# AI News, Support Vector Machines — Better than Artificial Neural Networks in which learning situations?

- On Sunday, September 30, 2018
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## Support Vector Machines — Better than Artificial Neural Networks in which learning situations?

And yet SVMs are routinely used for multi-class classification, which is accomplished with a processing wrapper around multiple SVM classifiers that work in a 'one against many' pattern--i.e., the training data is shown to the first SVM which classifies those instances as 'Class I' or 'not Class I'.

As far as i can tell, the studies reported in the literature confirm this, e.g., In the provocatively titled paper Sex with Support Vector Machines substantially better resolution for sex identification (Male/Female) in 12-square pixel images, was reported for SVM compared with that of a group of traditional linear classifiers;

My impression from reading this literature over the past decade or so, is that the majority of the carefully designed studies--by persons skilled at configuring and using both techniques, and using data sufficiently resistant to classification to provoke some meaningful difference in resolution--report the superior performance of SVM relative to NN.

For instance, in one study comparing the accuracy of SVM and NN in time series forecasting, the investigators reported that SVM did indeed outperform a conventional (back-propagating over layered nodes) NN but performance of the SVM was about the same as that of an RBF (radial basis function) NN.

here you might have in your training data, only a few data points labeled as 'fraudulent accounts' (and usually with questionable accuracy) versus the remaining >99% labeled 'not fraud.'

In particular, the training data consists of instances labeled 'not fraud' and 'unk' (or some other label to indicate they are not in the class)--in other words, 'inside the decision boundary' and 'outside the decision boundary.'

By contrast, SVMs are not only very difficult to code (in my opinion, by far the most difficult ML algorithm to implement in code) but also difficult to configure and implement as a pre-compiled library--e.g., a kernel must be selected, the results are very sensitive to how the data is re-scaled/normalized, etc.

- On Sunday, September 30, 2018
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## Class prediction for high-dimensional class-imbalanced data

Our results showed that some of the classifiers that are more frequently used for class prediction with high-dimensional data are highly sensitive to class imbalance.

This problem arises for two reasons: the probability of assigning a new sample to a given class depends on the prevalence of that class in the training set, and with variable selection this probability is further biased towards the majority class.

In most circumstances, the unequal predictive accuracies produced by class-imbalanced classifiers have the effect of slightly decreasing the difference in the class-specific predictive values, which is present when the predictive accuracies are equal and the classes are imbalanced;

As a consequence, the selected variables are those that have the biggest departures from the true values in the minority class, either indicating differences between classes that do not exist (null variables), or amplifying some differences that exist (non-null variables).

Over-sampling does not remove or attenuate the class imbalance problem [31] also in our settings because we considered classification rules and a variable selection method that are hardly modified by the presence of replicated samples;

On the other hand, simple down-sizing works well in removing the discrepancy between the class-specific predictive accuracies, but as expected it has a large variability and the predictive accuracy of the classifiers worsens when the effective sample size is reduced considerably because the class imbalance is large.

The relative benefit of multiple down-sizing over simple down-sizing depends on the amount of information discarded by simple down-sizing, i.e., on the level of class imbalance but also on the number of left-out samples.

We used penalized logistic regression (PLR) as a classification method and evaluated its predictive accuracy as the fraction of correctly classified samples (see the limitations of this approach in [36], page 247).

Using the threshold based on the imbalance from the training set, which works well for logistic regression, reduces but does not remove the classification bias towards the majority class, also when no variable selection is performed before fitting the PLR model;

- On Sunday, September 30, 2018
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## Support vector machine

In machine learning, support vector machines (SVMs, also support vector networks[1]) are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis.

Given a set of training examples, each marked as belonging to one or the other of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non-probabilistic binary linear classifier (although methods such as Platt scaling exist to use SVM in a probabilistic classification setting).

An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible.

In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.

When data is unlabelled, supervised learning is not possible, and an unsupervised learning approach is required, which attempts to find natural clustering of the data to groups, and then map new data to these formed groups.

algorithm created by Hava Siegelmann and Vladimir Vapnik, applies the statistics of support vectors, developed in the support vector machines algorithm, to categorize unlabeled data, and is one of the most widely used clustering algorithms in industrial applications.[citation needed]

If such a hyperplane exists, it is known as the maximum-margin hyperplane and the linear classifier it defines is known as a maximum margin classifier;

More formally, a support vector machine constructs a hyperplane or set of hyperplanes in a high- or infinite-dimensional space, which can be used for classification, regression, or other tasks like outliers detection[3].

