This is a list of notable JavaScript libraries. == Constraint programming == Cassowary (software) CHR.js == DOM (manipulation) oriented == Google Polymer Dojo Toolkit jQuery MooTools Prototype JavaScript Framework == Graphical/visualization (canvas, SVG, or WebGL related) == AnyChart Apache ECharts Babylon.js Chart.js Cytoscape D3.js Dojo Toolkit FusionCharts Google Charts JointJS p5.js Plotly.js Processing.js Raphaël RGraph SWFObject Teechart Three.js Velocity.js Verge3D Webix == GUI (Graphical user interface) and widget related == Angular (application platform) by Google AngularJS by Google Bootstrap Dojo Widgets Ext JS by Sencha Foundation by ZURB jQuery UI jQWidgets OpenUI5 by SAP Polymer (library) by Google qooxdoo React.js by Meta/Facebook Vue.js Webix WinJS Svelte === No longer actively developed === Glow Lively Kernel Script.aculo.us YUI Library == Pure JavaScript/Ajax == Google Closure Library JsPHP Microsoft's Ajax library MochiKit PDF.js Socket.IO Spry framework Underscore.js == Template systems == jQuery Mobile Mustache Jinja-JS Twig.js == Unit testing == Jasmine Mocha QUnit == Test automation == Playwright Cypress == Web-application related (MVC, MVVM) == Angular (application platform) by Google AngularJS by Google Backbone.js Echo Ember.js Enyo Express.js Ext JS Google Web Toolkit JsRender/JsViews Knockout Meteor Mojito MooTools Next.js Nuxt.js OpenUI5 by SAP Polymer (library) by Google Prototype JavaScript Framework qooxdoo React.js SproutCore svelte Vue.js == Other == Blockly Cannon.js MathJax Modernizr TensorFlow Brain.js
Glossary of machine vision
The following are common definitions related to the machine vision field. General related fields Machine vision Computer vision Image processing Signal processing == 0-9 == 1394. FireWire is Apple Inc.'s brand name for the IEEE 1394 interface. It is also known as i.Link (Sony's name) or IEEE 1394 (although the 1394 standard also defines a backplane interface). It is a personal computer (and digital audio/digital video) serial bus interface standard, offering high-speed communications and isochronous real-time data services. 1D. One-dimensional. 2D computer graphics. The computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. 3D computer graphics. 3D computer graphics are different from 2D computer graphics in that a three-dimensional representation of geometric data is stored in the computer for the purposes of performing calculations and rendering 2D images. Such images may be for later display or for real-time viewing. Despite these differences, 3D computer graphics rely on many of the same algorithms as 2D computer vector graphics in the wire frame model and 2D computer raster graphics in the final rendered display. In computer graphics software, the distinction between 2D and 3D is occasionally blurred; 2D applications may use 3D techniques to achieve effects such as lighting, and primarily 3D may use 2D rendering techniques. 3D scanner. This is a device that analyzes a real-world object or environment to collect data on its shape and possibly color. The collected data can then be used to construct digital, three dimensional models useful for a wide variety of applications. == A == Aberration. Optically, defocus refers to a translation along the optical axis away from the plane or surface of best focus. In general, defocus reduces the sharpness and contrast of the image. What should be sharp, high-contrast edges in a scene become gradual transitions. Algebraic distance or algebraic error. The algebraic distance from a point xi to a curve or surface defined by f ( x , β ) = 0 {\displaystyle f(x,\beta )=0} is the value of f ( x i , β ) {\displaystyle f(x_{i},\beta )} , i.e. the residual in the least squares problem with data point (xi, 0) and model function f. This term is mainly used in computer vision.[1][2] Aperture. In context of photography or machine vision, aperture refers to the diameter of the aperture stop of a photographic lens. The aperture stop can be adjusted to control the amount of light reaching the film or image sensor. aspect ratio (image). The aspect ratio of an image is its displayed width divided by its height (usually expressed as "x:y"). Angular resolution. Describes the resolving power of any image forming device such as an optical or radio telescope, a microscope, a camera, or an eye. Automated optical inspection. == B == Barcode. A barcode (also bar code) is a machine-readable representation of information in a visual format on a surface. Blob discovery. Inspecting an image for discrete blobs of connected pixels (e.g. a black hole in a grey object) as image landmarks. These blobs frequently represent optical targets for machining, robotic capture, or manufacturing failure. Bitmap. A raster graphics image, digital image, or