This document provides a practical guide for using support vector machines (SVMs) for classification tasks. It recommends beginners follow a simple procedure of transforming data, scaling it, using a radial basis function kernel, and performing cross-validation to select hyperparameters. Real-world examples show this procedure achieves better accuracy than approaches without these steps. The guide aims to help novices rapidly obtain acceptable SVM results without a deep understanding of the underlying theory.
This document proposes a simple procedure for beginners to obtain reasonable results when using support vector machines (SVMs) for classification tasks. The procedure involves preprocessing data through scaling, using a radial basis function kernel, selecting model parameters through cross-validation grid search, and training the full model on the preprocessed data. The document provides examples applying this procedure to real-world datasets, demonstrating improved accuracy over approaches without careful preprocessing and parameter selection.
This document describes a machine learning project that uses support vector machines (SVM) and k-nearest neighbors (k-NN) algorithms to segment gesture phases based on radial basis function (RBF) kernels and k-nearest neighbors. The project aims to classify frames of movement data into five gesture phases (rest, preparation, stroke, hold, retraction) using two classifiers. The SVM approach achieved 53.27% accuracy on test data while the k-NN approach achieved significantly higher accuracy of 92.53%. The document provides details on the dataset, feature extraction methods, model selection process and results of applying each classifier to the test data.
The document discusses text categorization and compares several machine learning algorithms for this task, including Support Vector Machines (SVM), Transductive SVM (TSVM), and SVM combined with K-Nearest Neighbors (SVM-KNN). It provides an overview of text categorization and challenges. It then describes SVM, TSVM which uses unlabeled data to improve classification, and SVM-KNN which combines SVM with KNN to better handle unlabeled data. Pseudocode is presented for the algorithms.
This document provides an overview of gradient boosting methods. It discusses that boosting is an ensemble method that builds models sequentially by focusing on misclassified examples from previous models. The gradient boosting algorithm updates weights based on misclassification rates and gradients. Key parameters for gradient boosting models include the number of trees, interaction depth, minimum observations per node, shrinkage, bag fraction, and train fraction. Tuning these hyperparameters is important for achieving the right balance of underfitting and overfitting.
Image Classification And Support Vector MachineShao-Chuan Wang
This document discusses support vector machines and their application to image classification. It provides an overview of SVM concepts like functional and geometric margins, optimization to maximize margins, Lagrangian duality, kernels, soft margins, and bias-variance tradeoff. It also covers multiclass SVM approaches, dimensionality reduction techniques, model selection via cross-validation, and results from applying SVM to an image classification problem.
The document discusses VC dimension in machine learning. It introduces the concept of VC dimension as a measure of the capacity or complexity of a set of functions used in a statistical binary classification algorithm. VC dimension is defined as the largest number of points that can be shattered, or classified correctly, by the algorithm. The document notes that test error is related to both training error and model complexity, which can be measured by VC dimension. A low VC dimension or large training set size can help reduce the gap between training and test error.
This document summarizes support vector machines (SVMs), a machine learning technique for classification and regression. SVMs find the optimal separating hyperplane that maximizes the margin between positive and negative examples in the training data. This is achieved by solving a convex optimization problem that minimizes a quadratic function under linear constraints. SVMs can perform non-linear classification by implicitly mapping inputs into a higher-dimensional feature space using kernel functions. They have applications in areas like text categorization due to their ability to handle high-dimensional sparse data.
2.6 support vector machines and associative classifiers revisedKrish_ver2
Support vector machines (SVMs) are a type of supervised machine learning model that can be used for both classification and regression analysis. SVMs work by finding a hyperplane in a multidimensional space that best separates clusters of data points. Nonlinear kernels can be used to transform input data into a higher dimensional space to allow for the detection of complex patterns. Associative classification is an alternative approach that uses association rule mining to generate rules describing attribute relationships that can then be used for classification.
This document proposes a simple procedure for beginners to obtain reasonable results when using support vector machines (SVMs) for classification tasks. The procedure involves preprocessing data through scaling, using a radial basis function kernel, selecting model parameters through cross-validation grid search, and training the full model on the preprocessed data. The document provides examples applying this procedure to real-world datasets, demonstrating improved accuracy over approaches without careful preprocessing and parameter selection.
This document describes a machine learning project that uses support vector machines (SVM) and k-nearest neighbors (k-NN) algorithms to segment gesture phases based on radial basis function (RBF) kernels and k-nearest neighbors. The project aims to classify frames of movement data into five gesture phases (rest, preparation, stroke, hold, retraction) using two classifiers. The SVM approach achieved 53.27% accuracy on test data while the k-NN approach achieved significantly higher accuracy of 92.53%. The document provides details on the dataset, feature extraction methods, model selection process and results of applying each classifier to the test data.
The document discusses text categorization and compares several machine learning algorithms for this task, including Support Vector Machines (SVM), Transductive SVM (TSVM), and SVM combined with K-Nearest Neighbors (SVM-KNN). It provides an overview of text categorization and challenges. It then describes SVM, TSVM which uses unlabeled data to improve classification, and SVM-KNN which combines SVM with KNN to better handle unlabeled data. Pseudocode is presented for the algorithms.
This document provides an overview of gradient boosting methods. It discusses that boosting is an ensemble method that builds models sequentially by focusing on misclassified examples from previous models. The gradient boosting algorithm updates weights based on misclassification rates and gradients. Key parameters for gradient boosting models include the number of trees, interaction depth, minimum observations per node, shrinkage, bag fraction, and train fraction. Tuning these hyperparameters is important for achieving the right balance of underfitting and overfitting.
Image Classification And Support Vector MachineShao-Chuan Wang
This document discusses support vector machines and their application to image classification. It provides an overview of SVM concepts like functional and geometric margins, optimization to maximize margins, Lagrangian duality, kernels, soft margins, and bias-variance tradeoff. It also covers multiclass SVM approaches, dimensionality reduction techniques, model selection via cross-validation, and results from applying SVM to an image classification problem.
The document discusses VC dimension in machine learning. It introduces the concept of VC dimension as a measure of the capacity or complexity of a set of functions used in a statistical binary classification algorithm. VC dimension is defined as the largest number of points that can be shattered, or classified correctly, by the algorithm. The document notes that test error is related to both training error and model complexity, which can be measured by VC dimension. A low VC dimension or large training set size can help reduce the gap between training and test error.
This document summarizes support vector machines (SVMs), a machine learning technique for classification and regression. SVMs find the optimal separating hyperplane that maximizes the margin between positive and negative examples in the training data. This is achieved by solving a convex optimization problem that minimizes a quadratic function under linear constraints. SVMs can perform non-linear classification by implicitly mapping inputs into a higher-dimensional feature space using kernel functions. They have applications in areas like text categorization due to their ability to handle high-dimensional sparse data.
