Questions tagged [kernel]

Kernel functions are a class of functions which transform the original data into a new space in which the classes of the data are easier to separate by a kernel algorithm.

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39 views

Can someone clarify what the linear assumption of PCA is?

0 For the past few hours I've been trying to search what this linear assumption is. Some of the articles states that that your independent variables have to be linear in relationship and need some ...
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13 views

How do I extract the kernel matrix for a classifier created using `sklearn.svm.SVC`?

I am currently using the kernels that come with sk-learn support vector machine library. How do I extract the kernel matrix for a classifier created using ...
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Difficulty understanding the dimension differences in kernel PCA

In Kernel PCA, the kernel trick works because we can show that there is an equivalency between eigenvectors of the kernel matrix and eigenvectors of the covariance matrix. I know the math to go from ...
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8 views

State-of-the-art methods for out-of-sample-extension

I'm using a kernel based dimensionality reduction algorithms, and interested in extending out-of-sample data points for further analysis. I've been using the Nystrom method for this task, and some ...
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32 views

Why are neural networks equivalent to kernel methods?

I read a recent paper by Pedro Domingos, claiming that Every Model Learned by Gradient Descent Is Approximately a Kernel Machine. I wanted to understand the key idea a little better. Why are neural ...
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22 views

How to evaluate KDE against histogram?

I am currently testing some approaches for density estimation, and I think the basic approach of histograms may not be the best option to me and KDE is certainly a good alternative to go. While ago I ...
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27 views

How do you choose a kernel for a discontinuous function in Gaussian Process Regression?

I'm doing Gaussian Process Regression and created a series of functions by gluing other functions together on random places. Here's an example: Perhaps this one is to complicated, but all the ...
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1answer
40 views

Kernel Density in Scikit Learn

I'm trying to understand how does the KernelDensity class in scikit-learn work. Consider the following two cases which build a kernel from two different arrays (a). I'm wondering why the result of ...
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21 views

Should kernel size always be a prime number?

Should kernel size always be a prime number? E.g. (3,3) (5,5) (7,7). While tinkering with sklearn.preprocessing.KernelCenterer(), I noticed that I could only get it ...
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600 views

Jupyter notebook kernel dies when reading CSV file on M1 Mac

Odd Jupyter notebook problem on M1 mac here. Using these steps I was able to get Jupyter Notebooks to run in the first place. It worked fine executing the following simple code: ...
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1answer
28 views

what are the main differences between parametric and non-parametric machine learning algorithms?

I am interested in parametric and non-parametric machine learning algorithms, their advantages and disadvantages and also their main differences regarding computational complexities. In particular I ...
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In classical kernel regression, is there a task which responds almost exclusively to a single kernel choice?

I'm curious if there is any well-known kernel regression/classification task which can only be "solved" using a specific choice of kernel?
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A question about dual representations, kernels and notations used in Bishop's book

I'm having hard times about kernel functions and dual representations on 'Pattern recognition from and machine learning' by Bishop. Here it is the page I'm trying to understand: Of course setting the ...
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16 views

Non semi positive definite kernel matrix

What happens if we run a support vector machine model using a kernel that does not satisfy requirements such as non-positive semi definite? This is my flow of thought: In kernel methods $w.x$ is ...
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21 views

SVD Kernel and Linear Algebra Kernel, is there a conceptual difference?

Is the term kernel used in Sklearn to execute the SVD machine learning algorithm conceptually related to the notion of a kernel in linear algebra ( null space )? Or do they happen to use this same ...
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1answer
100 views

Has anyone succeeded in finding a good Scala/Spark kernel for Jupyter?

The ones I've tried so far Almond: Works very well for just Scala, but you have to import dependencies, and it gets tedious after a while. And unfortunately can't run when using Spark with YARN ...
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24 views

Kernel approximation of a function known only point-wise?