bitmap, is a data file or structure representing a generally rectangular grid of pixels, or points of color, on a computer monitor, paper, or other display device. == C == Camera. A camera is a device used to take pictures, either singly or in sequence. A camera that takes pictures singly is sometimes called a photo camera to distinguish it from a video camera. Camera Link. Camera Link is a serial communication protocol designed for computer vision applications based on the National Semiconductor interface Channel-link. It was designed for the purpose of standardizing scientific and industrial video products including cameras, cables and frame grabbers. The standard is maintained and administered by the Automated Imaging Association, or AIA, the global machine vision industry's trade group. Charge-coupled device. A charge-coupled device (CCD) is a sensor for recording images, consisting of an integrated circuit containing an array of linked, or coupled, capacitors. CCD sensors and cameras tend to be more sensitive, less noisy, and more expensive than CMOS sensors and cameras. CIE 1931 Color Space. In the study of the perception of color, one of the first mathematically defined color spaces was the CIE XYZ color space (also known as CIE 1931 color space), created by the International Commission on Illumination (CIE) in 1931. CMOS. CMOS ("see-moss")stands for complementary metal-oxide semiconductor, is a major class of integrated circuits. CMOS imaging sensors for machine vision are cheaper than CCD sensors but more noisy. CoaXPress. CoaXPress (CXP) is an asymmetric high speed serial communication standard over coaxial cable. CoaXPress combines high speed image data, low speed camera control and power over a single coaxial cable. The standard is maintained by JIIA, the Japan Industrial Imaging Association. Color. The perception of the frequency (or wavelength) of light, and can be compared to how pitch (or a musical note) is the perception of the frequency or wavelength of sound. Color blindness. Also known as color vision deficiency, in humans is the inability to perceive differences between some or all colors that other people can distinguish Color temperature. "White light" is commonly described by its color temperature. A traditional incandescent light source's color temperature is determined by comparing its hue with a theoretical, heated black-body radiator. The lamp's color temperature is the temperature in kelvins at which the heated black-body radiator matches the hue of the lamp. Color vision. CV is the capacity of an organism or machine to distinguish objects based on the wavelengths (or frequencies) of the light they reflect or emit. computer vision. The study and application of methods which allow computers to "understand" image content. Contrast. In visual perception, contrast is the difference in visual properties that makes an object (or its representation in an image) distinguishable from other objects and the background. C-Mount. Standardized adapter for optical lenses on CCD - cameras. C-Mount lenses have a back focal distance 17.5 mm vs. 12.5 mm for "CS-mount" lenses. A C-Mount lens can be used on a CS-Mount camera through the use of a 5 mm extension adapter. C-mount is a 1" diameter, 32 threads per inch mounting thread (1"-32UN-2A.) CS-Mount. Same as C-Mount but the focal point is 5 mm shorter. A CS-Mount lens will not work on a C-Mount camera. CS-mount is a 1" diameter, 32 threads per inch mounting thread. == D == Data matrix. A two dimensional Barcode. Depth of field. In optics, particularly photography and machine vision, the depth of field (DOF) is the distance in front of and behind the subject which appears to be in focus. Depth perception. DP is the visual ability to perceive the world in three dimensions. It is a trait common to many higher animals. Depth perception allows the beholder to accurately gauge the distance to an object. Diaphragm. In optics, a diaphragm is a thin opaque structure with an opening (aperture) at its centre. The role of the diaphragm is to stop the passage of light, except for the light passing through the aperture. == E == Edge detection. ED marks the points in a digital image at which the luminous intensity changes sharply. It also marks the points of luminous intensity changes of an object or spatial-taxon silhouette. Electromagnetic interference. Radio Frequency Interference (RFI) is electromagnetic radiation which is emitted by electrical circuits carrying rapidly changing signals, as a by-product of their normal operation, and which causes unwanted signals (interference or noise) to be induced in other circuits. == F == FireWire. FireWire (also known as i. Link or IEEE 1394) is a personal computer (and digital audio/video) serial bus interface standard, offering high-speed communications. It is often used as an interface for industrial cameras. Fixed-pattern noise. Flat-field correction. Frame grabber. An electronic device that captures individual, digital still frames from an analog video signal or a digital video stream. Fringe Projection Technique. 