2.6 support vector machines and associative classifiers revisedKrish_ver2
Support vector machines (SVMs) are a type of supervised machine learning model that can be used for both classification and regression analysis. SVMs work by finding a hyperplane in a multidimensional space that best separates clusters of data points. Nonlinear kernels can be used to transform input data into a higher dimensional space to allow for the detection of complex patterns. Associative classification is an alternative approach that uses association rule mining to generate rules describing attribute relationships that can then be used for classification.
Welcome to the Supervised Machine Learning and Data Sciences.
Algorithms for building models. Support Vector Machines.
Classification algorithm explanation and code in Python ( SVM ) .
In machine learning, support vector machines (SVMs, also support vector networks[1]) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes forms the output, making it a non-probabilistic binary linear classifier.
Event classification & prediction using support vector machineRuta Kambli
This document provides an overview of event classification and prediction using support vector machines (SVM). It begins with an introduction to classification, machine learning, and SVM. It then discusses binary classification with SVM, including hard-margin and soft-margin SVM, kernels, and multiclass classification. The document presents case studies on classifying hand movements from electromyography data and predicting power grid blackouts using SVM. It concludes that SVM is effective for these classification tasks and can initiate prevention mechanisms for predicted events.
Support Vector Machine(SVM) with Iris and Mushroom DatasetPawandeep Kaur
This document discusses using support vector machines (SVM) with two datasets: Iris and Mushroom. SVM is used to classify the Iris dataset into three species (setosa, versicolor, virginica) based on four features. It is shown that the setosa species is linearly separable from the others. SVM with an RBF kernel achieves good performance on this dataset. The Mushroom dataset contains descriptions of mushrooms and whether they are edible or poisonous. SVM is able to accurately classify mushrooms in this binary classification problem based on their features. 10-fold and percentage split cross-validation techniques are used to evaluate the SVM models on both datasets.
Tong is a data scientist in Supstat Inc and also a master students of Data Mining. He has been an active R programmer and developer for 5 years. He is the author of the R package of XGBoost, one of the most popular and contest-winning tools on kaggle.com nowadays.
Agenda:
Introduction of Xgboost
Real World Application
Model Specification
Parameter Introduction
Advanced Features
Kaggle Winning Solution
The caret package allows users to streamline the process of creating predictive models. It contains tools for data splitting, pre-processing, feature selection, model tuning using resampling, and variable importance estimation. The document provides examples of using various caret functions for visualization, pre-processing, model training and tuning, performance evaluation, and feature selection.
SVMs are classifiers derived from statistical learning theory that maximize the margin between decision boundaries. They work by mapping data to a higher dimensional space using kernels to allow for nonlinear decision boundaries. SVMs find the linear decision boundary that maximizes the margin between the closest data points of each class by solving a quadratic programming optimization problem.
This document summarizes support vector machines (SVMs). It explains that SVMs find the optimal separating hyperplane that maximizes the margin between two classes of data points. The hyperplane is determined by support vectors, which are the data points closest to the hyperplane. SVMs can be solved as a quadratic programming problem. The document also discusses how kernels can map data into higher dimensional spaces to make non-separable problems separable by SVMs.
1. The document proposes representing text documents as graphs (graph-of-words) instead of bag-of-words and using frequent subgraph mining to extract features for text categorization.
2. It describes using the gSpan algorithm to efficiently mine frequent subgraphs from the graph-of-words representations to generate features.
3. An elbow method is used to select an optimal minimum support threshold that balances feature set size and accuracy. Representing documents as graphs and mining subgraph features is shown to improve accuracy over traditional bag-of-words on four text categorization datasets.
This document provides an overview of support vector machines (SVMs), including:
- SVMs find the maximum-margin hyperplane between two classes during training to create classifiers with good generalization.
- The kernel trick allows transforming data into a higher-dimensional space to find nonlinear decision boundaries.
- Soft-margin SVMs allow some misclassified examples to improve accuracy when data is not perfectly separable.
- Tutorial tasks demonstrate using LIBSVM to classify toy datasets and evaluate SVM performance by varying parameters.
In this presentation, we approach a two-class classification problem. We try to find a plane that separates the class in the feature space, also called a hyperplane. If we can't find a hyperplane, then we can be creative in two ways: 1) We soften what we mean by separate, and 2) We enrich and enlarge the featured space so that separation is possible.
This document summarizes Bigyan Bhar's seminar on using support vector machines (SVMs) for semi-supervised classification. It introduces classification and SVMs, describes how unlabeled data can be used for semi-supervised learning, and compares methods like transductive SVM and augmented Lagrangian techniques. Results show some semi-supervised methods like penalty methods are more robust than TSVM in certain cases. Future work could establish theoretical bounds for method accuracy and explore non-SVM semi-supervised classifiers.
The document provides a tutorial on support vector machines (SVM). It begins with an abstract briefly introducing SVM and discussing how the tutorial was compiled from various sources. It then provides an introduction on machine learning and how SVM relates. The core concepts of SVM are explained, including statistical learning theory, maximizing margins, soft-margin classifiers, and the kernel trick. Common kernel functions for SVM are also listed. The tutorial is intended to give a brief overview of SVM for readers familiar with linear algebra, analysis, neural networks, and artificial intelligence concepts.
This document provides an overview of support vector machines (SVMs). It discusses how SVMs can be used to perform classification tasks by finding optimal separating hyperplanes that maximize the margin between different classes. The document outlines how SVMs solve an optimization problem to find these optimal hyperplanes using techniques like Lagrange duality, kernels, and soft margins. It also covers model selection methods like cross-validation and discusses extensions of SVMs to multi-class classification problems.
OPTIMIZATION AS A MODEL FOR FEW-SHOT LEARNINGMLReview
This document proposes using meta-learning and an LSTM model to learn an optimization algorithm for few-shot learning. The model, called a meta-learner, is trained on multiple datasets to learn how to efficiently train a learner network on new small datasets. The meta-learner LSTM models the parameter updates of the learner network during training, learning an initialization and update rule. The inputs to the meta-learner are the loss, parameters, and gradient, and it outputs updated parameters. This learned update rule can then be used to train the learner network on new small datasets, enabling few-shot learning using only a small amount of labeled data.
The document discusses the process of automated text classification using natural language processing. It covers various machine learning techniques for text classification including supervised learning methods like Naive Bayes classification and k-nearest neighbors. The key steps of the text classification process include data preprocessing, creating a training set and test set, developing a classification model using an algorithm, and then classifying new text data. Specific methods like bag-of-words representation and document-term matrices are also discussed for transforming text into a numerical format that machine learning algorithms can understand.
