(Not to be confused with the lazy learning regime, see Neural tangent kernel). In machine learning, lazy learning is a learning method in which generalization of the training data is, in theory, delayed until a query is made to the system, as opposed to eager learning, where the system tries to generalize the training data before receiving queries. The primary motivation for employing lazy learning, as in the K-nearest neighbors algorithm, used by online recommendation systems ("people who viewed/purchased/listened to this movie/item/tune also ...") is that the data set is continuously updated with new entries (e.g., new items for sale at Amazon, new movies to view at Netflix, new clips at YouTube, new music at Spotify or Pandora). Because of the continuous update, the "training data" would be rendered obsolete in a relatively short time especially in areas like books and movies, where new best-sellers or hit movies/music are published/released continuously. Therefore, one cannot really talk of a "training phase". Lazy classifiers are most useful for large, continuously changing datasets with few attributes that are commonly queried. Specifically, even if a large set of attributes exist - for example, books have a year of publication, author/s, publisher, title, edition, ISBN, selling price, etc. - recommendation queries rely on far fewer attributes - e.g., purchase or viewing co-occurrence data, and user ratings of items purchased/viewed. == Advantages == The main advantage gained in employing a lazy learning method is that the target function will be approximated locally, such as in the k-nearest neighbor algorithm. Because the target function is approximated locally for each query to the system, lazy learning systems can simultaneously solve multiple problems and deal successfully with changes in the problem domain. At the same time they can reuse a lot of theoretical and applied results from linear regression modelling (notably PRESS statistic) and control. It is said that the advantage of this system is achieved if the predictions using a single training set are only developed for few objects. This can be demonstrated in the case of the k-NN technique, which is instance-based and function is only estimated locally. == Disadvantages == Theoretical disadvantages with lazy learning include: The large space requirement to store the entire training dataset. In practice, this is not an issue because of advances in hardware and the relatively small number of attributes (e.g., as co-occurrence frequency) that need to be stored. Particularly noisy training data increases the case base unnecessarily, because no abstraction is made during the training phase. In practice, as stated earlier, lazy learning is applied to situations where any learning performed in advance soon becomes obsolete because of changes in the data. Also, for the problems for which lazy learning is optimal, "noisy" data does not really occur - the purchaser of a book has either bought another book or hasn't. Lazy learning methods are usually slower to evaluate. In practice, for very large databases with high concurrency loads, the queries are not postponed until actual query time, but recomputed in advance on a periodic basis - e.g., nightly, in anticipation of future queries, and the answers stored. This way, the next time new queries are asked about existing entries in the database, the answers are merely looked up rapidly instead of having to be computed on the fly, which would almost certainly bring a high-concurrency multi-user system to its knees. Larger training data also entail increased cost. Particularly, there is the fixed amount of computational cost, where a processor can only process a limited amount of training data points. There are standard techniques to improve re-computation efficiency so that a particular answer is not recomputed unless the data that impact this answer has changed (e.g., new items, new purchases, new views). In other words, the stored answers are updated incrementally. This approach, used by large e-commerce or media sites, has long been used in the Entrez portal of the National Center for Biotechnology Information (NCBI) to precompute similarities between the different items in its large datasets: biological sequences, 3-D protein structures, published-article abstracts, etc. Because "find similar" queries are asked so frequently, the NCBI uses highly parallel hardware to perform nightly recomputation. The recomputation is performed only for new entries in the datasets against each other and against existing entries: the similarity between two existing entries need not be recomputed. == Examples of Lazy Learning Methods == K-nearest neighbors, which is a special case of instance-based learning. Local regression. Lazy naive Bayes rules, which are extensively used in commercial spam detection software. Here, the spammers keep getting smarter and revising their spamming strategies, and therefore the learning rules must also be continually updated.
