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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. . Related:  Machine Learning

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. This determines which character was read. Like other machine learning methods - systems that learn from data - neural networks have been used to solve a wide variety of tasks that are hard to solve using ordinary rule-based programming, including computer vision and speech recognition. Background[edit] History[edit] Farley and Wesley A. Models[edit] or both

Markov blanket In a Bayesian network, the Markov blanket of node A includes its parents, children and the other parents of all of its children. in a Bayesian network is the set of nodes composed of 's parents, its children, and its children's other parents. In a Markov network, the Markov blanket of a node is its set of neighboring nodes. A Markov blanket may also be denoted by Every set of nodes in the network is conditionally independent of when conditioned on the set , that is, when conditioned on the Markov blanket of the node . and The Markov blanket of a node contains all the variables that shield the node from the rest of the network. In a Bayesian network, the values of the parents and children of a node evidently give information about that node; however, its children's parents also have to be included, because they can be used to explain away the node in question. See also[edit] Moral graph Notes[edit] Jump up ^ Pearl, Judea (1988).

Kernel Methods for Pattern Analysis - The Book 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. LDA for two classes[edit] Consider a set of observations . and , respectively. because is Hermitian .

Eigenvalues and eigenvectors In this shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping, and since its length is unchanged its eigenvalue is 1. An eigenvector of a square matrix that, when the matrix is multiplied by , yields a constant multiple of , the multiplier being commonly denoted by . (Because this equation uses post-multiplication by , it describes a right eigenvector.) The number is called the eigenvalue of corresponding to In analytic geometry, for example, a three-element vector may be seen as an arrow in three-dimensional space starting at the origin. is an arrow whose direction is either preserved or exactly reversed after multiplication by . is an eigenfunction of the derivative operator " ", with eigenvalue , since its derivative is is the set of all eigenvectors with the same eigenvalue, together with the zero vector.[1] An eigenbasis for . Eigenvalues and eigenvectors have many applications in both pure and applied mathematics. and or

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. For example, units in the network could represent neurons and the connections could represent synapses. Spreading activation[edit] In most connectionist models, networks change over time. Neural networks[edit] Most of the variety among neural network models comes from: Biological realism[edit] Learning[edit] The weights in a neural network are adjusted according to some learning rule or algorithm.

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. Description[edit] Lafferty, McCallum and Pereira[1] define a CRF on observations and random variables as follows: Let be a graph such that, so that is indexed by the vertices of . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets and , the observed and output variables, respectively; the conditional distribution is then modeled. Inference[edit] Parameter Learning[edit] Learning the parameters . on . . .

PubMed Central, Figure 1: AMIA Annu Symp Proc. 2003; 2003: 21–25. Perceptron Een perceptron (of meerlaags perceptron) is een neuraal netwerk waarin de neuronen in verschillende lagen met elkaar verbonden zijn. Een eerste laag bestaat uit ingangsneuronen, waar de inputsignalen aangelegd worden. Vervolgens zijn er één of meerdere 'verborgen’ lagen, die zorgen voor meer 'intelligentie' en ten slotte is er de uitgangslaag, die het resultaat van het perceptron weergeeft. Alle neuronen van een bepaalde laag zijn verbonden met alle neuronen van de volgende laag, zodat het ingangssignaal voort propageert door de verschillende lagen heen. Single-layer Perceptron[bewerken] De single-layer perceptron is de simpelste vorm van een neuraal netwerk, in 1958 door Rosenblatt ontworpen (ook wel Rosenblatt's perceptron genoemd). Rosenblatt's Perceptron Het is mogelijk het aantal klassen uit te breiden naar meer dan twee, wanneer de output layer wordt uitgebreid met meerdere output neurons. Trainingsalgoritme[bewerken] Begrippen: = inputvector = gewichtsvector (weights vector) Met = bias

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 . Within a probabilistic framework, this is done by modeling the conditional probability distribution , which can be used for predicting from Discriminative models, as opposed to generative models, do not allow one to generate samples from the joint distribution of and Examples[edit] Examples of discriminative models used in machine learning include: See also[edit] Generative model References[edit] Jump up ^ P.

Visualizious: Visualizing Social Indexing Visualizious Visualizious is a research project about social indexing (a.k.a. social tagging), information retrieval and visualization. The project is carried out by Yusef Hassan Montero and Víctor Herrero Solana (University of Granada, Spain). Visualizing Social Indexing Semantics This prototype allows visualizing both the overview and detail of semantic relationships intrinsic in the folksonomy. Screenshots (click to enlarge) Related papers Hassan-Montero, Y.; Herrero-Solana, V. (2007) Visualizing Social Indexing Semantics. Improved Tag-Clouds Tag-Cloud is a simple and widely used visual interface model, but with some restrictions that limit its utility as visual information retrieval interface. Our work presents a novel approach to Tag-Cloud's tags selection, and proposes the use of clustering algorithms for visual layout, with the aim of improve browsing experience. Screenshot (click to enlarge) Related papers Previous Research (in spanish)

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. I.e., the training algorithm can be summarized as For each input x, Do a feed-forward pass to compute activations at all hidden layers, then at the output layer to obtain an output x̂ Training[edit]

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. 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. A hidden Markov model can be considered a generalization of a mixture model where the hidden variables (or latent variables), which control the mixture component to be selected for each observation, are related through a Markov process rather than independent of each other. Description in terms of urns[edit] Figure 1. Architecture[edit] is chosen given the hidden state at time , for a total of . for some .

The Use of Fuzzy Cognitive Maps in Modeling Systems BibTeX @INPROCEEDINGS{Stylios97theuse, author = {Chrysostomos D. Stylios and Voula C. Bookmark OpenURL Abstract This paper investigates a new theory, Fuzzy Cognitive Map (FCM) Theory, and its implementation in modeling systems. Citations

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