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Linear SVM vs Nonlinear SVM high dimensional data

stackoverflow.com › questions › 44606126 › linear-svm-vs-nonlinear-svm-high-dimensional-data

I think you question is about 'why linear SVM could classfy my hight Dimensions data well even the data should be non-linear'
some data set look like non-linear in low dimension just like you example image on right, but it is literally hard to say the data set is definitely non-linear in high dimension because a nD non-linear may be linear in (n+1)D space.So i dont know why you are 90% sure your data set is non-linear even it is a high Dimension one.
At the end, I think it is normal that you have a good test result in test samples, because it indicates that your data set just is linear or near linear in high Dimension or it wont work so well.Maybe cross-validation could help you comfirm that your approach is suitable or not.

Answer from FesianXu on Stack Overflow

Stanford NLP Group

nlp.stanford.edu › IR-book › html › htmledition › nonlinear-svms-1.html

Nonlinear SVMs

SVMs, and also a number of other linear classifiers, provide an easy and efficient way of doing this mapping to a higher dimensional space, which is referred to as ``the kernel trick ''. It's not really a trick: it just exploits the math that we have seen. The SVM linear classifier relies on a dot product between data point vectors.

GeeksforGeeks

geeksforgeeks.org › machine learning › ml-non-linear-svm

Non-Linear SVM - ML - GeeksforGeeks

November 13, 2025 - However, the standard (linear) ... or a hyperplane (in higher dimensions). Non-linear SVM extends SVM to handle complex, non-linearly separable data using kernels....

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Solved Support Vector Machine | Non-Linear SVM Example by Mahesh ...

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Linear SVM vs Non-Linear SVM algorithm SVM Classifier Support Vector ...

May 13, 2024

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Non-linear Support Vector Machines Explained

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SVM 4 - non-linear support vector machines

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Non Linear Support Vector Machines (Non Linear SVM)

scaler.com › home › topics › machine-learning › non-linear svm

Non-Linear SVM - Scaler Topics

May 4, 2023 - We use the linear SVM classifier to classify such data. Non-linear SVM: When the data is not linearly separable, we use the non-linear SVM classifier to separate the data points.

Stack Overflow

stackoverflow.com › questions › 44606126 › linear-svm-vs-nonlinear-svm-high-dimensional-data

Linear SVM vs Nonlinear SVM high dimensional data - Stack Overflow

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I think you question is about 'why linear SVM could classfy my hight Dimensions data well even the data should be non-linear'
some data set look like non-linear in low dimension just like you example image on right, but it is literally hard to say the data set is definitely non-linear in high dimension because a nD non-linear may be linear in (n+1)D space.So i dont know why you are 90% sure your data set is non-linear even it is a high Dimension one.
At the end, I think it is normal that you have a good test result in test samples, because it indicates that your data set just is linear or near linear in high Dimension or it wont work so well.Maybe cross-validation could help you comfirm that your approach is suitable or not.

Linear SVM vs Nonlinear SVM high dimensional data

stackoverflow.com › questions › 44606126 › linear-svm-vs-nonlinear-svm-high-dimensional-data

I think you question is about 'why linear SVM could classfy my hight Dimensions data well even the data should be non-linear'
some data set look like non-linear in low dimension just like you example image on right, but it is literally hard to say the data set is definitely non-linear in high dimension because a nD non-linear may be linear in (n+1)D space.So i dont know why you are 90% sure your data set is non-linear even it is a high Dimension one.
At the end, I think it is normal that you have a good test result in test samples, because it indicates that your data set just is linear or near linear in high Dimension or it wont work so well.Maybe cross-validation could help you comfirm that your approach is suitable or not.

Answer from FesianXu on Stack Overflow

ScienceDirect

sciencedirect.com › topics › engineering › nonlinear-support-vector-machine

Nonlinear Support Vector Machine - an overview | ScienceDirect Topics

Linear SVM: It is used when the data follows the linear separation behavior and can be classified into two classes. Nonlinear SVM: It is used when the data is non-linearly separated and hence not able to classify using a straight line.

Wikipedia

en.wikipedia.org › wiki › Support_vector_machine

Support vector machine - Wikipedia

2 days ago - In addition to performing linear classification, SVMs can efficiently perform non-linear classification using the kernel trick, representing the data only through a set of pairwise similarity comparisons between the original data points using ...

Motivation Applications History Linear SVM Nonlinear kernels Computing the SVM classifier Empirical risk minimization Properties Extensions Implementation Further reading

AITUDE

aitude.com › svm-difference-between-linear-and-non-linear-models

SVM: Difference Between Linear And Non-Linear Models - AITUDE

February 3, 2020 - When we can easily separate data with hyperplane by drawing a straight line is Linear SVM. When we cannot separate data with a straight line we use Non – Linear SVM. In this, we have Kernel functions.

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GeeksforGeeks

geeksforgeeks.org › ml-non-linear-svm

Non-Linear SVM – ML | GeeksforGeeks

May 19, 2025 - However, the standard (linear) ... or a hyperplane (in higher dimensions). Non-Linear SVM extends SVM to handle complex, non-linearly separable data using kernels....

Medium

medium.com › @misbah.anwar › support-vector-machines-svm-linear-and-non-linear-svms-4715398ab66c

Support Vector Machines (SVM) -Linear and Non-Linear SVMs | by misbahanwar | Medium

December 9, 2023 - Linear SVM: This type of SVM is used when input data is linearly separable, i.e, if a dataset can be classified into two classes by using a single straight line. Non-linear SVM: This type of SVM is used when input data is not linearly separable, ...

