Magnetic ink character recognition code, known in short as MICR code, is a character recognition technology used mainly by the banking industry to streamline the processing and clearance of cheques and other documents. MICR encoding, called the MICR line, is at the bottom of cheques and other vouchers and typically includes the document-type indicator, bank code, bank account number, cheque number, cheque amount (usually added after a cheque is presented for payment), and a control indicator. The format for the bank code and bank account number is country-specific. The technology allows MICR readers to scan and read the information directly into a data-collection device. Unlike barcode and similar technologies, MICR characters can be read easily by humans. MICR encoded documents can be processed much faster and more accurately than conventional OCR encoded documents. == Pre-Unicode standard representation == The ISO standard ISO 2033:1983, and the corresponding Japanese Industrial Standard JIS X 9010:1984 (originally JIS C 6229–1984), define character encodings for OCR-A, OCR-B and E-13B. == International spread == There are two major MICR fonts in use: E-13B and CMC-7. There is no particular international agreement on which countries use which font. In practice, this does not create particular problems as cheques and other vouchers do not usually flow out of a particular jurisdiction. The E-13B font has been adopted as an international standard in ISO 1004-1:2013, and is the standard in Australia, Canada, the United Kingdom, the United States, as well as Central America and much of Asia, besides other countries. The CMC-7 font has been adopted as an international standard in ISO 1004-2:2013, and is widely used in Europe, including France and Italy, Mexico, and South America, including Argentina, Brazil, Chile, besides other countries. Israel is the only country that can use both fonts simultaneously, though the practice makes the system significantly less efficient. This situation is the product of the Israelis adopting CMC-7, while the Palestinians opted for E-13B. == Fonts == === E-13B === E-13B is a 14-character set, comprising the 10 decimal digits, and the following symbols: ⑆ (transit: used to delimit a bank code); ⑈ (on-us: used to delimit a customer account number); ⑇ (amount: used to delimit a transaction amount); ⑉ (dash: used to delimit parts of numbers—e.g., routing numbers or account numbers). In the check printing and banking industries the E-13B MICR line is also commonly referred to as the TOAD line. This reference comes from the 4 characters: Transit, On-us, Amount, and Dash. Compared to CMC-7, some pairs of E-13B characters (notably 2 and 5) can produce relatively similar results when magnetically scanned; however, as a fallback if magnetic reading fails, E-13B also performs well under optical character recognition. The E-13B repertoire can be represented in Unicode (see below). The official Unicode names contain misnomers. For example, the ⑈ on-us symbol is official titled "OCR Dash". Prior to Unicode, it could be encoded according to ISO 2033:1983, which encodes digits in their usual ASCII locations, transit as 0x3A, on-us as 0x3C, amount as 0x3B, and dash as 0x3D. For EBCDIC, IBM code page 1001 encodes digits in their usual EBCDIC locations, transit as 0xDB, on-us as 0xEB, amount as 0xCB, and dash as 0xFB. IBM code page 1032 extends code page 1001 by adding alternative encodings for transit at 0x5C, 0x7A and 0xC1, on-us at 0x4C, 0x61 and 0xC3, amount at 0x5B, 0x5E and 0xC2 and dash at 0x60, 0x7E and 0xC4, in addition to a zero-width space at 0x5A. These alternative representations were added for interoperability with Siemens and Océ printers. === CMC-7 === CMC-7 includes 10 numeric digits, 26 capital letters, and 5 control characters: S I (internal), S II (terminator), S III (amount), S IV (an unused character), and S V (routing). CMC-7 has a barcode format, with every character having two distinct large gaps in different places, as well as distinct patterns in between, to minimize any chance for character confusion while reading magnetically; however, these bars are too close and narrow to be reliably recognised at a typical scan resolution if falling back to optical scanning. CMC-7 can also produce superficially successful, but incorrect, scans of upside-down MICR lines. Unicode does not include support for the CMC-7 control symbols. IBM code page 1033 encodes: Digits and capitals in their usual EBCDIC locations S I (internal) as 0x5E, 0x61 or 0xCB; S II (terminator) as 0x4C, 0x5B or 0xEB; S III (amount) as 0x60, 0x7E or 0xFB; S IV as 0x50, 0x7A or 0xDB; S V (routing) as 0x5C, 0x6E or 0xBB. == MICR reader == MICR characters are printed on documents in one of the two MICR fonts, using magnetizable (commonly known as magnetic) ink or toner, usually containing iron oxide. In scanning, the document is passed through a MICR reader, which performs two functions: magnetization of the ink, and detection of the characters. The characters are read by a MICR reader head, a