3D data acquisition technique employing projector displaying fringe pattern on a surface of measured piece, and one or more cameras recording image(s). Field of view. The field of view (FOV) is the part which can be seen by the machine vision system at one moment. The field of view depends from the lens of the system and from the working distance between object and camera. Focus. An image, or image point or region, is said to be in focus if light from object points is converged about as well as possible in the image; conversely, it is out of focus if light is not w
Consensus clustering
Consensus clustering is a method of aggregating (potentially conflicting) results from multiple clustering algorithms. Also called cluster ensembles or aggregation of clustering (or partitions), it refers to the situation in which a number of different (input) clusterings have been obtained for a particular dataset and it is desired to find a single (consensus) clustering which is a better fit in some sense than the existing clusterings. Consensus clustering is thus the problem of reconciling clustering information about the same data set coming from different sources or from different runs of the same algorithm. When cast as an optimization problem, consensus clustering is known as median partition, and has been shown to be NP-complete, even when the number of input clusterings is three. Consensus clustering for unsupervised learning is analogous to ensemble learning in supervised learning. == Issues with existing clustering techniques == Current clustering techniques do not address all the requirements adequately. Dealing with large number of dimensions and large number of data items can be problematic because of time complexity; Effectiveness of the method depends on the definition of "distance" (for distance-based clustering) If an obvious distance measure doesn't exist, we must "define" it, which is not always easy, especially in multidimensional spaces. The result of the clustering algorithm (that, in many cases, can be arbitrary itself) can be interpreted in different ways. == Justification for using consensus clustering == There are potential shortcomings for all existing clustering techniques. This may cause interpretation of results to become difficult, especially when there is no knowledge about the number of clusters. Clustering methods are also very sensitive to the initial clustering settings, which can cause non-significant data to be amplified in non-reiterative methods. An extremely important issue in cluster analysis is the validation of the clustering results, that is, how to gain confidence about the significance of the clusters provided by the clustering technique (cluster numbers and cluster assignments). Lacking an external objective criterion (the equivalent of a known class label in supervised analysis), this validation becomes somewhat elusive. Iterative descent clustering methods, such as the SOM and k-means clustering circumvent some of the shortcomings of hierarchical clustering by providing for univocally defined clusters and cluster boundaries. Consensus clustering provides a method that represents the consensus across multiple runs of a clustering algorithm, to determine the number of clusters in the data, and to assess the stability of the discovered clusters. The method can also be used to represent the consensus over multiple runs of a clustering algorithm with random restart (such as K-means, model-based Bayesian clustering, SOM, etc.), so as to account for its sensitivity to the initial conditions. It can provide data for a visualization tool to inspect cluster number, membership, and boundaries. However, they lack the intuitive and visual appeal of hierarchical clustering dendrograms, and the number of clusters must be chosen a priori. == The Monti consensus clustering algorithm == The Monti consensus clustering algorithm is one of the most popular consensus clustering algorithms and is used to determine the number of clusters, K {\displaystyle K} . Given a dataset of N {\displaystyle N} total number of points to cluster, this algorithm works by resampling and clustering the data, for each K {\displaystyle K} and a N × N {\displaystyle N\times N} consensus matrix is calculated, where each element represents the fraction of times two samples clustered together. A perfectly stable matrix would consist entirely of zeros and ones, representing all sample pairs always clustering together or not together