TutorialsPoint

tutorialspoint.com › non-linear-svm-in-machine-learning

Non-Linear SVM in Machine Learning

August 27, 2023 - From the above diagram we can see that in non linear SVM the hyperplane separating the two classes in non linear in nature.In the diagram above the two classes Class A and Class B are separated by anon linear or curved margin or hyperplane that tends to maximize the margin between the two classes.

scikit-learn

scikit-learn.org › 0.23 › auto_examples › svm › plot_svm_nonlinear.html

Non-linear SVM — scikit-learn 0.23.2 documentation

Perform binary classification using non-linear SVC with RBF kernel. The target to predict is a XOR of the inputs. The color map illustrates the decision function learned by the SVC. print(__doc__) import numpy as np import matplotlib.pyplot as plt from sklearn import svm xx, yy = np.meshgrid(np.linspace(-3, 3, 500), np.linspace(-3, 3, 500)) np.random.seed(0) X = np.random.randn(300, 2) Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0) # fit the model clf = svm.NuSVC(gamma='auto') clf.fit(X, Y) # plot the decision function for each datapoint on the grid Z = clf.decision_function(np.c_[xx.ravel(), yy

University of Washington

courses.washington.edu › ling572 › winter2017 › teaching_slides › class16_svm_p2.pdf pdf

Support vector machine (II): non-linear SVM LING 572 Fei Xia 1

Non-linear SVM · Decoding · Linear SVM: (without mapping) Non-linear SVM: w could be infinite dimensional · 14 · Kernel vs. features · 15 · A tree kernel · Common kernel functions · • Linear : • Polynominal: • Radial basis function (RBF): • Sigmoid: 17 ·

GeeksforGeeks

geeksforgeeks.org › machine learning › linear-vs-non-linear-classification-analyzing-differences-using-the-kernel-trick

Linear vs. Non-linear Classification: Analyzing Differences Using the Kernel Trick - GeeksforGeeks

July 23, 2025 - Linear SVMs are computationally efficient and work well with high-dimensional data, such as text classification tasks. Non-linear SVMs: Non-linear SVMs are employed when the data is not linearly separable.

Stack Exchange

stats.stackexchange.com › questions › 447386 › does-there-a-non-linear-svm-exist

Does there a non-linear SVM exist? - Cross Validated

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Wikipedia explains nonlinear SVM classification with

The original maximum-margin hyperplane algorithm proposed by Vapnik in 1963 constructed a linear classifier. However, in 1992, Bernhard E. Boser, Isabelle M. Guyon and Vladimir N. Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick (originally proposed by Aizerman et al.) to maximum-margin hyperplanes.

The resulting algorithm is formally similar, except that every dot product is replaced by a nonlinear kernel function. This allows the algorithm to fit the maximum-margin hyperplane in a transformed feature space.

The transformation may be nonlinear and the transformed space high-dimensional; although the classifier is a hyperplane in the transformed feature space, it may be nonlinear in the original input space.

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By "linear SVM" people mean SVM with linear kernel, while every other kernel is non-linear, so SVM using it is sometimes called "non-linear" as well.

NC State ISE

ise.ncsu.edu › wp-content › uploads › sites › 9 › 2022 › 08 › NonlinearOptimizationAndSuppor.pdf pdf

Nonlinear optimization and support vector machines

the unconstrained optimization problem is nonconvex and suitable safeguards (for instance, early stopping) must be adopted in order to avoid converging too quickly towards undesired · minima (in terms of generalization capabilities), the requirements of a training algorithm are · not well-deﬁned from an optimization point of view. The SVM training problem can be equivalently formulated as a (linearly constrained)

scikit-learn

scikit-learn.org › 1.4 › auto_examples › svm › plot_svm_nonlinear.html

Non-linear SVM — scikit-learn 1.4.2 documentation

Perform binary classification using non-linear SVC with RBF kernel. The target to predict is a XOR of the inputs. The color map illustrates the decision function learned by the SVC. import matplotlib.pyplot as plt import numpy as np from sklearn import svm xx, yy = np.meshgrid(np.linspace(-3, 3, 500), np.linspace(-3, 3, 500)) np.random.seed(0) X = np.random.randn(300, 2) Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0) # fit the model clf = svm.NuSVC(gamma="auto") clf.fit(X, Y) # plot the decision function for each datapoint on the grid Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]) Z =

ScienceDirect

sciencedirect.com › science › article › pii › S1877050923017623

Support Vector Machine Method for Predicting Non-Linear Data - ScienceDirect

November 25, 2023 - The aim of this research is to evaluate the performance of a classification model on nonlinear data. The study utilizes accuracy, precision, sensitivity, and specificity metrics based on data from e-commerce X sellers. The classification model is developed using the Support Vector Machine (SVM) approach, employing different kernel functions such as linear, polynomial, and Radial Basis Function (RBF).

scikit-learn

scikit-learn.org › stable › auto_examples › svm › plot_svm_nonlinear.html

Plot classification boundaries with different SVM Kernels

scikit-learn: machine learning in Python

freeCodeCamp

freecodecamp.org › news › svm-kernels-how-to-tackle-nonlinear-data-in-machine-learning

SVM Kernels Explained: How to Tackle Nonlinear Data in Machine Learning

January 7, 2025 - A kernel method is a technique used in SVM to transform non-linear data into higher dimensions. For example, if the data has a complex decision boundary in a 2-Dimensional space (as I’ll explain further in the later part of this article), it can be transformed into a 3-Dimensional space.

AIP Publishing

pubs.aip.org › aip › acp › article › 3036 › 1 › 040017 › 3275622 › Non-linear-support-vector-machine-classification

Non-linear support vector machine classification models using kernel tricks with applications | AIP Conference Proceedings | AIP Publishing

March 15, 2024 - Working with enormous datasets, ... by applying some non-linear kernel transformations, which are: linear, polynomial, radial basis, and multi-layer kernels....