Support Vector Machine (SVM) is a supervised machine learning algorithm that can be used for both classification and regression analysis. It works by finding a hyperplane in an N-dimensional space that distinctly classifies the data points. SVM selects the hyperplane that has the largest distance to the nearest training data points of any class, since larger the margin lower the generalization error of the classifier. SVM can efficiently perform nonlinear classification by implicitly mapping their inputs into high-dimensional feature spaces.
This document provides a practical guide for using support vector machines (SVMs) for classification tasks. It recommends beginners follow a simple procedure: 1) preprocess data by converting categorical features to numeric and scaling attributes, 2) use a radial basis function kernel, 3) perform cross-validation to select optimal values for hyperparameters C and γ, and 4) train the full model on the training set using the best hyperparameters. The guide explains why this procedure often provides reasonable results for novices and illustrates it using examples of real-world classification problems.
Application of combined support vector machines in process fault diagnosisDr.Pooja Jain
This document discusses applying combined support vector machines (C-SVM) for process fault diagnosis and compares its performance to other classifiers. The authors test C-SVM, k-nearest neighbors, and simple SVM on data from the Tennessee Eastman process simulator and a three tank system. Their results show C-SVM achieves the lowest classification error compared to the other methods, though its complexity increases with the number of faults. Principal component analysis did not improve performance over the other classifiers. Selecting important variables using contribution charts significantly enhanced classifier performance on the Tennessee Eastman data.
A parsimonious SVM model selection criterion for classification of real-world ...o_almasi
This paper proposes and optimizes a two-term cost function consisting of a sparseness term and a generalized v-fold cross-validation term by a new adaptive particle swarm optimization (APSO). APSO updates its parameters adaptively based on a dynamic feedback from the success rate of the each particle’s personal best. Since the proposed cost function is based on the choosing fewer numbers of support vectors, the complexity of SVM models decreased while the accuracy remains in an acceptable range. Therefore, the testing time decreases and makes SVM more applicable for practical applications in real data sets. A comparative study on data sets of UCI database is performed between the proposed cost function and conventional cost function to demonstrate the effectiveness of the proposed cost function.
Welcome to the Supervised Machine Learning and Data Sciences.
Algorithms for building models. Support Vector Machines.
Classification algorithm explanation and code in Python ( SVM ) .
In machine learning, support vector machines (SVMs, also support vector networks[1]) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes forms the output, making it a non-probabilistic binary linear classifier.
Event classification & prediction using support vector machineRuta Kambli
This document provides an overview of event classification and prediction using support vector machines (SVM). It begins with an introduction to classification, machine learning, and SVM. It then discusses binary classification with SVM, including hard-margin and soft-margin SVM, kernels, and multiclass classification. The document presents case studies on classifying hand movements from electromyography data and predicting power grid blackouts using SVM. It concludes that SVM is effective for these classification tasks and can initiate prevention mechanisms for predicted events.
Support Vector Machine(SVM) with Iris and Mushroom DatasetPawandeep Kaur
This document discusses using support vector machines (SVM) with two datasets: Iris and Mushroom. SVM is used to classify the Iris dataset into three species (setosa, versicolor, virginica) based on four features. It is shown that the setosa species is linearly separable from the others. SVM with an RBF kernel achieves good performance on this dataset. The Mushroom dataset contains descriptions of mushrooms and whether they are edible or poisonous. SVM is able to accurately classify mushrooms in this binary classification problem based on their features. 10-fold and percentage split cross-validation techniques are used to evaluate the SVM models on both datasets.
Tong is a data scientist in Supstat Inc and also a master students of Data Mining. He has been an active R programmer and developer for 5 years. He is the author of the R package of XGBoost, one of the most popular and contest-winning tools on kaggle.com nowadays.
Agenda:
Introduction of Xgboost
Real World Application
Model Specification
Parameter Introduction
Advanced Features
Kaggle Winning Solution
The caret package allows users to streamline the process of creating predictive models. It contains tools for data splitting, pre-processing, feature selection, model tuning using resampling, and variable importance estimation. The document provides examples of using various caret functions for visualization, pre-processing, model training and tuning, performance evaluation, and feature selection.
SVMs are classifiers derived from statistical learning theory that maximize the margin between decision boundaries. They work by mapping data to a higher dimensional space using kernels to allow for nonlinear decision boundaries. SVMs find the linear decision boundary that maximizes the margin between the closest data points of each class by solving a quadratic programming optimization problem.
This document summarizes support vector machines (SVMs). It explains that SVMs find the optimal separating hyperplane that maximizes the margin between two classes of data points. The hyperplane is determined by support vectors, which are the data points closest to the hyperplane. SVMs can be solved as a quadratic programming problem. The document also discusses how kernels can map data into higher dimensional spaces to make non-separable problems separable by SVMs.
1. The document proposes representing text documents as graphs (graph-of-words) instead of bag-of-words and using frequent subgraph mining to extract features for text categorization.
2. It describes using the gSpan algorithm to efficiently mine frequent subgraphs from the graph-of-words representations to generate features.
3. An elbow method is used to select an optimal minimum support threshold that balances feature set size and accuracy. Representing documents as graphs and mining subgraph features is shown to improve accuracy over traditional bag-of-words on four text categorization datasets.
This document provides an overview of support vector machines (SVMs), including:
- SVMs find the maximum-margin hyperplane between two classes during training to create classifiers with good generalization.
- The kernel trick allows transforming data into a higher-dimensional space to find nonlinear decision boundaries.
- Soft-margin SVMs allow some misclassified examples to improve accuracy when data is not perfectly separable.
- Tutorial tasks demonstrate using LIBSVM to classify toy datasets and evaluate SVM performance by varying parameters.
In this presentation, we approach a two-class classification problem. We try to find a plane that separates the class in the feature space, also called a hyperplane. If we can't find a hyperplane, then we can be creative in two ways: 1) We soften what we mean by separate, and 2) We enrich and enlarge the featured space so that separation is possible.
This document summarizes Bigyan Bhar's seminar on using support vector machines (SVMs) for semi-supervised classification. It introduces classification and SVMs, describes how unlabeled data can be used for semi-supervised learning, and compares methods like transductive SVM and augmented Lagrangian techniques. Results show some semi-supervised methods like penalty methods are more robust than TSVM in certain cases. Future work could establish theoretical bounds for method accuracy and explore non-SVM semi-supervised classifiers.
The document provides a tutorial on support vector machines (SVM). It begins with an abstract briefly introducing SVM and discussing how the tutorial was compiled from various sources. It then provides an introduction on machine learning and how SVM relates. The core concepts of SVM are explained, including statistical learning theory, maximizing margins, soft-margin classifiers, and the kernel trick. Common kernel functions for SVM are also listed. The tutorial is intended to give a brief overview of SVM for readers familiar with linear algebra, analysis, neural networks, and artificial intelligence concepts.
