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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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Literature suggestions: Guarantees for GPs with subset of data

I am currently trying to solve the following problem: Given a fixed set of query points (or if possible even better: a region where I want to obtain accurate predictions), approximate the GP such that ...
L208's user avatar
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Remove feature from kernel matrix

I am pretty new to machine learning so please bear with me :) I am trying to do a binary classification task using an SVM with precomuted kernel (in python using sklearn). I created my train kernel ...
Georgia's user avatar
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What is normalized winning frequency in kernel self organizing map(SOM)?

In the k-means based kernel SOM, proposed by MacDonald and Fyfe (2000), the update of the mean is based on a soft learning algorithm ...
Anshuman Jayaprakash's user avatar
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Using Maximum Mean Discrepancy (MMD) to Compare Kernel Density Estimates (KDEs)

I'm interested in comparing two Kernel Density Estimates (KDEs) and I've come across the Maximum Mean Discrepancy (MMD) metric ...
Adham Enaya's user avatar
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2 answers
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Kernel Kmeans formula

I'm trying to implement the Kernel Kmeans algorithm but I struggle with the following formula : Let's say I have a case in one dimension with three points : 1, 5, 9. Let's say I want two clusters. ...
app_idea54's user avatar
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Is Maximum Mean Discrepancy (MMD) suitable for comparing distributions with different sample sizes?

I'm working on a project where I need to compare the similarity of two probability distributions using MMD. However, the two datasets have different sample sizes. I've read that MMD can be affected by ...
Adham Enaya's user avatar
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Kernel Kmeans implementation

I'm currently trying to implement the Kernel Kmeans from scratch. At the time I'm writing this post, my implementation is perfectly working on nested circles dataset or even on Iris dataset (see ...
app_idea54's user avatar
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Multiple kernel SVM is equal to one ANN - Is Kernel SVM better that one ANN?

I'm comparing multiple Kernel SVM with one neural network, e.g one ANN with one hidden layer. I have succesfully trained a neural network by using multiple Kernel ...
euraad's user avatar
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SVM kernel for detecting if a substring appears in some given string

I'm trying to do the exercise in 16.1 in the book Understanding Machine Learning, Ben-David, et al. formulated as follows: Consider the task of learning to find a sequence of characters ("...
Tran Khanh's user avatar
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107 views

Why linear kernel regression is equivalent to plain linear regression?

I am trying to understand either intuitively/geometricaly and/or mathematicaly why the followings are equivalent: Classic Ordinay Least Squares linear regression Linear-kernelized Ordinary Least ...
mocquin's user avatar
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kernel methods and parameter updates

Background information: (it might be helpful to read the first 5 pages of this:https://cs229.stanford.edu/summer2020/cs229-notes3.pdf before answering the question). I’m currently learning machine ...
the_blue_pizza's user avatar
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Why don't we increase the parameter from 64 to 128 in this CNN model?

I'm looking at an example lab from a coursera course titled Intro to Tensorflow. In this CNN model, they're gradually increasing the no. of filters from 16 to 32 and then 64. Why don't we increase it ...
karak87rt0's user avatar
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Epanechnikov kernel smoothing and Priestley-Chao (PC) kernel estimate

I wrote the Python code below to try to automate the application of kernel smoothing using the Epanechnikov kernel with a bandwidth of h = 0.4 calculating the Priestley-Chao kernel estimate of the ...
A BCDEFG's user avatar
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A mathematician from the outside looking in

I am wondering if anybody could give a survey of applications of approximation theory to data science. One application I am familiar with are, for example, wavelet neural networks. Does anybody know ...
Joe Shmo's user avatar
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Kernel ridge regression (KRR), accuracy scale?

What does a good range for the accuracy score look like for the KRR model? For example, RMSE produces a value between 0 and 1, where values closer to 0 represent better fitting models. What's the ...
noor h's user avatar
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memory bound for kernel tricks in machine learning

Based on Andrew Ng's lecture on Kernel, you use training samples (referred as landmarks l) and use them during prediction to construct the higher dimensional representation of the given sample. This ...
Brandon Lee's user avatar
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why layer of dimension 1 is outputting image of size n

I am studying a model where landmarks from an image are calculated. The work comes from Convolutional Experts Constrained Local Model for 3D Facial Landmark Detection. I need to confirm why the ...
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What is custom SVM kernel?