Depth peeling
In computer graphics, depth peeling is an exact multipass method of order-independent transparency that extracts transparent fragments into depth layers and composites those layers in depth order. Depth peeling has the advantage of being able to generate correct results even for complex images containing intersecting transparent objects. == Method == Depth peeling works by rendering the image multiple times. Depth peeling uses two Z buffers, one that works conventionally, and one that is not modified, and sets the minimum distance at which a fragment can be drawn without being discarded. For each pass, the previous pass' conventional Z-buffer is used as the minimal Z-buffer, so each pass removes already-captured nearer fragments and draws the next depth layer behind them. The resulting images can then be composited in depth order to form a single image. A major drawback of classical depth peeling is performance: it requires one geometry pass per peeled layer, so scenes with high depth complexity require many passes that each re-rasterize the transparent geometry. Later variants reduce the number of passes by peeling multiple layers or both front and back layers in a pass. Dual depth peeling reduces the geometry-pass count from N to N/2+1 by peeling one layer from the front and one from the back in each pass, while multi-layer depth peeling peels several layers per pass and reported up to an 8x speed-up in RGBA8 settings.
GeWorkbench
geWorkbench (genomics Workbench) is an open-source software platform for integrated genomic data analysis. It is a desktop application written in the programming language Java. geWorkbench uses a component architecture. As of 2016, there are more than 70 plug-ins available, providing for the visualization and analysis of gene expression, sequence, and structure data. geWorkbench is the Bioinformatics platform of MAGNet, the National Center for the Multi-scale Analysis of Genomic and Cellular Networks, one of the 8 National Centers for Biomedical Computing funded through the NIH Roadmap (NIH Common Fund). Many systems and structure biology tools developed by MAGNet investigators are available as geWorkbench plugins. == Features == Computational analysis tools such as t-test, hierarchical clustering, self-organizing maps, regulatory network reconstruction, BLAST searches, pattern-motif discovery, protein structure prediction, structure-based protein annotation, etc. Visualization of gene expression (heatmaps, volcano plot), molecular interaction networks (through Cytoscape), protein sequence and protein structure data (e.g., MarkUs). Integration of gene and pathway annotation information from curated sources as well as through Gene Ontology enrichment analysis. Component integration through platform management of inputs and outputs. Among data that can be shared between components are expression datasets, interaction networks, sample and marker (gene) sets and sequences. Dataset history tracking - complete record of data sets used and input settings. Integration with 3rd party tools such as GenePattern, Cytoscape, and Genomespace. Demonstrations of each feature described can be found at GeWorkbench-web Tutorials. == Versions == geWorkbench is open-source software that can be downloaded and installed locally. A zip file of the released version Java source is also available. Prepackaged installer versions also exist for Windows, Macintosh, and Linux.
Radial basis function
In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input and some fixed point, either the origin, so that φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} , or some other fixed point c {\textstyle \mathbf {c} } , called a center, so that φ ( x ) = φ ^ ( ‖ x − c ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} -\mathbf {c} \right\|)} . Any function φ {\textstyle \varphi } that satisfies the property φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection { φ k } k {\displaystyle \{\varphi _{k}\}_{k}} which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which stemmed from Michael J. D. Powell's seminal research from 1977. RBFs are also used as a kernel in support vector classification. The technique has proven effective and flexible enough that radial basis functions are now applied in a variety of engineering applications. == Definition == A radial function is a function φ : [ 0 , ∞ ) → R {\textstyle \varphi :[0,\infty )\to \mathbb {R} } . When paired with a norm ‖ ⋅ ‖ : V → [ 0 , ∞ ) {\textstyle \|\cdot \|:V\to [0,\infty )} on a vector space, a function of the form φ c = φ ( ‖ x − c ‖ ) {\textstyle \varphi _{\mathbf {c} }=\varphi (\|\mathbf {x} -\mathbf {c} \|)} is said to be a radial kernel centered at c ∈ V {\textstyle \mathbf {c} \in V} . A radial function and the associated radial kernels are said to be radial basis functions if, for any finite set of