This document provides an overview of support vector machines (SVMs). It discusses how SVMs can be used to perform classification tasks by finding optimal separating hyperplanes that maximize the margin between different classes. The document outlines how SVMs solve an optimization problem to find these optimal hyperplanes using techniques like Lagrange duality, kernels, and soft margins. It also covers model selection methods like cross-validation and discusses extensions of SVMs to multi-class classification problems.
OPTIMIZATION AS A MODEL FOR FEW-SHOT LEARNINGMLReview
This document proposes using meta-learning and an LSTM model to learn an optimization algorithm for few-shot learning. The model, called a meta-learner, is trained on multiple datasets to learn how to efficiently train a learner network on new small datasets. The meta-learner LSTM models the parameter updates of the learner network during training, learning an initialization and update rule. The inputs to the meta-learner are the loss, parameters, and gradient, and it outputs updated parameters. This learned update rule can then be used to train the learner network on new small datasets, enabling few-shot learning using only a small amount of labeled data.
The document discusses the process of automated text classification using natural language processing. It covers various machine learning techniques for text classification including supervised learning methods like Naive Bayes classification and k-nearest neighbors. The key steps of the text classification process include data preprocessing, creating a training set and test set, developing a classification model using an algorithm, and then classifying new text data. Specific methods like bag-of-words representation and document-term matrices are also discussed for transforming text into a numerical format that machine learning algorithms can understand.
Support Vector Machine (SVM) is a supervised machine learning algorithm that can be used for both classification and regression analysis. It works by finding a hyperplane in an N-dimensional space that distinctly classifies the data points. SVM selects the hyperplane that has the largest distance to the nearest training data points of any class, since larger the margin lower the generalization error of the classifier. SVM can efficiently perform nonlinear classification by implicitly mapping their inputs into high-dimensional feature spaces.
This document provides a practical guide for using support vector machines (SVMs) for classification tasks. It recommends beginners follow a simple procedure: 1) preprocess data by converting categorical features to numeric and scaling attributes, 2) use a radial basis function kernel, 3) perform cross-validation to select optimal values for hyperparameters C and γ, and 4) train the full model on the training set using the best hyperparameters. The guide explains why this procedure often provides reasonable results for novices and illustrates it using examples of real-world classification problems.
Application of combined support vector machines in process fault diagnosisDr.Pooja Jain
This document discusses applying combined support vector machines (C-SVM) for process fault diagnosis and compares its performance to other classifiers. The authors test C-SVM, k-nearest neighbors, and simple SVM on data from the Tennessee Eastman process simulator and a three tank system. Their results show C-SVM achieves the lowest classification error compared to the other methods, though its complexity increases with the number of faults. Principal component analysis did not improve performance over the other classifiers. Selecting important variables using contribution charts significantly enhanced classifier performance on the Tennessee Eastman data.
A parsimonious SVM model selection criterion for classification of real-world ...o_almasi
This paper proposes and optimizes a two-term cost function consisting of a sparseness term and a generalized v-fold cross-validation term by a new adaptive particle swarm optimization (APSO). APSO updates its parameters adaptively based on a dynamic feedback from the success rate of the each particle’s personal best. Since the proposed cost function is based on the choosing fewer numbers of support vectors, the complexity of SVM models decreased while the accuracy remains in an acceptable range. Therefore, the testing time decreases and makes SVM more applicable for practical applications in real data sets. A comparative study on data sets of UCI database is performed between the proposed cost function and conventional cost function to demonstrate the effectiveness of the proposed cost function.
Analytical study of feature extraction techniques in opinion miningcsandit
Although opinion mining is in a nascent stage of development but still the ground is set for
dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction
in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first
part discusses various techniques and second part makes a detailed appraisal of the major
techniques used for feature extraction
ANALYTICAL STUDY OF FEATURE EXTRACTION TECHNIQUES IN OPINION MININGcsandit
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction
Radial Basis Function Neural Network (RBFNN), Induction Motor, Vector control...cscpconf
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction.
This document provides an overview of various machine learning algorithms and concepts, including supervised learning techniques like linear regression, logistic regression, decision trees, random forests, and support vector machines. It also discusses unsupervised learning methods like principal component analysis and kernel-based PCA. Key aspects of linear regression, logistic regression, and random forests are summarized, such as cost functions, gradient descent, sigmoid functions, and bagging. Kernel methods are also introduced, explaining how the kernel trick can allow solving non-linear problems by mapping data to a higher-dimensional feature space.
Focal Loss for Dense Object Detection proposes a novel focal loss function to address the extreme foreground-background class imbalance encountered in training dense object detectors. The focal loss focuses training on hard examples and prevents easy negatives from overwhelming the detector. RetinaNet, a simple dense detector designed with a ResNet-FPN backbone and focal loss, achieves state-of-the-art accuracy while running faster than existing two-stage detectors. Extensive experiments demonstrate the focal loss enables training highly accurate dense detectors on datasets with vast numbers of background examples like COCO.
The document describes the implementation of support vector machines (SVM) on a medical dataset. It discusses transforming the raw data into two datasets, testing LIBSVM on the transformed data with different distributions, and obtaining accuracy rates in the high 80% range. Parameter tuning was performed using grid search to find the best cost and gamma values. The transformed data was challenging to model due to its large size and highly imbalanced class distribution, with over 97% of data belonging to just a few classes.
Data Science - Part IX - Support Vector MachineDerek Kane
This lecture provides an overview of Support Vector Machines in a more relatable and accessible manner. We will go through some methods of calibration and diagnostics of SVM and then apply the technique to accurately detect breast cancer within a dataset.
FIDUCIAL POINTS DETECTION USING SVM LINEAR CLASSIFIERScsandit
Currently, there is a growing interest from the scientific and/or industrial community in respect
to methods that offer solutions to the problem of fiducial points detection in human faces. Some
methods use the SVM for classification, but we observed that some formulations of optimization
problems were not discussed. In this article, we propose to investigate the performance of
mathematical formulation C-SVC when applied in fiducial point detection system. Futhermore,
we explore new parameters for training the proposed system. The performance of the proposed
system is evaluated in a fiducial points detection problem. The results demonstrate that the
method is competitive.
This document discusses tuning hyperparameters using cross validation. It begins by motivating the need for model selection to choose hyperparameters that provide a good balance between model complexity and accuracy. It then discusses assessing model quality using measures like error rate from a test set. Cross validation techniques like k-fold and leave-one-out are presented as methods for estimating accuracy without using all the data for training. The document concludes by discussing strategies for implementing model selection like using grids to search hyperparameters and evaluating results.