Assume that I have a set of $N$ points $x_i, i=1,...,N,$ in some space $\mathbb{R}^D$, and corresponding point-wise (scalar) function evaluations $f(x_i)$. It is my goal to approximate the unknown ...
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27 views

KLMS in machine learning

As Least Mean Square is a very popular choice to be used in combination with neural networks topologies, what would be the most common machine learning algorithms (and easily) to combine with Kernel ...
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28 views

Bottleneck Distance

Is there a range of values for the bottleneck distance in persim package (python) to conclude that the two datasets are similar? Also, does it make sense to compute the bottleneck distance using $H_0$ ...
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1answer
106 views

Why do we use 2D kernel for RGB data?

I have recently started kearning CNN and I coukdnt understand that why are we using a 2D kernel like of shape (3x3) for a RGB data in place of a 3D kernel like of shape (3x3x3)? Are we sharing the ...
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2answers
51 views

PCA vs.KernelPCA: which one to use for high dimensional data?

I have a dataset which contains a lot of features (>>3). For computational reasons, I would like to apply a dimensionality reduction. At this point I could use different techniques: standard PCA ...
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91 views

Gaussian Process Classifier and specifying kernel

I am using scikitlearn's gaussian process classifier and either I don't think I understand how the kernel is used (more likely), or there is an error in the module (less likely). In short, the ...
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54 views

How to create anisotropic exponential and gaussian correlation function in Python for kernel? [duplicate]

I have a dataset of 1000 observed samples of 6 features that form the X and one target variable that forms the Y. I am using kriging or Gaussian Process Regressor to train my models. I would like to ...
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1answer
44 views

How to use a RBF kernel to create a “Kernel Space” using the similarity of each pair of point?

I am trying to use Semi-Unsupervised clustering using reinforcement learning following this paper. Assume I have n data-points each of which has d dimensions. I also have c pairwise constraints of ...
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39 views

How to implement SVM from scratch?

I am trying to build a SVM from scrath and I would like to maximize this Lagrarian expression: I know what variables means but I would like to know how this maximization is implemeted. Should I start ...
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68 views

Understanding SVM Kernels

Following Andrew Ng's machine learning course, he explains SVM kernels by manually selecting 3 landmarks and defining 3 gaussian function based on them. Then he says that we are actually defining 3 ...
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64 views

How to choose a kernel function and a feature mapping function?

Although, after extensive of reading, I know the concepts of support vector machines pretty well by now, I have trouble translating the concept of the kernel function $K$ and the feature mapping ...
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60 views

GP derivative in GpyTorch

I am working on a project using GP-regression models to model transition and measurements models in a Kalman Filter. This means I need to be able to sample from the derivative of the original GP model....
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19 views

What is the kernel matrix used for in the kernel trick?

I have $n$ linearly inseperable datapoints, $x_1 \dots , x_n$. I use the kernel trick to map and compute the dot product in higher dimensions (without actually mapping / transforming the data). ...
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70 views

Generalized quadratic loss learning

I'm studying a binary classification task with an objective function, derived from SVM, defined so: $\vec{\xi}' S \vec{\xi}$ with: $y_i (f(\vec{x}_i)) >= 1 - \xi_i, i=1..l$ and: $\xi_i >=0, i=1....
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1answer
72 views

Support Vector Machine (SVM) for classification problem based on Earth Mover's Distance (EMD)

I would like to run SVM for my classification problem using the Earth Mover's Distance (EMD) as a distance measurement. As I understood the documentation for Python scikit-learn (https://scikit-learn....
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2answers
75 views

Many separation line using RBF kernel in SVM

Below is my code, it take a range of a number, creates a new column label that contains either -1 or 1. In case the number is ...
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1answer
43 views

What is a good method for detecting local minims and maxims?

I'm using kernel density estimation in order to compute probability density function for item occurrence. Using this output, i want to find all the local minims and maxims. I'm interested in different ...
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38 views

Kernel engineering, valid kernels, multipliying by constant =0?

