Classification of electronic nose data with support vector machines Matteo Pardo , Giorgio Sberveglieri.
- Support Vector Machine In Chemistry : Nianyi Chen : .
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Feature selection in quantitative structure-activity relationships. Patrick Walters , Brain B Goldman. Odor classification using similarity-based representation Manuele Bicego. Trafalis , Olutayo Oladunni , Dimitrios V.
Lee , J. Song , Sang-Oak Song. Netzeva , John C. Dearden , Rod Edwards , Andrew D. Worgan , Mark T D Cronin. Related Papers. Feature selection in quantitative structure-activity relationships. Patrick Walters , Brain B Goldman. Odor classification using similarity-based representation Manuele Bicego.
Trafalis , Olutayo Oladunni , Dimitrios V. Lee , J.
Song , Sang-Oak Song. Netzeva , John C.
Support Vector Machine in Chemistry by Nianyi Chen (ebook)
We would then like to choose a hypothesis that minimizes the expected risk :. In these cases, a common strategy is to choose the hypothesis that minimizes the empirical risk:. This approach is called empirical risk minimization, or ERM. This approach is called Tikhonov regularization. In light of the above discussion, we see that the SVM technique is equivalent to empirical risk minimization with Tikhonov regularization, where in this case the loss function is the hinge loss.
From this perspective, SVM is closely related to other fundamental classification algorithms such as regularized least-squares and logistic regression. In the classification setting, we have:. This extends the geometric interpretation of SVM—for linear classification, the empirical risk is minimized by any function whose margins lie between the support vectors, and the simplest of these is the max-margin classifier.
SVMs belong to a family of generalized linear classifiers and can be interpreted as an extension of the perceptron. They can also be considered a special case of Tikhonov regularization. A special property is that they simultaneously minimize the empirical classification error and maximize the geometric margin ; hence they are also known as maximum margin classifiers. The effectiveness of SVM depends on the selection of kernel, the kernel's parameters, and soft margin parameter C. Typically, each combination of parameter choices is checked using cross validation , and the parameters with best cross-validation accuracy are picked.
Support Vector Machine Prediction of Drug Solubility on GPUs
The final model, which is used for testing and for classifying new data, is then trained on the whole training set using the selected parameters. SVC is a similar method that also builds on kernel functions but is appropriate for unsupervised learning. It is considered a fundamental method in data science. Multiclass SVM aims to assign labels to instances by using support-vector machines, where the labels are drawn from a finite set of several elements. The dominant approach for doing so is to reduce the single multiclass problem into multiple binary classification problems.
Crammer and Singer proposed a multiclass SVM method which casts the multiclass classification problem into a single optimization problem, rather than decomposing it into multiple binary classification problems. Transductive support-vector machines extend SVMs in that they could also treat partially labeled data in semi-supervised learning by following the principles of transduction.
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Formally, a transductive support-vector machine is defined by the following primal optimization problem: . SVMs have been generalized to structured SVMs , where the label space is structured and of possibly infinite size. Vapnik , Harris Drucker, Christopher J. Burges, Linda Kaufman and Alexander J. The model produced by support-vector classification as described above depends only on a subset of the training data, because the cost function for building the model does not care about training points that lie beyond the margin.
Analogously, the model produced by SVR depends only on a subset of the training data, because the cost function for building the model ignores any training data close to the model prediction. Training the original SVR means solving . Slack variables are usually added into the above to allow for errors and to allow approximation in the case the above problem is infeasible. In it was shown by Polson and Scott that the SVM admits a Bayesian interpretation through the technique of data augmentation.
This extended view allows the application of Bayesian techniques to SVMs, such as flexible feature modeling, automatic hyperparameter tuning, and predictive uncertainty quantification. The parameters of the maximum-margin hyperplane are derived by solving the optimization.
There exist several specialized algorithms for quickly solving the quadratic programming QP problem that arises from SVMs, mostly relying on heuristics for breaking the problem down into smaller, more manageable chunks. Another approach is to use an interior-point method that uses Newton -like iterations to find a solution of the Karush—Kuhn—Tucker conditions of the primal and dual problems.
To avoid solving a linear system involving the large kernel matrix, a low-rank approximation to the matrix is often used in the kernel trick. Another common method is Platt's sequential minimal optimization SMO algorithm, which breaks the problem down into 2-dimensional sub-problems that are solved analytically, eliminating the need for a numerical optimization algorithm and matrix storage. This algorithm is conceptually simple, easy to implement, generally faster, and has better scaling properties for difficult SVM problems.
The special case of linear support-vector machines can be solved more efficiently by the same kind of algorithms used to optimize its close cousin, logistic regression ; this class of algorithms includes sub-gradient descent e. Each convergence iteration takes time linear in the time taken to read the train data, and the iterations also have a Q-linear convergence property, making the algorithm extremely fast.
The general kernel SVMs can also be solved more efficiently using sub-gradient descent e. P-packSVM  , especially when parallelization is allowed. From Wikipedia, the free encyclopedia.
Machine learning and data mining Problems. Dimensionality reduction. Structured prediction. Graphical models Bayes net Conditional random field Hidden Markov.