This document discusses using unsupervised support vector analysis to increase the efficiency of simulation-based functional verification. It describes applying an unsupervised machine learning technique called support vector analysis to filter redundant tests from a set of verification tests. By clustering similar tests into regions of a similarity metric space, it aims to select the most important tests to verify a design while removing redundant tests, improving verification efficiency. The approach trains an unsupervised support vector model on an initial set of simulated tests and uses it to filter future tests by comparing them to support vectors that define regions in the similarity space.
Support Vector Machines USING MACHINE LEARNING HOW IT WORKSrajalakshmi5921
This document discusses support vector machines (SVM), a supervised machine learning algorithm used for classification and regression. It explains that SVM finds the optimal boundary, known as a hyperplane, that separates classes with the maximum margin. When data is not linearly separable, kernel functions can transform the data into a higher-dimensional space to make it separable. The document discusses SVM for both linearly separable and non-separable data, kernel functions, hyperparameters, and approaches for multiclass classification like one-vs-one and one-vs-all.
LNCS 5050 - Bilevel Optimization and Machine Learningbutest
This document discusses using bilevel optimization and machine learning techniques to improve model selection in machine learning problems. It proposes framing machine learning model selection as a bilevel optimization problem, where the inner level problems involve optimizing models on training data and the outer level problem selects hyperparameters to minimize error on test data. This bilevel framing allows for systematic optimization of hyperparameters and enables novel machine learning approaches. The document illustrates the approach for support vector regression, formulating model selection as a Stackelberg game and solving the resulting mathematical program with equilibrium constraints.
The Russian Doll Search algorithm improves upon the Depth First Branch and Bound algorithm for solving constraint optimization problems. It does this by performing n successive searches on nested subproblems, where n is the number of variables in the problem. Each search solves a subproblem involving a subset of the variables and records the optimal solution. This recorded information is then used to improve the lower bound estimate for partial assignments during subsequent searches on larger subproblems, allowing earlier pruning of search branches. On benchmark problems, this approach yields better results than a standard Depth First Branch and Bound.
House Price Estimation as a Function Fitting Problem with using ANN ApproachYusuf Uzun
This document summarizes a student's machine learning term project on using an artificial neural network (ANN) to estimate house prices from the UCI Housing dataset. The student:
1) Describes the UCI Housing dataset and ANN approach.
2) Explains how to use Matlab's Neural Network Toolbox to set up, train, and evaluate an ANN model on the housing data.
3) Performs experiments comparing different data splits, training algorithms, and hidden layer sizes. The best results came from a 80-10-10 training-validation-test split.
Heuristic design of experiments w meta gradient searchGreg Makowski
Once you have started learning about predictive algorithms, and the basic knowledge discovery in databases process, what is the next level of detail to learn for a consulting project?
* Give examples of the many model training parameters
* Track results in a "model notebook"
* Use a model metric that combines both accuracy and generalization to rank models
* How to strategically search over the model training parameters - use a gradient descent approach
* One way to describe an arbitrarily complex predictive system is by using sensitivity analysis
Iterative Determinant Method for Solving Eigenvalue Problemsijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Support vector machines (SVMs) are a supervised machine learning algorithm used for classification and regression analysis. SVMs find the optimal boundary, known as a hyperplane, that separates classes of data. This hyperplane maximizes the margin between the two classes. Extensions to the basic SVM model include soft margin classification to allow some misclassified points, methods for multi-class classification like one-vs-one and one-vs-all, and the use of kernel functions to handle non-linear decision boundaries. Real-world applications of SVMs include face detection, text categorization, image classification, and bioinformatics.
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...Aggregage
This webinar will explore cutting-edge, less familiar but powerful experimentation methodologies which address well-known limitations of standard A/B Testing. Designed for data and product leaders, this session aims to inspire the embrace of innovative approaches and provide insights into the frontiers of experimentation!
Build applications with generative AI on Google CloudMárton Kodok
We will explore Vertex AI - Model Garden powered experiences, we are going to learn more about the integration of these generative AI APIs. We are going to see in action what the Gemini family of generative models are for developers to build and deploy AI-driven applications. Vertex AI includes a suite of foundation models, these are referred to as the PaLM and Gemini family of generative ai models, and they come in different versions. We are going to cover how to use via API to: - execute prompts in text and chat - cover multimodal use cases with image prompts. - finetune and distill to improve knowledge domains - run function calls with foundation models to optimize them for specific tasks. At the end of the session, developers will understand how to innovate with generative AI and develop apps using the generative ai industry trends.
4th Modern Marketing Reckoner by MMA Global India & Group M: 60+ experts on W...Social Samosa
The Modern Marketing Reckoner (MMR) is a comprehensive resource packed with POVs from 60+ industry leaders on how AI is transforming the 4 key pillars of marketing – product, place, price and promotions.
End-to-end pipeline agility - Berlin Buzzwords 2024Lars Albertsson
We describe how we achieve high change agility in data engineering by eliminating the fear of breaking downstream data pipelines through end-to-end pipeline testing, and by using schema metaprogramming to safely eliminate boilerplate involved in changes that affect whole pipelines.
A quick poll on agility in changing pipelines from end to end indicated a huge span in capabilities. For the question "How long time does it take for all downstream pipelines to be adapted to an upstream change," the median response was 6 months, but some respondents could do it in less than a day. When quantitative data engineering differences between the best and worst are measured, the span is often 100x-1000x, sometimes even more.
A long time ago, we suffered at Spotify from fear of changing pipelines due to not knowing what the impact might be downstream. We made plans for a technical solution to test pipelines end-to-end to mitigate that fear, but the effort failed for cultural reasons. We eventually solved this challenge, but in a different context. In this presentation we will describe how we test full pipelines effectively by manipulating workflow orchestration, which enables us to make changes in pipelines without fear of breaking downstream.
Making schema changes that affect many jobs also involves a lot of toil and boilerplate. Using schema-on-read mitigates some of it, but has drawbacks since it makes it more difficult to detect errors early. We will describe how we have rejected this tradeoff by applying schema metaprogramming, eliminating boilerplate but keeping the protection of static typing, thereby further improving agility to quickly modify data pipelines without fear.
1. A Practical Guide to Support Vector Classification
Chih-Wei Hsu, Chih-Chung Chang, and Chih-Jen Lin
Department of Computer Science
National Taiwan University, Taipei 106, Taiwan
http://www.csie.ntu.edu.tw/~cjlin
Initial version: 2003 Last updated: April 15, 2010
Abstract
The support vector machine (SVM) is a popular classification technique.
However, beginners who are not familiar with SVM often get unsatisfactory
results since they miss some easy but significant steps. In this guide, we propose
a simple procedure which usually gives reasonable results.
