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.org/stable/modules/svm.html#svm-kernels) it is possible to use custom kernel functions: import numpy as np from sklearn import svm def my_kernel(X, Y): return np.dot(X, Y.T) clf = svm.SVC(kernel=my_kernel) Also there is a package with EMD implemented (https://pypi.org/project/pyemd/). I tried to run it similar as in example using my own data (below). I have distributions …

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.

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 higher than 14000 , we label it with -1 (outlier) In case the number is lower than 14000 , we label it with 1 (normal) ## Here I just import all the libraries and import the column with my dataset ## Yes, I am trying to find anomalies using only the data from …

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 Spectral, The spectral algorithm goes in the following way Project data into $R^n$ matrix Define an Affinity matrix A , using a Gaussian Kernel K or an Adjacency matrix Construct the Graph Laplacian from A (i.e. decide on a normalization) Solve the Eigenvalue problem Select …

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 set. I asked someone and he suggested that basis expansion might help. Can someone please provide a reference for the same, I am not able to find any. Also, he suggested "basis expansion using kernel method".

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 all input channels. The number of parameters in a conv(m,n,kernel) operation is: m x n x size(kernel) i.e. for conv(3,5,kernel(2,4)) we would have 3 * 5 * (2 * 4) = 120 parameters, correct? In general, for every one of the n output …

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 be right to assume that kernelized approaches (e.g. SVM) would perform better for unseen combinations of predictor variables, when compared to neural networks etc? As I understood, many ML models generally fail to provide accurate prediction when the new inputs are out of distributions they were initially trained on. …

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 Least Mean Square?

I have read about SVM and although I did not understand the math behind it completly, I know that it produces decision plane with maximum margin between examples of different classes and role of support vectors in the process. I also know that SVM is a kind of dual learing algorithm(algorithms that operate only using the dot product between examples). It uses kernel functions to calculate dot product(measure of similarity) between training examples. What I want to understand in simple …

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 Kernel Trick? ('rbf' or 'polynomial')

Guassian kernel is so important in SVM as we know. The parameter gamma is designed for this kind of kernel. My question is what makes Guassian kernel so unique? What advantage does it have over other kernels?

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 function $\phi$ to a simple example such as the following. My example data $x \in \mathbb{R}^2$: $(1,0), (4,0)$ are from one class, $(2,0), (3,0)$ are from another. So here are my two questions: Would $\phi((x_1,x_2))=(x_1,x_2,(x_1-2.5)^2)$ be a wise choice for the mapping function $\phi:\mathbb{R}^2 \to \mathbb{R}^3$ ? If …

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 predictions of Kernel Adaptive Filter (KAF) models trained on different stocks in different international stock markets. In their results, they compare this model against individual KAF models trained and inferred on individual stocks. The refer to these individual models as 'KAF-based methods' and refer to their model as 'Proposal'. I am quite …

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 unanswered. GPs have the disadvantage that they are expensive: they grow with the number of samples. I tried doing some research on this topic, but haven't found any relevant paper discussing this! Any paper which discusses this or at least gives some information on the cons of this …

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 regularisation for simplicity), let ${\bf x_i}$ be row-vectors of data of length $p$ (for instance, each coordinate $x_{i,j}$ might be the value of expression of gene $j$ in patient $i$). Let the corresponding data matrix $X = \begin{pmatrix} {\bf x_1} \\ {\bf x_2} \\ …

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 $3 \times 4=12$ channels? Or those outputs are just stacked on each other (summed) and the input to the next neural network is still 3 channels? Edit: I am pretty sure that the input for the next convolution would still be $3$, but why is …

So I recently started learning about CNNs, and one question struck out to menthe filters used in the second layer are a combination of the filters used in the first layer, right? Lets say I make use of 4 filters in my first layer, and my second layer, I decide to combine any two, to give one filter, does this mean that during training, all I need to learn are the low level features, and it'll be propagated to the …

when studying kernel methods a few years ago I got a bit confused with the concepts of feature space, hypothesis space and reproducing kernel Hilbert space. Recently, I thought a little about questions that I asked myself back then (with newly acquired math background) and noticed that some things are still unclear to me. I appreciate help and pointers to good - mathematical - literature. Let's consider the following learning problem: We are given a training sample $((x_1, y_1), \dots, …

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 instead of Local. Spylon-kernel: Kernels connects, but gets stuck in the initializing stage. Apache Toree: I would've loved this so much only if it worked. Lots of language support, magics, incubated by apache. However, this kernel doesn't connect. Get's stuck on the "Kernel Connecting" stage. …

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 Kernel PCA (with a gaussian kernel) and t-SNE. My question is, do you know some theoretical resons on when to use t-SNE or kernel PCA? Do you know which are their relative strenghts/weaknesses? Is there some known cases where one is better from the other? Do their results have different characteristics …