} \left[ n \right] $$
We're trying to ...
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3
votes
Accepted
Principal Component Analysis definition
By projecting a vector x using PCA (on the PCs), you maximize the variance in the reduced space. Initially, the space is not optimal in terms of maximizing the variance.
So:
PCA projects vector 𝑥 ...
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3
votes
Accepted
Apply Principal Component Analysis (PCA) for RGB Images
General Idea
The general idea of Principal Component Analysis (PCA) is as following (Intuition over formalism):
Given a set of points in space (Inner Product Space) find a set of vectors (Directions) ...
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3
votes
Accepted
ICA and Gaussianity: A Misleading Example in the Book Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition
The example given in the book Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition (4th Estition):
The point in this example is to show the property of the method used: Find a ...
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3
votes
Can Principal Component Analysis (PCA) Solve the Cocktail Party Problem?
Speech Source Separation (SSS) or Audio Source Separation (ASS) can be seen as a specialized version of source separation. I mention these expressions under which one can find additional works. One ...
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3
votes
Accepted
Whitening signal vs. whitening its DFT
Provided you define it appropriately, the DFT is just an orthonormal transformation: the vectors that make up the DFT matrix are orthogonal to each other and are unit vectors.
does that mean that ...
- 26k
3
votes
Accepted
How to express one image in terms of another one
I found an answer which is good-enough for me. As @Stanley Pawlukiewicz has pointed out in the comments, this is hard to do for a general case when there is little correlation between the images. I, ...
2
votes
PCA to reduce dimensionality to 99% variance
If what you want is PC compression, a more useful form of PCA would be achieved via Singular Value Decomposition (which is, in many cases, more accurate and faster than an eigendecomposition).
...
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2
votes
What Is the Difference Between PCA and Karhunen Loeve (KL) Transform?
See:
Jan J. Gerbrands,
On the relationships between SVD, KLT and PCA,
Pattern Recognition,Volume 14, Issues 1–6, 1981, Pages 375-381,
ISSN 0031-3203,https://doi.org/10.1016/0031-3203(81)90082-0.
(...
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2
votes
Accepted
What Is the Difference Between PCA and Karhunen Loeve (KL) Transform?
For discrete data both are the same - Finding set of orthogonal directions which maximizes the Variance (Energy) of data along them. Sometimes those are called the natural axis of the data (Inferred ...
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2
votes
Discrete Cosine Transform (DCT) as the Limit of Principal Component Analysis (PCA)
I can see that some papers refer to IEEE - N. Ahmed; T. Natarajan; K.R. Rao - Discrete Cosine Transform as a reference to the assertion that DCT is an approximation of the KLT.
Pay attention, to the ...
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2
votes
ICA and Gaussianity: A Misleading Example in the Book Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition
I don't know the rest of the problem statement, nor the result they arrive at, but consider this:
If you add two independent normal random variables, you just get a new normal variable (with its mean ...
- 32.5k
2
votes
Apply Principal Component Analysis (PCA) for RGB Images
One option is called Multilinear principal component analysis:
Multilinear principal component analysis (MPCA) is a multilinear
extension of principal component analysis (PCA). MPCA is employed ...
- 32.3k
1
vote
Apply Principal Component Analysis (PCA) for RGB Images
I've just recently reviewed a paper that used the t-svd as a multidimensional extension to the PCA. They've explicitly tested this on RGB images and claimed to achieve good results. Might be another ...
- 2,463
1
vote
Accepted
How Can PCA Be Used in Image Analysis
Imagine you have a set of 10,000 images (32 x 32) of faces.
An intuitive way is to think they have a lot in common.
One step farther would be that if you take one of the faces you could generate it ...
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1
vote
Face Classification. Is it OK to only use geometric features?
The first approach assumes that you already have identified local features, special points on the face. This identification task is not always straightforward to perform: imagine a face with ...
- 32.3k
1
vote
Face Classification. Is it OK to only use geometric features?
What lies at the heart of pattern recognition and pattern classification is the selection of the correct features that is used in decisions. And the most important properties of correct features are 1-...
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1
vote
Principal Component Analysis (PCA) on Convolutional Neural Network (CNN) Features
We are applying something similar like so:
A CNN is trained on a particular image dataset.
PCA (or some other transform) is performed on the feature vectors to obtain the main axes of variation.
The ...
- 3,636
1
vote
Principal Component Analysis (PCA) on Convolutional Neural Network (CNN) Features
I'm not into details of this specific case but I can see some logic.
A convolution layer can be reformulated as a Matrix Multiplication:
$$ y = W x $$
Let's say we trained on Data Set $ {x}^{1} $ ...
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1
vote
Principal Component Analysis (PCA) on Convolutional Neural Network (CNN) Features
It does appear that the (re)ranking code is using the wrong dataset, i.e. the Oxford model with the Paris images. This question was raised in the following github issue: wrong dataset name #6.
...
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