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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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 ...
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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 ...
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Creating a prediction matrix for kernel regression in numpy

I need to create a rectangular matrix from timeseries data which is T time bins by L, the sum of the length of the set of events of interest occurring in the timeseries within certain times referred ...
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1 answer
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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 ...
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SVM's support vectors decision function representataion

I am currently using SVM for my project with 'rbf' kernel. What i understand from the theory is that the decision function value ...
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Dual function for kernel learning

I am asked to derive the dual loss function for the kernel logisitic regression because i should learn how to apply the kernel trick/representer theorem. Now the loss function is given by $L(\theta) = ...
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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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2 votes
1 answer
153 views

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.
1 vote
1 answer
108 views

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 ...
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reducing number of kernels in CNN by using mapping just some of the input channels to each output channel?

so, I am currently learning about CNNs. And I am using pytorch to implement small models. What I don't understand, yet, is, why typically a new channel is formed by the sum of the kernel outputs of ...
1 vote
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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 ...
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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 ...
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 ...
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1 vote
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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 ...
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1 answer
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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 ...
3 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 ...
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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 ...
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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 ...
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1 vote
1 answer
565 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 ...
3 votes
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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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47 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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116 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 ...
1 vote
1 answer
243 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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1 answer
55 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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2 votes
1 answer
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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 ...
1 vote
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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?
2 votes
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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 ...
4 votes
1 answer
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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 ...
2 votes
1 answer
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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 ...
1 vote
1 answer
653 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 ...
1 vote
2 answers
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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 ...
1 vote
1 answer
78 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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2 votes
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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 ...
0 votes
1 answer
159 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 ...
1 vote
1 answer
173 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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1 vote
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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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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). ...
1 vote
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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....
0 votes
1 answer
177 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....
2 votes
2 answers
126 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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3 votes
1 answer
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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 ...
2 votes
0 answers
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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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12 votes
1 answer
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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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6 votes
3 answers
386 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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0 answers
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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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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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4 votes
1 answer
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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 ...
2 votes
1 answer
1k views

Keras: Misunderstanding the Conv2D's param "filters"?

From https://keras.io/layers/convolutional/ (Conv2D): ...
3 votes
1 answer
174 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\|...
2 votes
2 answers
374 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 ...