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Support vector machine

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 and recognize patterns, used for classification and regression analysis. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other, making it a non-probabilistic binary linear classifier. 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. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on. Definition[edit] 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. Note that if . belongs. .

http://en.wikipedia.org/wiki/Support_vector_machine

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Connectionism Connectionism is a set of approaches in the fields of artificial intelligence, cognitive psychology, cognitive science, neuroscience, and philosophy of mind, that models mental or behavioral phenomena as the emergent processes of interconnected networks of simple units. There are many forms of connectionism, but the most common forms use neural network models. Basic principles[edit] The central connectionist principle is that mental phenomena can be described by interconnected networks of simple and often uniform units. The form of the connections and the units can vary from model to model.

Principal component analysis PCA of a multivariate Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the (0.878, 0.478) direction and of 1 in the orthogonal direction. The vectors shown are the eigenvectors of the covariance matrix scaled by the square root of the corresponding eigenvalue, and shifted so their tails are at the mean. Principal component analysis (PCA) is a statistical procedure that uses orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. PCA is closely related to factor analysis. Factor analysis typically incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix.

Artificial neural network An artificial neural network is an interconnected group of nodes, akin to the vast network of neurons in a brain. Here, each circular node represents an artificial neuron and an arrow represents a connection from the output of one neuron to the input of another. For example, a neural network for handwriting recognition is defined by a set of input neurons which may be activated by the pixels of an input image. After being weighted and transformed by a function (determined by the network's designer), the activations of these neurons are then passed on to other neurons. This process is repeated until finally, an output neuron is activated.

Empirical risk minimization Empirical risk minimization (ERM) is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on the performance of learning algorithms. Background[edit] Consider the following situation, which is a general setting of many supervised learning problems. We have two spaces of objects and and would like to learn a function

Linear discriminant analysis LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements.[1][2] However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label).[3] Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method. LDA works when the measurements made on independent variables for each observation are continuous quantities.

Autoencoder An autoencoder, autoassociator or Diabolo network[1]:19 is an artificial neural network used for learning efficient codings.[2] The aim of an auto-encoder is to learn a compressed, distributed representation (encoding) for a set of data, typically for the purpose of dimensionality reduction. Overview[edit] Architecturally, the simplest form of the autoencoder is a feedforward, non-recurrent neural net that is very similar to the multilayer perceptron (MLP), with an input layer, an output layer and one or more hidden layers connecting them. The difference with the MLP is that in an autoencoder, the output layer has equally many nodes as the input layer, and instead of training it to predict some target value y given inputs x, an autoencoder is trained to reconstruct its own inputs x.

Binary classification medical testing to determine if a patient has certain disease or not (the classification property is the presence of the disease)quality control in factories; i.e. deciding if a new product is good enough to be sold, or if it should be discarded (the classification property is being good enough)deciding whether a page or an article should be in the result set of a search or not (the classification property is the relevance of the article, or the usefulness to the user) Statistical classification in general is one of the problems studied in computer science, in order to automatically learn classification systems; some methods suitable for learning binary classifiers include the decision trees, Bayesian networks, support vector machines, neural networks, probit regression, and logit regression. Sometimes, classification tasks are trivial. Given 100 balls, some of them red and some blue, a human with normal color vision can easily separate them into red ones and blue ones.

Conditional random field Conditional random fields (CRFs) are a class of statistical modelling method often applied in pattern recognition and machine learning, where they are used for structured prediction. Whereas an ordinary classifier predicts a label for a single sample without regard to "neighboring" samples, a CRF can take context into account; e.g., the linear chain CRF popular in natural language processing predicts sequences of labels for sequences of input samples. CRFs are a type of discriminative undirected probabilistic graphical model. It is used to encode known relationships between observations and construct consistent interpretations. It is often used for labeling or parsing of sequential data, such as natural language text or biological sequences[1] and in computer vision.[2] Specifically, CRFs find applications in shallow parsing,[3] named entity recognition[4] and gene finding, among other tasks, being an alternative to the related hidden Markov models. Description[edit]

Feedforward neural network In a feed forward network information always moves one direction; it never goes backwards. A feedforward neural network is an artificial neural network where connections between the units do not form a directed cycle. This is different from recurrent neural networks. The feedforward neural network was the first and simplest type of artificial neural network devised.

Rademacher complexity In statistics and machine learning, Rademacher complexity, named after Hans Rademacher, measures richness of a class of real-valued functions with respect to a probability distribution. Given a training sample , and a hypotheses set (where is a class of real-valued functions defined on a domain space Discriminative model Discriminative models, also called conditional models, are a class of models used in machine learning for modeling the dependence of an unobserved variable on an observed variable .

Feature learning Feature learning or representation learning[1] is a set of techniques in machine learning that learn a transformation of "raw" inputs to a representation that can be effectively exploited in a supervised learning task such as classification. Feature learning algorithms themselves may be either unsupervised or supervised, and include autoencoders,[2] dictionary learning, matrix factorization,[3] restricted Boltzmann machines[2] and various form of clustering.[2][4][5] When the feature learning can be performed in an unsupervised way, it enables a form of semisupervised learning where first, features are learned from an unlabeled dataset, which are then employed to improve performance in a supervised setting with labeled data.[6][7] Clustering as feature learning[edit]

M-estimator In statistics, M-estimators are a broad class of estimators, which are obtained as the minima of sums of functions of the data. Least-squares estimators are M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. The statistical procedure of evaluating an M-estimator on a data set is called M-estimation. Historical motivation[edit] The method of least squares is a prototypical M-estimator, since the estimator is defined as a minimum of the sum of squares of the residuals. Hidden Markov model In simpler Markov models (like a Markov chain), the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a hidden Markov model, the state is not directly visible, but output, dependent on the state, is visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states. Note that the adjective 'hidden' refers to the state sequence through which the model passes, not to the parameters of the model; the model is still referred to as a 'hidden' Markov model even if these parameters are known exactly. Hidden Markov models are especially known for their application in temporal pattern recognition such as speech, handwriting, gesture recognition,[7] part-of-speech tagging, musical score following,[8] partial discharges[9] and bioinformatics.

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