over all resampling iterations. The relative stability of the consensus matrices can be used to infer the optimal K {\displaystyle K} . More specifically, given a set of points to cluster, D = { e 1 , e 2 , . . . e N } {\displaystyle D=\{e_{1},e_{2},...e_{N}\}} , let D 1 , D 2 , . . . , D H {\displaystyle D^{1},D^{2},...,D^{H}} be the list of H {\displaystyle H} perturbed (resampled) datasets of the original dataset D {\displaystyle D} , and let M h {\displaystyle M^{h}} denote the N × N {\displaystyle N\times N} connectivity matrix resulting from applying a clustering algorithm to the dataset D h {\displaystyle D^{h}} . The entries of M h {\displaystyle M^{h}} are defined as follows: M h ( i , j ) = { 1 , if points i and j belong to the same cluster 0 , otherwise {\displaystyle M^{h}(i,j)={\begin{cases}1,&{\text{if}}{\text{ points i and j belong to the same cluster}}\\0,&{\text{otherwise}}\end{cases}}} Let I h {\displaystyle I^{h}} be the N × N {\displaystyle N\times N} identicator matrix where the ( i , j ) {\displaystyle (i,j)} -th entry is equal to 1 if points i {\displaystyle i} and j {\displaystyle j} are in the same perturbed dataset D h {\displaystyle D^{h}} , and 0 otherwise. The indicator matrix is used to keep track of which samples were selected during each resampling iteration for the normalisation step. The consensus matrix C {\displaystyle C} is defined as the normalised sum of all connectivity matrices of all the perturbed datasets and a different one is calculated for every K {\displaystyle K} . C ( i , j ) = ( ∑ h = 1 H M h ( i , j ) ∑ h = 1 H I h ( i , j ) ) {\displaystyle C(i,j)=\left({\frac {\textstyle \sum _{h=1}^{H}M^{h}(i,j)\displaystyle }{\sum _{h=1}^{H}I^{h}(i,j)}}\right)} That is the entry ( i , j ) {\displaystyle (i,j)} in the consensus matrix is the number of times points i {\displaystyle i} and j {\displaystyle j} were clustered together divided by the total number of times they were selected together. The matrix is symmetric and each element is defined within the range [ 0 , 1 ] {\displaystyle [0,1]} . A consensus matrix is calculated for each K {\displaystyle K} to be tested, and the stability of each matrix, that is how far the matrix is towards a matrix of perfect stability (just zeros and ones) is used to determine the optimal K {\displaystyle K} . One way of quantifying the stability of the K {\displaystyle K} th consensus matrix is examining its CDF curve (see below). == Over-interpretation potential of the Monti consensus clustering algorithm == Monti consensus clustering can be a powerful tool for identifying clusters, but it needs to be applied with caution as shown by Şenbabaoğlu et al. It has been shown that the Monti consensus clustering algorithm is able to claim apparent stability of chance partitioning of null datasets drawn from a unimodal distribution, and thus has the potential to lead to over-interpretation of cluster stability in a real study. If clusters are not well separated, consensus clustering could lead one to conclude apparent structure when there is none, or declare cluster stability when it is subtle. Identifying false positive clusters is a common problem throughout cluster research, and has been addressed by methods such as SigClust and the GAP-statistic. However, these methods rely on certain assumptions for the null model that may not always be appropriate. Şenbabaoğlu et al demonstrated the original delta K metric to decide K {\displaystyle K} in the Monti algorithm performed poorly, and proposed a new superior metric for measuring the stability of consensus matrices using their CDF curves. In the CDF curve of a consensus matrix, the lower left portion represents sample pairs rarely clustered together, the upper right portion represents those almost always clustered together, whereas the middle segment represent those with ambiguous assignments in different clustering runs. The proportion of ambiguous clustering (PAC) score measure quantifies this middle segment; and is defined as the fraction of sample pairs with consensus indices falling in the interval (u1, u2) ∈ [0, 1] where u1 is a value close to 0 and u2 is a value close to 1 (for instance u1=0.1 and u2=0.9). A low value of PAC indicates a flat middle segment, and a low rate of discordant assignments across permuted clustering runs. One can therefore infer the optimal number of clusters by the K {\displaystyle K} value having the lowest PAC. == Related work == Clustering ensemble (Strehl and Ghosh): They considered various formulations for the problem, most of which reduce the problem to a hyper-graph partitioning problem. In one of their formulations they considered the same graph as in the correlation clustering problem. The solution they proposed is to compute the best k-partition of the graph, which does not take into account the penalty for merging two nodes that are far apart. Clustering aggregation (Fern and Brodley): They applied the clustering aggregation idea to a collection of soft clusterings they obtained by random projections. They used an agglomerative algorithm
