# support vector machines

Published articles for support vector machines.

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## Formulating the Support Vector Machine Optimization Problem

DevFeed: [Formulating the Support Vector Machine Optimization Problem](<https://devfeed.tech/articles/formulating-the-support-vector-machine-optimization-problem-40411.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2017/06/05/formulating-the-support-vector-machine-optimization-problem/>)

Published: 2017-06-05T08:00:46Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Optimization](<https://devfeed.tech/topics/optimization.md>), [math](<https://devfeed.tech/topics/math.md>), [Machine Learning & Artificial Intelligence](<https://devfeed.tech/topics/machine-learning-artificial-intelligence.md>), [data](<https://devfeed.tech/topics/data.md>)

Tags: [blog-post](<https://devfeed.tech/tags/blog-post.md>), [data-visualization](<https://devfeed.tech/tags/data-visualization.md>), [inner-product](<https://devfeed.tech/tags/inner-product.md>), [javascript](<https://devfeed.tech/tags/javascript.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [support-vector-machines](<https://devfeed.tech/tags/support-vector-machines.md>)

### AI overview

A tutorial formulates the support vector machine optimization problem using separating hyperplanes, labeled training data, vector-and-scalar bias terms, and the goal of choosing a separator that generalizes well.

### Source excerpt

The hypothesis and the setup This blog post has an interactive demo (mostly used toward the end of the post). The source for this demo is available in a Github repository. Last time we saw how the inner product of two vectors gives rise to a decision rule: if $ w$ is the normal to a line (or hyperplane) $ L$, the sign of the inner product $ \langle x, w \rangle$ tells you whether $ x$ is on the same side of $ L$ as $ w$.

## The Inner Product as a Decision Rule

DevFeed: [The Inner Product as a Decision Rule](<https://devfeed.tech/articles/the-inner-product-as-a-decision-rule-40410.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2017/05/22/the-inner-product-as-a-decision-rule/>)

Published: 2017-05-22T08:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [math](<https://devfeed.tech/topics/math.md>), [Code](<https://devfeed.tech/topics/code.md>)

Tags: [arithmetic](<https://devfeed.tech/tags/arithmetic.md>), [inner-product](<https://devfeed.tech/tags/inner-product.md>), [javascript](<https://devfeed.tech/tags/javascript.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [programming](<https://devfeed.tech/tags/programming.md>), [projection](<https://devfeed.tech/tags/projection.md>), [support-vector-machines](<https://devfeed.tech/tags/support-vector-machines.md>), [vectors](<https://devfeed.tech/tags/vectors.md>)

### AI overview

This article explains how the standard inner product, or dot product, acts as a geometric decision rule. It shows how the sign of the product determines which side of a line through the origin a vector lies on, while zero indicates that the vector lies on the line. The explanation connects this behavior to vector projection.

### Source excerpt

The standard inner product of two vectors has some nice geometric properties. Given two vectors $ x, y \in \mathbb{R}^n$, where by $ x_i$ I mean the $ i$-th coordinate of $ x$, the standard inner product (which I will interchangeably call the dot product) is defined by the formula $$\displaystyle \langle x, y \rangle = x_1 y_1 + \dots + x_n y_n$$ This formula, simple as it is, produces a lot of interesting geometry.

## Machine Learning -- Introduction

DevFeed: [Machine Learning -- Introduction](<https://devfeed.tech/articles/machine-learning-introduction-40283.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/08/04/machine-learning-introduction/>)

Published: 2012-08-04T19:59:42Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Machine Learning & Artificial Intelligence](<https://devfeed.tech/topics/machine-learning-artificial-intelligence.md>), [Algorithms](<https://devfeed.tech/topics/algorithms.md>), [data](<https://devfeed.tech/topics/data.md>), [Optimization](<https://devfeed.tech/topics/optimization.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [data](<https://devfeed.tech/tags/data.md>), [decision-trees](<https://devfeed.tech/tags/decision-trees.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [neural-networks](<https://devfeed.tech/tags/neural-networks.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [support-vector-machines](<https://devfeed.tech/tags/support-vector-machines.md>)

### AI overview

This introduction presents machine learning as a broad toolbox that draws on optimization, statistical inference, linear algebra, graph theory, functional analysis, and topology. It outlines a recurring process of developing algorithms or mathematical models, testing them on datasets, and refining them with domain knowledge, while emphasizing mathematical foundations, implementation efficiency, and the structure of natural data.

### Source excerpt

A Series on Machine Learning These days an absolutely staggering amount of research and development work goes into the very coarsely defined field of "machine learning." Part of the reason why it's so coarsely defined is because it borrows techniques from so many different fields. Many problems in machine learning can be phrased in different but equivalent ways. While they are often purely optimization problems, such techniques can be expressed in terms of statistical inference, have biological interpretations, or have a distinctly geometric and topological flavor.