Have you ever wondered how ๐ฆ๐๐ฝ๐ฝ๐ผ๐ฟ๐ ๐ฉ๐ฒ๐ฐ๐๐ผ๐ฟ ๐ ๐ฎ๐ฐ๐ต๐ถ๐ป๐ฒ๐ (SVM) can handle non-linear data?
The "๐๐ฒ๐ฟ๐ป๐ฒ๐น ๐ง๐ฟ๐ถ๐ฐ๐ธ" is a fascinating mathematical technique that allows efficient calculations and delivers powerful results!
Let's learn more about it ๐งต ๐
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In SVM, the kernel trick is a clever way to perform complex calculations in a higher-dimensional feature space without explicitly transforming the original data into that space.
It's like finding a hidden pathway to handle non-linear relationships between data points.
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Let's imagine we have a dataset with 2 classes of points that aren't linearly separable in a 2D space.
The kernel trick enables us to find a decision boundary, or hyperplane, that effectively separates these classes.
But without having to transform the data explicitly! ๐คฏ
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Instead of undergoing costly or even impossible transformations, the kernel trick allows us to calculate the inner product between pairs of data points in the higher-dimensional space without actually carrying out the transformation.
How? With a kernel function ๐
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The kernel function computes the similarity or distance between two points in the original feature space.
By using different kernel functions โ like linear, polynomial, or radial basis function (RBF) kernels โ SVM captures complex relationships between data points.
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โถ๏ธ With the kernel trick, SVM operates efficiently in these high-dimensional spaces, making it a powerful tool for solving both linear and non-linear classification problems.
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