Persian Speech Corpus
The Persian Speech Corpus is a Modern Persian speech corpus for speech synthesis. The corpus contains phonetic and orthographic transcriptions of about 2.5 hours of Persian speech aligned with recorded speech on the phoneme level, including annotations of word boundaries. Previous spoken corpora of Persian include FARSDAT, which consists of read aloud speech from newspaper texts from 100 Persian speakers and the Telephone FARsi Spoken language DATabase (TFARSDAT) which comprises seven hours of read and spontaneous speech produced by 60 native speakers of Persian from ten regions of Iran. The Persian Speech Corpus was built using the same methodologies laid out in the doctoral project on Modern Standard Arabic of Nawar Halabi at the University of Southampton. The work was funded by MicroLinkPC, who own an exclusive license to commercialise the corpus, though the corpus is available for non-commercial use through the corpus' website. It is distributed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. The corpus was built for speech synthesis purposes, but has been used for building HMM based voices in Persian. It can also be used to automatically align other speech corpora with their phonetic transcript and could be used as part of a larger corpus for training speech recognition systems. == Contents == The corpus is downloadable from its website, and contains the following: 396 .wav files containing spoken utterances 396 .lab files containing text utterances 396 .TextGrid files containing the phoneme labels with time stamps of the boundaries where these occur in the .wav files. phonetic-transcript.txt which has the form "[wav_filename]" "[Phoneme Sequence]" in every line orthographic-transcript.txt which has the form "[wav_filename]" "[Orthographic Transcript]" in every line
Recursive neural network
A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order. These networks were first introduced to learn distributed representations of structure (such as logical terms), but have been successful in multiple applications, for instance in learning sequence and tree structures in natural language processing (mainly continuous representations of phrases and sentences based on word embeddings). == Architectures == === Basic === In the simplest architecture, nodes are combined into parents using a weight matrix (which is shared across the whole network) and a non-linearity such as the tanh {\displaystyle \tanh } hyperbolic function. If c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} are n {\displaystyle n} -dimensional vector representations of nodes, their parent will also be an n {\displaystyle n} -dimensional vector, defined as: p 1 , 2 = tanh ( W [ c 1 ; c 2 ] ) {\displaystyle p_{1,2}=\tanh(W[c_{1};c_{2}])} where W {\displaystyle W} is a learned n × 2 n {\displaystyle n\times 2n} weight matrix. This architecture, with a few improvements, has been used for successfully parsing natural scenes, syntactic parsing of natural language sentences, and recursive autoencoding and generative modeling of 3D shape structures in the form of cuboid abstractions. === Recursive cascade correlation (RecCC) === RecCC is a constructive neural network approach to deal with tree domains with pioneering applications to chemistry and extension to directed acyclic graphs. === Unsupervised RNN === A framework for unsupervised RNN has been introduced in 2004. === Tensor === Recursive neural tensor networks use a single tensor-based composition function for all nodes in the tree. == Training == === Stochastic gradient descent === Typically, stochastic gradient descent (SGD) is used to train the network. The gradient is computed using backpropagation through structure (BPTS), a variant of backpropagation through time used for recurrent neural networks. == Properties == The universal approximation capability of RNNs over trees has been proved in literature. == Related models == === Recurrent neural networks === Recurrent neural networks are recursive artificial neural networks with a certain structure: that of a linear chain. Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step. === Tree Echo State Networks === An efficient approach to implement recursive neural networks is given by the Tree Echo State Network within the reservoir computing paradigm. === Extension to graphs === Extensions to graphs include graph neural network (GNN), Neural Network for Graphs (NN4G), and more recently convolutional neural networks for graphs.