1 Introduction
SVMs (Support Vector Machines) are a useful technique for data classification. Al-
though SVM is considered easier to use than Neural Networks, users not familiar with
it often get unsatisfactory results at first. Here we outline a “cookbook” approach
which usually gives reasonable results.
Note that this guide is not for SVM researchers nor do we guarantee you will
achieve the highest accuracy. Also, we do not intend to solve challenging or diffi-
cult problems. Our purpose is to give SVM novices a recipe for rapidly obtaining
acceptable results.
Although users do not need to understand the underlying theory behind SVM, we
briefly introduce the basics necessary for explaining our procedure. A classification
task usually involves separating data into training and testing sets. Each instance
in the training set contains one “target value” (i.e. the class labels) and several
“attributes” (i.e. the features or observed variables). The goal of SVM is to produce
a model (based on the training data) which predicts the target values of the test data
given only the test data attributes.
Given a training set of instance-label pairs (xi, yi), i = 1, . . . , l where xi ∈ Rn
and
y ∈ {1, −1}l
, the support vector machines (SVM) (Boser et al., 1992; Cortes and
Vapnik, 1995) require the solution of the following optimization problem:
min
w,b,ξ
1
2
wT
w + C
l
i=1
ξi
subject to yi(wT
φ(xi) + b) ≥ 1 − ξi, (1)
ξi ≥ 0.
1
2. Table 1: Problem characteristics and performance comparisons.
Applications #training #testing #features #classes Accuracy Accuracy
data data by users by our
procedure
Astroparticle1
3,089 4,000 4 2 75.2% 96.9%
Bioinformatics2
391 04
20 3 36% 85.2%
Vehicle3
1,243 41 21 2 4.88% 87.8%
Here training vectors xi are mapped into a higher (maybe infinite) dimensional space
by the function φ. SVM finds a linear separating hyperplane with the maximal margin
in this higher dimensional space. C > 0 is the penalty parameter of the error term.
Furthermore, K(xi, xj) ≡ φ(xi)T
φ(xj) is called the kernel function. Though new
kernels are being proposed by researchers, beginners may find in SVM books the
following four basic kernels:
• linear: K(xi, xj) = xT
i xj.
• polynomial: K(xi, xj) = (γxi
T
xj + r)d
, γ > 0.
• radial basis function (RBF): K(xi, xj) = exp(−γ xi − xj
2
), γ > 0.
• sigmoid: K(xi, xj) = tanh(γxi
T
xj + r).
Here, γ, r, and d are kernel parameters.
1.1 Real-World Examples
Table 1 presents some real-world examples. These data sets are supplied by our users
who could not obtain reasonable accuracy in the beginning. Using the procedure
illustrated in this guide, we help them to achieve better performance. Details are in
Appendix A.
These data sets are at http://www.csie.ntu.edu.tw/~cjlin/papers/guide/
data/
1
Courtesy of Jan Conrad from Uppsala University, Sweden.
2
Courtesy of Cory Spencer from Simon Fraser University, Canada (Gardy et al., 2003).
3
Courtesy of a user from Germany.
4
As there are no testing data, cross-validation instead of testing accuracy is presented here.
Details of cross-validation are in Section 3.2.
2
3. 1.2 Proposed Procedure
Many beginners use the following procedure now:
• Transform data to the format of an SVM package
• Randomly try a few kernels and parameters
• Test
We propose that beginners try the following procedure first:
• Transform data to the format of an SVM package
• Conduct simple scaling on the data
• Consider the RBF kernel K(x, y) = e−γ x−y 2
• Use cross-validation to find the best parameter C and γ
• Use the best parameter C and γ to train the whole training set5
• Test
We discuss this procedure in detail in the following sections.
2 Data Preprocessing
2.1 Categorical Feature
SVM requires that each data instance is represented as a vector of real numbers.
Hence, if there are categorical attributes, we first have to convert them into numeric
data. We recommend using m numbers to represent an m-category attribute. Only
one of the m numbers is one, and others are zero. For example, a three-category
attribute such as {red, green, blue} can be represented as (0,0,1), (0,1,0), and (1,0,0).
Our experience indicates that if the number of values in an attribute is not too large,
this coding might be more stable than using a single number.
5
The best parameter might be affected by the size of data set but in practice the one obtained
from cross-validation is already suitable for the whole training set.
3
4. 2.2 Scaling
Scaling before applying SVM is very important. Part 2 of Sarle’s Neural Networks
FAQ Sarle (1997) explains the importance of this and most of considerations also ap-
ply to SVM. The main advantage of scaling is to avoid attributes in greater numeric
ranges dominating those in smaller numeric ranges. Another advantage is to avoid
numerical difficulties during the calculation. Because kernel values usually depend on
the inner products of feature vectors, e.g. the linear kernel and the polynomial ker-
nel, large attribute values might cause numerical problems. We recommend linearly
scaling each attribute to the range [−1, +1] or [0, 1].
Of course we have to use the same method to scale both training and testing
data. For example, suppose that we scaled the first attribute of training data from
[−10, +10] to [−1, +1]. If the first attribute of testing data lies in the range [−11, +8],
we must scale the testing data to [−1.1, +0.8]. See Appendix B for some real examples.
3 Model Selection
Though there are only four common kernels mentioned in Section 1, we must decide
which one to try first. Then the penalty parameter C and kernel parameters are
chosen.
3.1 RBF Kernel
In general, the RBF kernel is a reasonable first choice. This kernel nonlinearly maps
samples into a higher dimensional space so it, unlike the linear kernel, can handle the
case when the relation between class labels and attributes is nonlinear. Furthermore,
the linear kernel is a special case of RBF Keerthi and Lin (2003) since the linear
kernel with a penalty parameter ˜C has the same performance as the RBF kernel with
some parameters (C, γ). In addition, the sigmoid kernel behaves like RBF for certain
parameters (Lin and Lin, 2003).
The second reason is the number of hyperparameters which influences the com-
plexity of model selection. The polynomial kernel has more hyperparameters than
the RBF kernel.
Finally, the RBF kernel has fewer numerical difficulties. One key point is 0 <
Kij ≤ 1 in contrast to polynomial kernels of which kernel values may go to infinity
(γxi
T
xj + r > 1) or zero (γxi
T
xj + r < 1) while the degree is large. Moreover, we
must note that the sigmoid kernel is not valid (i.e. not the inner product of two
4
5. vectors) under some parameters (Vapnik, 1995).
There are some situations where the RBF kernel is not suitable. In particular,
when the number of features is very large, one may just use the linear kernel. We
discuss details in Appendix C.