device similar to the playback head of a tape recorder. As each character passes over the head, it produces a unique waveform that can be easily identified by the system. MICR readers are the primary tool for cheque sorting and are used across the cheque distribution network at multiple stages. For example, a merchant will use a MICR reader to sort cheques by bank and send the sorted cheques to a clearing house for redistribution to those banks. Upon receipt, the banks perform another MICR sort to determine which customer's account is charged and to which branch the cheque should be sent on its way back to the customer. However, many banks no longer offer this last step of returning the cheque to the customer. Instead, cheques are scanned and stored digitally. Sorting of cheques is done as per the geographical coverage of banks in a nation. == Unicode == OCR and MICR characters have been included in the Unicode Standard since at least version 1.1 (June 1993). Since the Unicode Character Database only tracks characters starting with version 1.1, they may also have been present in Unicode 1.0 or 1.0.1. The Unicode block that includes OCR and MICR characters is called Optical Character Recognition and covers U+2440–U+245F. Of the characters in this block, four are from the MICR E-13B font: U+2446 ⑆ OCR BRANCH BANK IDENTIFICATION U+2447 ⑇ OCR AMOUNT OF CHECK U+2448 ⑈ OCR DASH (corrected alias MICR ON US SYMBOL) U+2449 ⑉ OCR CUSTOMER ACCOUNT NUMBER (corrected alias MICR DASH SYMBOL) The names of the latter two characters were inadvertently switched when they were named in ISO/IEC 10646:1993, and they have been assigned accurate names as formal aliases. Per the Unicode Stability Policy, the existing names remain, allowing their use as stable identifiers. Additionally, all four characters have informative (non-formal) aliases in the Unicode charts: "transit", "amount", "on-us", and "dash" respectively. Prior to Unicode, these symbols had been encoded by the ISO-IR-98 encoding defined by ISO 2033:1983, in which they were simply named SYMBOL ONE through SYMBOL FOUR. They were encoded immediately following the digits, which were encoded at their ASCII locations. Although ISO 2033 also specifies encoding for OCR-A and OCR-B, its encoding for E-13B is known simply as ISO_2033-1983 by the IANA. == History == Before the mid-1940s, cheques were processed manually using the Sort-A-Matic or Top Tab Key method. The processing and cheque clearing was very time-consuming and was a significant cost in cheque clearance and bank operations. As the number of cheques increased, ways were sought for automating the process. Standards were developed to ensure uniformity in financial institutions. By the mid-1950s, the Stanford Research Institute and General Electric Computer Laboratory had developed the first automated system to process cheques using MICR. The same team also developed the E-13B MICR font. "E" refers to the font being the fifth considered, and "B" to the fact that it was the second version. The "13" refers to the 0.013-inch character grid. The trial of MICR E-13B font was shown to the American Bankers Association (ABA) in July 1956, which adopted it in 1958 as the MICR standard for negotiable documents in the United States. ABA adopted MICR as its standard because machines could read MICR accurately, and MICR could be printed using existing technology. In addition, MICR remained machine readable, even through overstamping, marking, mutilation and more. The first cheques using MICR were printed by the end of 1959. Although compliance with MICR standards was voluntary in the United States, it had been almost universally adopted in the United States by 1963. In 1963, ANSI adopted the ABA's E-13B font as the American standard for MICR printing, and E-13B was also standardized as ISO 1004:1995. Other countries set their own standards, though the MICR readers and m
Molecular graphics
Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules, and these representations have had an important influence on modern molecular graphics. Colour molecular graphics are often used on chemistry journal covers artistically. == History == Prior to the use of computer graphics in representing molecular structure, Robert Corey and Linus Pauling developed a system for representing atoms or groups of atoms from hard wood on a scale of 1 inch = 1 angstrom connected by a clamping device to maintain the molecular configuration. These early models also established the CPK coloring scheme that is still used today to differentiate the different types of atoms in molecular models (e.g. carbon = black, oxygen = red, nitrogen = blue, etc). This early model was improved upon in 1966 by W.L. Koltun and are now known as Corey-Pauling-Koltun (CPK) models. The earliest efforts to produce models of molecular structure was done by Project MAC using wire-frame models displayed on a cathode ray tube in the mid 1960s. In 1965, Carroll Johnson distributed the Oak Ridge thermal ellipsoid plot (ORTEP) that visualized molecules as a