Deep learning
In machine learning, deep learning (DL) focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and revolves around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Early forms of neural networks were inspired by information processing and distributed communication nodes in biological systems, particularly the human brain. However, current neural networks do not intend to model the brain function of organisms, and are generally seen as low-quality models for that purpose. == Overview == Most modern deep learning models are based on multi-layered neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines. Fundamentally, deep learning refers to a class of machine learning algorithms in which a hierarchy of layers is used to transform input data into a progressively more abstract and composite representation. For example, in an image recognition model, the raw input may be an image (represented as a tensor of pixels). The first representational layer may attempt to identify basic shapes such as lines and circles, the second layer may compose and encode arrangements of edges, the third layer may encode a nose and eyes, and the fourth layer may recognize that the image contains a face. Importantly, a deep learning process can learn which features to optimally place at which level on its own. Prior to deep learning, machine learning techniques often involved hand-crafted feature engineering to transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted and the model discovers useful feature representations from the data automatically. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction. The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited. No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than two. CAP of depth two has been shown to be a universal approximator in the sense that it can emulate any function. Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > two) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively. Deep learning architectures can be constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance. Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data is more abundant than labeled data. Examples of deep structures that can be trained in an unsupervised manner are deep belief networks. The term deep learning was introduced to the machine learning community by Rina Dechter in 1986, and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons. The etymology of the term is more complicated. == Interpretations == Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference. The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as Kunihiko Fukushima's rectified linear unit. The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator. The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop. == History == === Before 1980 === There are two types of artificial neural network (ANN): feedforward neural network (FNN) or multilayer perceptron (MLP) and recurrent neural networks (RNN). RNNs have cycles in their connectivity structure, whereas FNNs do not. In the 1920s, Wilhelm Lenz and Ernst Ising created the Ising model which is essentially a non-learning RNN architecture consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was republished by John Hopfield in 1982. Other early recurrent neural networks were published by Kaoru Nakano in 1971. Already in 1948, Alan Turing produced work on "Intelligent Machinery" that was not published in his lifetime, containing "ideas related to artificial evolution and learning RNNs". Frank Rosenblatt (1958) proposed the perceptron, an MLP with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. He later published a 1962 book that also introduced variants and computer experiments, including a version with four-layer perceptrons "with adaptive preterminal networks" where the last two layers have learned weights (here he credits H. D. Block and B. W. Knight). The book cites an earlier network by R. D. Joseph (1960) "functionally equivalent to a variation of" this four-layer system (the book mentions Joseph over 30 times). Should Joseph therefore be considered the originator of proper adaptive multilayer perceptrons with learning hidden units? Unfortunately, the learning algorithm was not a functional one, and fell into oblivion. The first working deep learning algorithm was the Group method of data handling, a method to train arbitrarily deep neural networks, published by Alexey Ivakhnenko and Lapa in 1965. They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron to handle more complex, nonlinear, and hierarchical relationships. A 1971 paper described a deep network with eight layers trained by this method, which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates". The first deep learning multilayer perceptron trained by stochastic gradient descent was published in 1967 by Shun'ichi
Fitness approximation
Fitness approximation aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation. Fitness approximation in evolutionary optimization can be seen as a sub-area of data-driven evolutionary optimization. == Approximate models in function optimization == === Motivation === In many real-world optimization problems including engineering problems, the number of fitness function evaluations needed to obtain a good solution dominates the optimization cost. In order to obtain efficient optimization algorithms, it is crucial to use prior information gained during the optimization process. Conceptually, a natural approach to utilizing the known prior information is building a model of the fitness function to assist in the selection of candidate solutions for evaluation. A variety of techniques for constructing such a model, often also referred to as surrogates, metamodels or approximation models – for computationally expensive optimization problems have been considered. === Approaches === Common approaches to constructing approximate models based on learning and interpolation from known fitness values of a small population include: Low-degree polynomials and regression models Fourier surrogate modeling Artificial neural networks including Multilayer perceptrons Radial basis function network Support vector machines Due to the limited number of training samples and high dimensionality encountered in engineering design optimization, constructing a globally valid approximate model remains difficult. As a result, evolutionary algorithms using such approximate fitness functions may converge to local optima. Therefore, it can be beneficial to selectively use the original fitness function together with the approximate model.