3.2 Cross-validation and Grid-search
There are two parameters for an RBF kernel: C and γ. It is not known beforehand
which C and γ are best for a given problem; consequently some kind of model selection
(parameter search) must be done. The goal is to identify good (C, γ) so that the
classifier can accurately predict unknown data (i.e. testing data). Note that it may
not be useful to achieve high training accuracy (i.e. a classifier which accurately
predicts training data whose class labels are indeed known). As discussed above, a
common strategy is to separate the data set into two parts, of which one is considered
unknown. The prediction accuracy obtained from the “unknown” set more precisely
reflects the performance on classifying an independent data set. An improved version
of this procedure is known as cross-validation.
In v-fold cross-validation, we first divide the training set into v subsets of equal
size. Sequentially one subset is tested using the classifier trained on the remaining
v − 1 subsets. Thus, each instance of the whole training set is predicted once so the
cross-validation accuracy is the percentage of data which are correctly classified.
The cross-validation procedure can prevent the overfitting problem. Figure 1
represents a binary classification problem to illustrate this issue. Filled circles and
triangles are the training data while hollow circles and triangles are the testing data.
The testing accuracy of the classifier in Figures 1a and 1b is not good since it overfits
the training data. If we think of the training and testing data in Figure 1a and 1b
as the training and validation sets in cross-validation, the accuracy is not good. On
the other hand, the classifier in 1c and 1d does not overfit the training data and gives
better cross-validation as well as testing accuracy.
We recommend a “grid-search” on C and γ using cross-validation. Various pairs
of (C, γ) values are tried and the one with the best cross-validation accuracy is
picked. We found that trying exponentially growing sequences of C and γ is a
practical method to identify good parameters (for example, C = 2−5
, 2−3
, . . . , 215
,
γ = 2−15
, 2−13
, . . . , 23
).
The grid-search is straightforward but seems naive. In fact, there are several
advanced methods which can save computational cost by, for example, approximating
the cross-validation rate. However, there are two motivations why we prefer the simple
5
6. (a) Training data and an overfitting classifier (b) Applying an overfitting classifier on testing
data
(c) Training data and a better classifier (d) Applying a better classifier on testing data
Figure 1: An overfitting classifier and a better classifier (G and L: training data;
and : testing data).
grid-search approach.
One is that, psychologically, we may not feel safe to use methods which avoid
doing an exhaustive parameter search by approximations or heuristics. The other
reason is that the computational time required to find good parameters by grid-
search is not much more than that by advanced methods since there are only two
parameters. Furthermore, the grid-search can be easily parallelized because each
(C, γ) is independent. Many of advanced methods are iterative processes, e.g. walking
along a path, which can be hard to parallelize.
Since doing a complete grid-search may still be time-consuming, we recommend
6
7. Figure 2: Loose grid search on C = 2−5
, 2−3
, . . . , 215
and γ = 2−15
, 2−13
, . . . , 23
.
Figure 3: Fine grid-search on C = 21
, 21.25
, . . . , 25
and γ = 2−7
, 2−6.75
, . . . , 2−3
.
7
8. using a coarse grid first. After identifying a “better” region on the grid, a finer grid
search on that region can be conducted. To illustrate this, we do an experiment on
the problem german from the Statlog collection (Michie et al., 1994). After scaling
this set, we first use a coarse grid (Figure 2) and find that the best (C, γ) is (23
, 2−5
)
with the cross-validation rate 77.5%. Next we conduct a finer grid search on the
neighborhood of (23
, 2−5
) (Figure 3) and obtain a better cross-validation rate 77.6%
at (23.25
, 2−5.25
). After the best (C, γ) is found, the whole training set is trained again
to generate the final classifier.
The above approach works well for problems with thousands or more data points.
For very large data sets a feasible approach is to randomly choose a subset of the
data set, conduct grid-search on them, and then do a better-region-only grid-search
on the complete data set.
4 Discussion
In some situations the above proposed procedure is not good enough, so other tech-
niques such as feature selection may be needed. These issues are beyond the scope of
this guide. Our experience indicates that the procedure works well for data which do
not have many features. If there are thousands of attributes, there may be a need to
choose a subset of them before giving the data to SVM.
Acknowledgments
We thank all users of our SVM software LIBSVM and BSVM, who helped us to
identify possible difficulties encountered by beginners. We also thank some users (in
particular, Robert Campbell) for proofreading the paper.
A Examples of the Proposed Procedure
In this appendix we compare accuracy by the proposed procedure with that often
used by general beginners. Experiments are on the three problems mentioned in
Table 1 by using the software LIBSVM (Chang and Lin, 2001). For each problem, we
first list the accuracy by direct training and testing. Secondly, we show the difference
in accuracy with and without scaling. From what has been discussed in Section 2.2,
the range of training set attributes must be saved so that we are able to restore
them while scaling the testing set. Thirdly, the accuracy by the proposed procedure
8
9. (scaling and then model selection) is presented. Finally, we demonstrate the use
of a tool in LIBSVM which does the whole procedure automatically. Note that a
similar parameter selection tool like the grid.py presented below is available in the
R-LIBSVM interface (see the function tune).
A.1 Astroparticle Physics
• Original sets with default parameters
$ ./svm-train svmguide1
$ ./svm-predict svmguide1.t svmguide1.model svmguide1.t.predict
→ Accuracy = 66.925%
• Scaled sets with default parameters
$ ./svm-scale -l -1 -u 1 -s range1 svmguide1 > svmguide1.scale
$ ./svm-scale -r range1 svmguide1.t > svmguide1.t.scale
$ ./svm-train svmguide1.scale
$ ./svm-predict svmguide1.t.scale svmguide1.scale.model svmguide1.t.predict
→ Accuracy = 96.15%
• Scaled sets with parameter selection (change to the directory tools, which
contains grid.py)
$ python grid.py svmguide1.scale
· · ·
2.0 2.0 96.8922
(Best C=2.0, γ=2.0 with five-fold cross-validation rate=96.8922%)
$ ./svm-train -c 2 -g 2 svmguide1.scale
$ ./svm-predict svmguide1.t.scale svmguide1.scale.model svmguide1.t.predict
→ Accuracy = 96.875%
• Using an automatic script
$ python easy.py svmguide1 svmguide1.t
Scaling training data...
Cross validation...
9
12. B Common Mistakes in Scaling Training and Test-
ing Data
Section 2.2 stresses the importance of using the same scaling factors for training and
testing sets. We give a real example on classifying traffic light signals (courtesy of an
anonymous user) It is available at LIBSVM Data Sets.
If training and testing sets are separately scaled to [0, 1], the resulting accuracy is
lower than 70%.
$ ../svm-scale -l 0 svmguide4 > svmguide4.scale
$ ../svm-scale -l 0 svmguide4.t > svmguide4.t.scale
$ python easy.py svmguide4.scale svmguide4.t.scale
Accuracy = 69.2308% (216/312) (classification)
Using the same scaling factors for training and testing sets, we obtain much better
accuracy.
