Time Complexity Analysis of Support Vector Machines (SVM) in LibSVM

Abstract

Support Vector Machines (SVM) is one of machine learning methods that can be used to perform classification task. Many researchers using SVM library to accelerate their research development. Using such a library will save their time and avoid to write codes from scratch. LibSVM is one of SVM library that has been widely used by researchers to solve their problems. The library also integrated to WEKA, one of popular Data Mining tools. This article contain results of our work related to complexity analysis of Support Vector Machines. Our work has focus on SVM algorithm and its implementation in LibSVM. We also using two popular programming languages i.e C++ and Java with three different dataset to test our analysis and experiment. The results of our research has proved that the complexity of SVM (LibSVM) is O(n3) and the time complexity shown that C++ faster than Java, both in training and testing, beside that the data growth will be affect and increase the time of computation.

Determining the most representative image on a Web page

“…We focus on practical estimates of runtime against dataset size. For a theoretical overview of the time complexity of SVM in the LibSVM library [3] , we refer to [1] . In order to assess the runtime for smaller datasets, we use stratified sampling, grouped based on images being representative or not as based on our ground truth dataset [34] .…”

Review of machine learning methods for Big satellite Data classification

“…Проте метод SVM потребує значно більше обчис-лювальних ресурсів. Його складність лежить у діапазоні між O(n 2 ) та O(n 3 ) залежно від типу ядра та реалізації [47,48], у той же час виявляється складність багатошарового персептрона O(n) [49,50]. Як наслідок викори-стовувати метод SVM для аналізу великих обсягів даних неможливо, а традиційні моделі багатошарового перцептрона, які застосовувалися для розпізнавання зображень, через повну зв'язність між вузлами потерпають від «прокляття розмірності», тому не масштабуються на зображення вищого розрізнення, а величезна кількість параметрів швидко веде до перенавчання.…”

Sliding Mode Control based Support Vector Machine RBF Kernel Parameter Optimization

“…When dealing with non-linearly separable data, SVM maps the data into higher dimensional space using kernels prior to performing the classification [4]. SVM formulates a quadratic programming (QP) problem to find a separating hyperplane, which maximizes the margin between two classes of the data [3], [5], [6]. Since SVM achieves a unique solution and learns from dimensionality of feature space, it is more robust than other techniques to over fitting [4], [6], [7].…”

“…SVM formulates a quadratic programming (QP) problem to find a separating hyperplane, which maximizes the margin between two classes of the data [3], [5], [6]. Since SVM achieves a unique solution and learns from dimensionality of feature space, it is more robust than other techniques to over fitting [4], [6], [7]. Despite all the advantages and applications of the SVM [8], [9], its classification speed is deteriorated when dealing with large scale problems as it uses large number of support vectors.…”