What is custom kernel in the Support Vector Machine. How is it different from Polynomial kernel. How to implement a custom kernel. Can you provide a code to implement a custom kernel.
Sahil Bhatti's user avatar
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1 answer
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What are the benefits of using spectral k-means over simple k-means?

I have understood why k-means can get stuck in local minima. Now, I am curious to know how the spectral k-means helps to avoid this local minima problem. According to this paper A tutorial on ...
Amartya's user avatar
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Bayesian Linear Regression using the Kernel Trick vs Constructing features using Kernels as Prototypes

How different is it to do Bayesian linear regression using the GP approach (kernel trick) versus constructing features using kernels to prototypes? As far as I know, this very basic question is ...
Robert's user avatar
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2 votes
2 answers
184 views

Kernel trick derivation: why this simplification is incorrect?

I am trying to derive kernel trick from linear regression, and I have a mistake in the very end, which leads to an expression too simple. Basic linear regression For a basic linear regression (with no ...
Boris Burkov's user avatar
1 vote
1 answer
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which type of machine learning algorithms perform better at extrapolation (in general)

Assuming that: the problem lies in the field of natural science, i.e. relationships between variables are physics-based and does not change depending on context its a regression based model Would it ...
tabumis's user avatar
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Can a CNN have a different number of convolutional layers and kernel and what does it mean?

So if I have $3$ RGB channels, $6$ convolutional layers and $4$ kernels, does this mean that each kernel does a convolution on each channel and so the input for the next convolution will be $3 \times ...
plastico's user avatar
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1 answer
602 views

When should I use 'rbf' and 'polynomial' kernel trick in machine learning algo?

I have a problem about hate-speech classification using support-vector machine algorithm. The task is to identify the sentence that contains 'positive' or 'negative' sentiment. Which is the best ...
devins10's user avatar
5 votes
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Theoretical differences between KPCA and t-SNE?

I (think I) understand the underlying principles of most dimensionality reduction methods (MDS, IsoMap, t-SNE, Spectral Embedding, Diffusion maps, etc...). Some of the algorithms I use the most are ...
Rayamon's user avatar
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Radial Basis Function (Gaussian) kernel question

I have followed the mathematics of the RBF kernel and understand how to show that the input space is mapped into an infinite-dimensional feature space. However, I'm struggling to make sense of the ...
Nitram's user avatar
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478 views

Does linear kernel make SVM a linear model?

I have deleloped several SVR models for my case study using the linear kernel, and those models were optimized using the RMSE as criterion. Now Im searching for additional evaluation metrics and it ...
tabumis's user avatar
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1 answer
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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 ...
Jiaming He's user avatar
3 votes
1 answer
537 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 ...
robbmorganf's user avatar
1 vote
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95 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 ...
Adelson Araújo's user avatar
2 votes
0 answers
201 views

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

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 ...
J. Dionisio's user avatar
1 vote
1 answer
507 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 ...
physics_2015's user avatar
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103 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 ...
Kermit's user avatar
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2 votes
1 answer
120 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 ...
JackEarl's user avatar
1 vote
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16 views

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?
theskylordcrook's user avatar
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148 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 ...
user3812405's user avatar
4 votes
1 answer
1k 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 ...
Varun Gawande's user avatar
2 votes
1 answer
136 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 ...
Brezeanu Bianca's user avatar
2 votes
1 answer
1k 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 ...
Shrijit Basak's user avatar
1 vote
2 answers
156 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 ...
Federico Gentile's user avatar
1 vote
1 answer
105 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 ...
raff7's user avatar
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2 votes
1 answer
156 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 ...
Javier Jiménez de la Jara's user avatar
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1 answer
230 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 ...
Mehran Torki's user avatar
1 vote
1 answer
274 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 ...
Tekef's user avatar
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1 vote
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209 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....
Michael's user avatar
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1 vote
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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). ...
user13341805's user avatar
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1 answer
284 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....
Egor Levchenko's user avatar
2 votes
2 answers
145 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 ...
E199504's user avatar
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3 votes
1 answer
161 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 ...
cristian hantig's user avatar
2 votes
0 answers
59 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 ...
mlnoob's user avatar
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