Intuitively, a good separation is achieved by the hyperplane that has the largest distance to the nearest training-data point of any class (so-called functional margin), since in general the larger the margin the lower the generalization error of the classifier[4].

Whereas the original problem may be stated in a finite dimensional space, it often happens that the sets to discriminate are not linearly separable in that space.

To keep the computational load reasonable, the mappings used by SVM schemes are designed to ensure that dot products of pairs input data vectors may be computed easily in terms of the variables in the original space, by defining them in terms of a kernel function

The hyperplanes in the higher-dimensional space are defined as the set of points whose dot product with a vector in that space is constant, where such a set of vector is an orthogonal (and thus minimal) set of vectors that defines a hyperplane.

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In this way, the sum of kernels above can be used to measure the relative nearness of each test point to the data points originating in one or the other of the sets to be discriminated.

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If the training data is linearly separable, we can select two parallel hyperplanes that separate the two classes of data, so that the distance between them is as large as possible.

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the second term in the loss function will become negligible, hence, it will behave similar to the hard-margin SVM, if the input data are linearly classifiable, but will still learn if a classification rule is viable or not.

Vapnik suggested a way to create nonlinear classifiers by applying the kernel trick (originally proposed by Aizerman et al.[14]) to maximum-margin hyperplanes.[12]

It is noteworthy that working in a higher-dimensional feature space increases the generalization error of support vector machines, although given enough samples the algorithm still performs well.[15]

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{\displaystyle k({\vec {x_{i}}},{\vec {x_{j}}})=\varphi ({\vec {x_{i}}})\cdot \varphi ({\vec {x_{j}}})}

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{\displaystyle \textstyle {\vec {w}}\cdot \varphi ({\vec {x}})=\sum _{i}\alpha _{i}y_{i}k({\vec {x}}_{i},{\vec {x}})}

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.) Suppose now that we would like to learn a nonlinear classification rule which corresponds to a linear classification rule for the transformed data points

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Both techniques have proven to offer significant advantages over the traditional approach when dealing with large, sparse datasets—sub-gradient methods are especially efficient when there are many training examples, and coordinate descent when the dimension of the feature space is high.

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As such, traditional gradient descent (or SGD) methods can be adapted, where instead of taking a step in the direction of the functions gradient, a step is taken in the direction of a vector selected from the function's sub-gradient.

The soft-margin support vector machine described above is an example of an empirical risk minimization (ERM) algorithm for the hinge loss.

Seen this way, support vector machines belong to a natural class of algorithms for statistical inference, and many of its unique features are due to the behavior of the hinge loss.

(for example, that they are generated by a finite Markov process), if the set of hypotheses being considered is small enough, the minimizer of the empirical risk will closely approximate the minimizer of the expected risk as

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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

The difference between the three lies in the choice of loss function: regularized least-squares amounts to empirical risk minimization with the square-loss,

The difference between the hinge loss and these other loss functions is best stated in terms of target functions - the function that minimizes expected risk for a given pair of random variables

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Thus, in a sufficiently rich hypothesis space—or equivalently, for an appropriately chosen kernel—the SVM classifier will converge to the simplest function (in terms of

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.[18]

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.[20]

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.

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.[25]

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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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.

This extended view allows for the application of Bayesian techniques to SVMs, such as flexible feature modeling, automatic hyperparameter tuning, and predictive uncertainty quantification.

There exist several specialized algorithms for quickly solving the QP problem that arises from SVMs, mostly relying on heuristics for breaking the problem down into smaller, more-manageable chunks.

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.

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;

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.

- On Sunday, September 30, 2018
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## Comparison of support vector machine, random forest and neural network classifiers for tree species classification on airborne hyperspectral APEX imagesEdwin Raczko University of Warsaw, Faculty of Geography and Regional Studies, Department of Geoinformatics, Cartography and Remote Sensing, Warsaw, PolandCorrespondenceedwin.raczko@student.uw.edu.plView further author information Bogdan Zagajewski University of Warsaw, Faculty of Geography and Regional Studies, Department of Geoinformatics, Cartography and Remote Sensing, Warsaw, Polandhttp://orcid.org/0000-0001-7882-5318View further author information

Knowledge about the vegetation condition of a forested area is important both for monitoring of protected areas (Nagendra et al., 2013 Nagendra, H., Lucas, R., Honradoc, J.P., Jongman, R.H.G., Tarantino, C., Adamo, M., &

Integrated management requires accurate and multifaceted mastery of forest information, of which the forest ecosystem cover is the most basic and important component (Shen, Sakai, Hoshino, 2010).