nodes { x k } k = 1 n ⊆ V {\displaystyle \{\mathbf {x} _{k}\}_{k=1}^{n}\subseteq V} , all of the following conditions are true: === Examples === Commonly used types of radial basis functions include (writing r = ‖ x − x i ‖ {\textstyle r=\left\|\mathbf {x} -\mathbf {x} _{i}\right\|} and using ε {\textstyle \varepsilon } to indicate a shape parameter that can be used to scale the input of the radial kernel): == Approximation == Radial basis functions are typically used to build up function approximations of the form where the approximating function y ( x ) {\textstyle y(\mathbf {x} )} is represented as a sum of N {\displaystyle N} radial basis functions, each associated with a different center x i {\textstyle \mathbf {x} _{i}} , and weighted by an appropriate coefficient w i . {\textstyle w_{i}.} The weights w i {\textstyle w_{i}} can be estimated using the matrix methods of linear least squares, because the approximating function is linear in the weights w i {\textstyle w_{i}} . Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behaviour and 3D reconstruction in computer graphics (for example, hierarchical RBF and Pose Space Deformation). == RBF Network == The sum can also be interpreted as a rather simple single-layer type of artificial neural network called a radial basis function network, with the radial basis functions taking on the role of the activation functions of the network. It can be shown that any continuous function on a compact interval can in principle be interpolated with arbitrary accuracy by a sum of this form, if a sufficiently large number N {\textstyle N} of radial basis functions is used. The approximant y ( x ) {\textstyle y(\mathbf {x} )} is differentiable with respect to the weights w i {\textstyle w_{i}} . The weights could thus be learned using any of the standard iterative methods for neural networks. Using radial basis functions in this manner yields a reasonable interpolation approach provided that the fitting set has been chosen such that it covers the entire range systematically (equidistant data points are ideal). However, without a polynomial term that is orthogonal to the radial basis functions, estimates outside the fitting set tend to perform poorly. == RBFs for PDEs == Radial basis functions are used to approximate functions and so can be used to discretize and numerically solve Partial Differential Equations (PDEs). This was first done in 1990 by E. J. Kansa who developed the first RBF based numerical method. It is called the Kansa method and was used to solve the elliptic Poisson equation and the linear advection-diffusion equation. The function values at points x {\displaystyle \mathbf {x} } in the domain are approximated by the linear combination of RBFs: The derivatives are approximated as such: where N {\displaystyle N} are the number of points in the discretized domain, d {\displaystyle d} the dimension of the domain and λ {\displaystyle \lambda } the scalar coefficients that are unchanged by the differential operator. Different numerical methods based on Radial Basis Functions were developed thereafter. Some methods are the RBF-FD method, the RBF-QR method and the RBF-PUM method.
Deterministic blockmodeling
Deterministic blockmodeling is an approach in blockmodeling that does not assume a probabilistic model, and instead relies on the exact or approximate algorithms, which are used to find blockmodel(s). This approach typically minimizes some inconsistency that can occur with the ideal block structure. Such analysis is focused on clustering (grouping) of the network (or adjacency matrix) that is obtained with minimizing an objective function, which measures discrepancy from the ideal block structure. However, some indirect approaches (or methods between direct and indirect approaches, such as CONCOR) do not explicitly minimize inconsistencies or optimize some criterion function. This approach was popularized in the 1970s, due to the presence of two computer packages (CONCOR and STRUCTURE) that were used to "find a permutation of the rows and columns in the adjacency matrix leading to an approximate block structure". The opposite approach to deterministic blockmodeling is a stochastic blockmodeling approach.
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
Confirmatory blockmodeling
Confirmatory blockmodeling is a deductive approach in blockmodeling, where a blockmodel (or part of it) is prespecify before the analysis, and then the analysis is fit to this model. When only a part of analysis is prespecify (like individual cluster(s) or location of the block types), it is called partially confirmatory blockmodeling. This is so-called indirect approach, where the blockmodeling is done on the blockmodel fitting (e.g., a priori hypothesized blockmodel). Opposite approach to the confirmatory blockmodeling is an inductive exploratory blockmodeling.