AdaBoost While every learning algorithm will tend to suit some problem types better than others, and will typically have many different parameters and configurations to be adjusted before achieving optimal performance on a dataset, AdaBoost (with decision trees as the weak learners) is often referred to as the best out-of-the-box classifier. When used with decision tree learning, information gathered at each stage of the AdaBoost algorithm about the relative 'hardness' of each training sample is fed into the tree growing algorithm such that later trees tend to focus on harder to classify examples. Overview[edit] Training[edit] AdaBoost refers to a particular method of training a boosted classifier. where each is a weak learner that takes an object as input and returns a real valued result indicating the class of the object. -layer classifier will be positive if the sample is believed to be in the positive class and negative otherwise. Each weak learner produces an output, hypothesis of the resulting .
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 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. PCA is closely related to factor analysis. PCA is also related to canonical correlation analysis (CCA). Details[edit] Mathematically, the transformation is defined by a set of p-dimensional vectors of weights or loadings that map each row vector of X to a new vector of principal component scores , given by First component[edit] The first loading vector w(1) thus has to satisfy Further components[edit] Covariances[edit]
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.
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. and and would like to learn a function (often called hypothesis) which outputs an object , given . where is an input and is the corresponding response that we wish to get from To put it more formally, we assume that there is a joint probability distribution over , and that the training set consists of instances drawn i.i.d. from . is not a deterministic function of , but rather a random variable with conditional distribution for a fixed We also assume that we are given a non-negative real-valued loss function which measures how different the prediction of a hypothesis is from the true outcome is then defined as the expectation of the loss function: , where is the indicator notation.
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
Decision tree Traditionally, decision trees have been created manually. A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. Overview[edit] A decision tree is a flowchart-like structure in which internal node represents test on an attribute, each branch represents outcome of test and each leaf node represents class label (decision taken after computing all attributes). In decision analysis a decision tree and the closely related influence diagram is used as a visual and analytical decision support tool, where the expected values (or expected utility) of competing alternatives are calculated. A decision tree consists of 3 types of nodes: Decision tree building blocks[edit] See also[edit]
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 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]
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. Example[edit]
Vis Group | Orion: A System for Modeling, Transformation and Visualization of Multidimensional Heterogeneous Networks Orion Visualizations of Online Health Communities. From left-to-right: (a) A sorted matrix view of an online asthma forum. A few central leaders divide up responses among incoming questions. (b) Node-link diagram of highly active cluster of the same forum. abstract The study of complex activities such as scientific production and software development often require modeling connections among heterogeneous entities including people, institutions and artifacts. materials and links citation IEEE Visual Analytics Science & Technology (VAST), 2011