# Tagged Questions

1answer
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### Where can I use kernels other than Gaussian (like Cauchy, laplacian) in kernel methods in machine learning? Or maybe in kernel density estimation?

In few papers I read that - kernel used doesn't really matter for kernel density estimation but bandwidth of the kernel is the most important factor. But I did not see any mathematical explanation to ...
0answers
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### How accurate sum of kernel function needs to be, so that we can use it in Mean shift algorithm (may be for image segmentation)?

Mean shift is a procedure for locating the maxima of a density function given discrete data sampled from that function. It is useful for detecting the modes of this density. This is an iterative ...
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### In RVM, is the kernel allowed to depend on the full dataset?

I want to use Relevance Vector Machines and need to define my custom made kernel. I was wondering if it is allowed for the kernel to depend on the full dataset. For exampe, I can calculate a certain ...
1answer
70 views

### Understand the reasons of using Kernel method in SVM

I understand that one can use kernel functions (i.e. radial kernel) to create non-linear decision boundary. However, there is something with my logic and I am sure there is something that I clearly ...
1answer
54 views

### Clustering structured data: Assessing the similarity of documents that appear in tree structure

Usually when performing text document clustering, similarities across documents are assessed based on the lexical content of documents. But, in my problem, I wish to consider both the lexical content ...
1answer
55 views

### Cascade Combination of Kernel Functions

I have a question regarding machine learning and specifically kernel functions. Suppose we have a Kernel function, say $K(x)$, and also another distinct one, say $K'(x)$. I want to know is $K(K'(x))$ ...
1answer
91 views

### SVM basic theory?

I have some questions about SVM: In SVM there is a nonlinear and linear SVM. What is the difference between them? To do classification in SVM, we will find the linearly separable boundary ...
0answers
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### What is the difference between the metric window width and Nearest-neighbor's window in Kernel Smoothing methods?

I'm learning Kernel smoothing methods. I didn't really get the difference between the metric window width and Nearest-neighbor's window. For me both seem the same. Can anybody explain it to me? for ...
1answer
72 views

### Binary classification using radial basis kernel SVM with a single feature

Is there any interpretation (graphical or otherwise) of a radial basis kernel SVM being trained with a single feature? I can visualize the effect in 2 dimensions (the result being a separation ...
0answers
27 views

### kernel for a (semi-) metric space

Let's say I have a metric space $(\mathcal{X}, d)$. Is there any kernel function that I can use with SVM? If we change the RBF kernel a little bit, we have $k(x,y) = e^{-d(x,y)^2}$. Is this a valid ...
1answer
124 views

### Poorness of Kernel methods on visual pattern recegnition?

I am currently reading the recent papers mainly written by Y. Bengio [1],[2],[3]. There are very strong claims about poorness of Kernel methods on recognizing handwritings in many general cases but ...
1answer
119 views

### Applying kernel function to input data before giving it to algorithm

I have gene expression data, I do dimensionality reduction and clustering with self organizing maps, but self organizing maps do not perform well with my data. I want to map my data to feature space ...
1answer
251 views

### What are the limitations of Kernel methods and when to use kernel methods?

Kernel methods are very effective in many supervised classification tasks. So what are the limitations of kernel methods and when to use kernel methods? Especially in the large scale data era, what ...
2answers
715 views

### Linear kernel and non-linear kernel for support vector machine?

When using support vector machine, are there any guidelines on choosing linear kernel vs. nonlinear kernel, like RBF? I once heard that non-linear kernel tends not to perform well once the number of ...
1answer
128 views

### Relationship between the kernel and the value of C in SVM's

How exactly does the value of C relate across different kernels that we can use for SVM's? As in, how does it vary when changing the polynomial degree of a kernel or while using a Gaussian kernel?
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136 views

### I am still confused with Gaussian kernel in SVM

From the slides http://www.csie.ntu.edu.tw/~cjlin/talks/kuleuven_svm.pdf, $$\min \frac{1}{2}w^Tw$$ subject to $$y_i(w^T\phi(x_i)+b)\ge 1,i=1,\cdots,n$$ I think most people are very familiar with ...
2answers
412 views

### The Gaussian kernel

In SVM, the Gaussian kernel is defined as: $$K(x,y)=\exp\left({-\frac{\|x-y\|_2^2}{2\sigma^2}}\right)=\phi(x)^T\phi(y)$$ where $x, y\in \mathbb{R^n}$. I do not know the explicit equation of $\phi$. I ...
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### Support vector machine for text classification

I am currently having a data set, class 1 with about 8000 short text files and class 2 with about 3000 short text files. I applied LibSVM and tried a couple of parameter combinations in the ...
0answers
275 views

### Regarding kernel-based naive Bayesian classifier

Are there any good references for kernel-based Naive Bayesian classifier?
2answers
2k views

### How to select best parameter for polynomial kernel?

I am using LibSVM library for classification. For my problem I am using polynomial kernel and I need to select best parameters (d = degree of polynomial kernel, and ...
4answers
285 views

### Kernel Selection

I am not an expert in SVM and kernel, so please excuse me if I ask stupid question. Actually, first I want to know how to analyze a dataset to discover its pattern. And second, how can I select ...
0answers
404 views

### SVM using RBF and nearest neighbor classification method

SVM using RBF kernel is claimed to be similar (equivalent) to the K nearest neighbor classification method. I am not very clear about the analysis process of building this kind of relationship. Thanks ...
2answers
1k views

### Kernel logistic regression

I heard Kernel Logistic Regression is a classical combination of kernel methods and Logistic regression, but I cannot find any major reference (book, or paper) on this topic. Can you give me any ...
2answers
374 views

### Polynomial kernel function

Consider SMV with the polynomial kernel $k(x_1,x_2)=(\langle x_1, x_2\rangle + 1)^d,$ where $d > 1.$ Is it true that if the dataset is separated with a hyperplane then the SVM (with the kernel $k$) ...
0answers
255 views

### Behavior of a sum of kernel functions

Suppose we have 2 kernel functions $K_1(x,y)$ and $K_2(x,y)$. We know, that the dataset ($(x_1,y_1),\ldots,(x_l,y_l),$ $y_i \in \{-1,1\}$ ) is separated with the first one (that is, there are $w,$ ...
1answer
342 views

### How to run K-means clustering on data points of varying dimensionality?

I'm trying to aggregate $T$ local image descriptors (i.e. histograms) into a vector, namely, the Fisher Vector as described in this paper by H. Jégou et al., Aggregating local image descriptors into ...
3answers
133 views