I am reading Bishop, Pattern Recognition and Machine Learning. In the chapter about kernels rules are given for constructing kernels from existing valid kernels. The first one being let k(x,y) be a ...
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173 views

What are practical differences between kernel k-means and spectral clustering?

I've been lately wondering about kernel k-means and spectral clustering algorithms and their differences. I know that spectral clustering is a more broad term and different settings can affect the ...
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209 views

Why spectral clustering results in disjointed cluster?

I'm working on a project where I have to dynamically cluster the position of objects with respect to one coordinate. So I'm essentially dealing with subsequent frames and each frame represents a one-...
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72 views

Implementing a Kernel Adaptive Filtering model explained in a paper

In this paper, Stock price prediction using kernel adaptive filtering within a stock market interdependence approach, the authors propose a method for predicting stock prices by combining the ...
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1answer
51 views

Kernel Trick and Inner Product Preservation

I understand that the point of using the kernel trick is to project the problem onto a higher dimensional space, where the problem is linearly separable. In this explanation, https://www.quora.com/...
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Designing Custom Kernel from my Mathematical model

I derived a mathematical model for a porous system and the final function looks like this , after going through the Mercers Theorem and its condition for a kernel I would love to write an SVM kernel ...
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1answer
999 views

Keras: Misunderstanding the Conv2D's param “filters”?

From https://keras.io/layers/convolutional/ (Conv2D): ...
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1answer
129 views

Does it matter whether we put regularization parameter ($C$) with error or weight term in Kernel ridge regression?

Kernel ridge regression associate a regularization parameter $C$ with weight term ($\beta$): $\text{Minimize}: {KRR}=C\frac{1}{2} \left \|\beta\right\|^{2} + \frac{1}{2}\sum_{i=1}^{\mathcal{N}}\left\|...
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2answers
262 views

Kernel PCA and K largest eigenvectors

How can one prove that the optimal kPCA solution $a^*=\{a_1...a_K\}$ are the $k$-largest Eigenvectors of the (centered) kernel matrix $K$? I referred to a lot of resources and couldn't find a proper ...
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47 views

Implementing SVM with Gaussian Kernel

This is referencing Prof. Andrew Ng's course on machine learning. In the part that details implementing an SVM with the Gaussian kernel, we are supposed to use all the training examples as our ...
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1answer
3k views

Does increasing kernel size in a CNN result in higher accuracy on the training set?

In a convolutional neural network, does increasing the size of kernel always result in better training set accuracy? For example, if I use 5x5 kernels in a CNN instead of 3x3 ones, will it always ...
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117 views

Is there any conceptual relationship between 'kernel' in SVM and 'kernel' in convolution neural net?

In SVM, we have kernel function that maps an input raw data space into a higher dimensional feature space In CNN, we also have a 'kernel' mask that travels the input raw data space (image as a matrix)...
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20 views

Finding the kernel in which the data will have the highest ratio of leading eigenvalue to trace

I have a method which works well with the data where a ratio of a leading eigenvalue or of first few leading eigenvalues to trace is high. Is it possible to find a kernel transformation which is ...
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1answer
2k views

Computation of kernel matrix using radial basis kernel in svm

I want to compute a kernel matrix using RBF on my own. The training data is multidimensional. My query is whether we will apply $$e^{-\gamma(x-y)^2}$$ for each dimension and then sum the values across ...
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1answer
1k views

Does Convolution kernel size affect number of channels?

I am going through Dilated Residual Network blog post. In this, Under 2.Multi-scale Context aggregation heading, author mentioned this. The last one is the 1×1 ...
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1answer
61 views

Positive semidefinite kernel matrix from Gower distance

I have a dataframe with continuous and categorical variables and I want to obtain a kernel matrix for classification. The kernel matrix must be symmetric and positive semidefinite, so that no ...
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1answer
49 views

Basis expansion for regression using neural network?

I am trying to approximate a nonlinear function using a neural network. There are 3-4 input units. The network is struggling a bit to generalize the function outside the vicinity of the training data ...