More than 30 years ago, a rapid expansion of industry in the surrounding areas combined with the particular landscape of Karkonosze to cause acid rains that exposed the fragile mountain ecosystem to insect infestation (Jadczyk, 2009 Jadczyk, P.

The synergic effect of acid rains, air pollution, drought and insect outbreak which all happened at that time contributed to the severity of the damage done to the ecosystem.

It is also worth mentioning that spruces planted in the Karkonosze before 1980 were not typical of a mountain ecosystem and had lower resistance to the rough mountain climate.

Although damage was not as severe as some predicted, it is the evidence of unreasonable decisions and a lack of planning and foresight in treating areas of special value (Raj, 2014 Raj, A.

Knapik (ed.), Konferencja Naukowa z okazji 55-lecia Karkonoskiego Parku Narodowego: 25 lat po klęsce ekologicznej w Karkonoszach i Górach Izerskich – obawy a rzeczywistość (pp.

The large amount of information contained in hyperspectral data allows for much more accurate and detailed classifications of tree species and vegetation (Masaitis &

doi:10.3173/air.19.71 [Google Scholar]) concluded that the best tree species classification results were achieved using spectral angle mapper, followed closely by support vector machine (Shen et al., 2010 Shen, G., Sakai, K., &

It was proven that high spectral resolution data can be effectively used to map diverse mountain tree and non-tree vegetation with a high degree of accuracy (Marcinkowska et al., 2014 Marcinkowska, A., Zagajewski, B., Ochtyra, A., Jarocińska, A., Raczko, E., Kupkova, L., … Meuleman, K.

Ocena przydatności sieci neuronowych i danych hiperspektralnych do klasyfikacji roślinności Tatr Wysokich [assessment of neural networks and imaging spectroscopy for vegetation classification of the high tatras].

Successful tree species mapping using airborne imaging spectrometer for applications (AISA) hyperspectral data was conducted by Peerbhay et al.

The authors used the near infrared (NIR) spectral range for classification of six exotic tree species, achieving 88% overall accuracy with a kappa coefficient of 0.87 (Peerbhay et al., 2013 Peerbhay, K., Mutanga, O., &

Most forest researchers focus on the NIR spectral range for forest-related analysis because most features typical to green vegetation can be found in this region (red edge, chlorophyll and other pigment absorption bands).

Some studies show that adding shortwave infrared data from the spectral range between 1000 and 2500 nm can improve tree species classification accuracy (Lucas, Bunting, Paterson, &

Studies using hyperspectral data for forest sciences showed that RF can be successfully used to detect insect infestations, extract physiological plant characteristics (Doktor, Lausch, Spengler, &

The hybrid approach proposed by the authors proved an overall accuracy of 87%, which was significantly higher than the model using only spectral data (80%) (Naidoo, Cho, Mathieu, &

A framework for mapping tree species combining hyperspectral and LiDAR data: Role of selected classifiers and sensor across three spatial scales.

using information in a broader electromagnetic spectrum (450–2500 nm) focused on classifying five tree species in managed forests of central Germany using SVM and RF on Hyperion and HyMap data.

A framework for mapping tree species combining hyperspectral and LiDAR data: Role of selected classifiers and sensor across three spatial scales.

used a multilayered feed-forward ANN to map tree species on WorldView-2 (WV-2) data, achieving results comparable to those obtained from other classification algorithms (Omer, Mutanga, Abdel-Rahman, &

Performance of support vector machines and artificial neural network for mapping endangered tree species using WorldView-2 data in Dukuduku forest, South Africa.

A systematic search of the literature revealed that in recent years there has been a high number of studies on the use of ANN in remote sensing (Fassnacht et al., 2016 Fassnacht, F., Latifi, H., Stereńczak, K., Modzelewska, A., Lefsky, M., Waser, L., … Ghosh, A.

The aim of this paper is to evaluate three nonparametric classification algorithms (SVM, RF and ANN) in an attempt to classify the five most common tree species of the Szklarska Poręba area: spruce (Picea alba L.

- On Friday, January 18, 2019

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