$ ../svm-scale -l 0 -s range4 svmguide4 > svmguide4.scale
$ ../svm-scale -r range4 svmguide4.t > svmguide4.t.scale
$ python easy.py svmguide4.scale svmguide4.t.scale
Accuracy = 89.4231% (279/312) (classification)
With the correct setting, the 10 features in svmguide4.t.scale have the following
maximal values:
0.7402, 0.4421, 0.6291, 0.8583, 0.5385, 0.7407, 0.3982, 1.0000, 0.8218, 0.9874
Clearly, the earlier way to scale the testing set to [0, 1] generates an erroneous set.
C When to Use Linear but not RBF Kernel
If the number of features is large, one may not need to map data to a higher di-
mensional space. That is, the nonlinear mapping does not improve the performance.
Using the linear kernel is good enough, and one only searches for the parameter C.
While Section 3.1 describes that RBF is at least as good as linear, the statement is
true only after searching the (C, γ) space.
Next, we split our discussion to three parts:
12
13. C.1 Number of instances number of features
Many microarray data in bioinformatics are of this type. We consider the Leukemia
data from the LIBSVM data sets (http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/
datasets). The training and testing sets have 38 and 34 instances, respectively. The
number of features is 7,129, much larger than the number of instances. We merge the
two files and compare the cross validation accuracy of using the RBF and the linear
kernels:
• RBF kernel with parameter selection
$ cat leu leu.t > leu.combined
$ python grid.py leu.combined
· · ·
8.0 3.0517578125e-05 97.2222
(Best C=8.0, γ = 0.000030518 with five-fold cross-validation rate=97.2222%)
• Linear kernel with parameter selection
$ python grid.py -log2c -1,2,1 -log2g 1,1,1 -t 0 leu.combined
· · ·
0.5 2.0 98.6111
(Best C=0.5 with five-fold cross-validation rate=98.61111%)
Though grid.py was designed for the RBF kernel, the above way checks various
C using the linear kernel (-log2g 1,1,1 sets a dummy γ).
The cross-validation accuracy of using the linear kernel is comparable to that of using
the RBF kernel. Apparently, when the number of features is very large, one may not
need to map the data.
In addition to LIBSVM, the LIBLINEAR software mentioned below is also effective
for data in this case.
C.2 Both numbers of instances and features are large
Such data often occur in document classification. LIBSVM is not particularly good for
this type of problems. Fortunately, we have another software LIBLINEAR (Fan et al.,
2008), which is very suitable for such data. We illustrate the difference between
13
14. LIBSVM and LIBLINEAR using a document problem rcv1 train.binary from the
LIBSVM data sets. The numbers of instances and features are 20,242 and 47,236,
respectively.
$ time libsvm-2.85/svm-train -c 4 -t 0 -e 0.1 -m 800 -v 5 rcv1_train.binary
Cross Validation Accuracy = 96.8136%
345.569s
$ time liblinear-1.21/train -c 4 -e 0.1 -v 5 rcv1_train.binary
Cross Validation Accuracy = 97.0161%
2.944s
For five-fold cross validation, LIBSVM takes around 350 seconds, but LIBLINEAR uses
only 3. Moreover, LIBSVM consumes more memory as we allocate some spaces to
store recently used kernel elements (see -m 800). Clearly, LIBLINEAR is much faster
than LIBSVM to obtain a model with comparable accuracy.
LIBLINEAR is efficient for large-scale document classification. Let us consider a
large set rcv1 test.binary with 677,399 instances.
$ time liblinear-1.21/train -c 0.25 -v 5 rcv1_test.binary
Cross Validation Accuracy = 97.8538%
68.84s
Note that reading the data takes most of the time. The training of each train-
ing/validation split is less than four seconds.
C.3 Number of instances number of features
As the number of features is small, one often maps data to higher dimensional spaces
(i.e., using nonlinear kernels). However, if you really would like to use the linear
kernel, you may use LIBLINEAR with the option -s 2. When the number of features
is small, it is often faster than the default -s 1. Consider the data http://www.csie.
ntu.edu.tw/~cjlin/libsvmtools/datasets/binary/covtype.libsvm.binary.scale.
bz2. The number of instances 581,012 is much larger than the number of features 54.
We run LIBLINEAR with -s 1 (default) and -s 2.
$ time liblinear-1.21/train -c 4 -v 5 -s 2 covtype.libsvm.binary.scale
Cross Validation Accuracy = 75.67%
67.224s
$ time liblinear-1.21/train -c 4 -v 5 -s 1 covtype.libsvm.binary.scale
14
15. Cross Validation Accuracy = 75.6711%
452.736s
Clearly, using -s 2 leads to shorter training time.
References
B. E. Boser, I. Guyon, and V. Vapnik. A training algorithm for optimal margin
classifiers. In Proceedings of the Fifth Annual Workshop on Computational Learning
Theory, pages 144–152. ACM Press, 1992.
C.-C. Chang and C.-J. Lin. LIBSVM: a library for support vector machines, 2001.
Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm.
C. Cortes and V. Vapnik. Support-vector network. Machine Learning, 20:273–297,
1995.
R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin. LIBLINEAR: A
library for large linear classification. Journal of Machine Learning Research, 9:1871–
1874, 2008. URL http://www.csie.ntu.edu.tw/~cjlin/papers/liblinear.
pdf.
J. L. Gardy, C. Spencer, K. Wang, M. Ester, G. E. Tusnady, I. Simon, S. Hua,
K. deFays, C. Lambert, K. Nakai, and F. S. Brinkman. PSORT-B: improving
protein subcellular localization prediction for gram-negative bacteria. Nucleic Acids
Research, 31(13):3613–3617, 2003.
S. S. Keerthi and C.-J. Lin. Asymptotic behaviors of support vector machines with
Gaussian kernel. Neural Computation, 15(7):1667–1689, 2003.
H.-T. Lin and C.-J. Lin. A study on sigmoid kernels for SVM and the training of non-
PSD kernels by SMO-type methods. Technical report, Department of Computer
Science, National Taiwan University, 2003. URL http://www.csie.ntu.edu.tw/
~cjlin/papers/tanh.pdf.
D. Michie, D. J. Spiegelhalter, C. C. Taylor, and J. Campbell, editors. Machine
learning, neural and statistical classification. Ellis Horwood, Upper Saddle River,
NJ, USA, 1994. ISBN 0-13-106360-X. Data available at http://archive.ics.
uci.edu/ml/machine-learning-databases/statlog/.
15
16. W. S. Sarle. Neural Network FAQ, 1997. URL ftp://ftp.sas.com/pub/neural/
FAQ.html. Periodic posting to the Usenet newsgroup comp.ai.neural-nets.
V. Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag, New York,
NY, 1995.
16