ball-and-stick model with lines representing the bonds between atoms and ellipsoids to represent the probability of thermal motion. Thermal ellipsoid plots quickly became the de facto standard used in the display of X-ray crystallography data, and are still in wide use today. The first practical use of molecular graphics was a simple display of the protein myoglobin using a wireframe representation in 1966 by Cyrus Levinthal and Robert Langridge working at Project MAC. Among the milestones in high-performance molecular graphics was the work of Nelson Max in "realistic" rendering of macromolecules using reflecting spheres. Initially much of the technology concentrated on high-performance 3D graphics. During the 1970s, methods for displaying 3D graphics using cathode ray tubes were developed using continuous tone computer graphics in combination with electro-optic shutter viewing devices. The first devices used an active shutter 3D system, generating different perspective views for the left and right channel to provide the illusion of three-dimensional viewing. Stereoscopic viewing glasses were designed using lead lanthanum zirconate titanate (PLZT) ceramics as electronically controlled shutter elements. Active 3D glasses require batteries and work in concert with the display to actively change the presentation by the lenses to the wearer's eyes. Many modern 3D glasses use a passive, polarized 3D system that enables the wearer to visualize 3D effects based on their own perception. Passive 3D glasses are more common today since they are less expensive. The requirements of macromolecular crystallography also drove molecular graphics because the traditional techniques of physical model-building could not scale. The first two protein structures solved by molecular graphics without the aid of the Richards' Box were built with Stan Swanson's program FIT on the Vector General graphics display in the laboratory of Edgar Meyer at Texas A&M University: First Marge Legg in Al Cotton's lab at A&M solved a second, higher-resolution structure of staph. nuclease (1975) and then Jim Hogle solved the structure of monoclinic lysozyme in 1976. A full year passed before other graphics systems were used to replace the Richards' Box for modelling into density in 3-D. Alwyn Jones' FRODO program (and later "O") were developed to overlay the molecular electron density determined from X-ray crystallography and the hypothetical molecular structure. === Timeline === == Types == === Ball-and-stick models === In the ball-and-stick model, atoms are drawn as small sphered connected by rods representing the chemical bonds between them. === Space-filling models === In the space-filling model, atoms are drawn as solid spheres to suggest the space they occupy, in proportion to their van der Waals radii. Atoms that share a bond overlap with each other. === Surfaces === In some models, the surface of the molecule is approximated and shaded to represent a physical property of the molecule, such as electronic charge density. === Ribbon diagrams === Ribbon diagrams are schematic representations of protein structure and are one of the most common methods of protein depiction used today. The ribbon shows the overall path and organization of the protein backbone in 3D, and serves as a visual framework on which to hang details of the full atomic structure, such as the balls for the oxygen atoms bound to the active site of myoglobin in the adjacent image. Ribbon diagrams are generated by interpolating a smooth curve through the polypeptide backbone. α-helices are shown as coiled ribbons or thick tubes, β-strands as arrows, and non-repetitive coils or loops as lines or thin tubes. The direction of the polypeptide chain is shown locally by the arrows, and may be indicated overall by a colour ramp along the length of the ribbon.
Amazon Rekognition
Amazon Rekognition is a cloud-based software as a service (SaaS) computer vision platform that was launched in 2016. It has been sold to, and used by, a number of United States government agencies, including U.S. Immigration and Customs Enforcement (ICE) and Orlando, Florida police, as well as private entities. == Capabilities == Rekognition provides a number of computer vision capabilities, which can be divided into two categories: Algorithms that are pre-trained on data collected by Amazon or its partners, and algorithms that a user can train on a custom dataset. As of July 2019, Rekognition provides the following computer vision capabilities. === Pre-trained algorithms === Celebrity recognition in images Facial attribute detection in images, including gender, age range, emotions (e.g. happy, calm, disgusted), whether the face has a beard or mustache, whether the face has eyeglasses or sunglasses, whether the eyes are open, whether the mouth is open, whether the person is smiling, and the location of several markers such as the pupils and jaw line. People Pathing enables tracking of people through a video. An advertised use-case of this capability is to track sports players for post-game analysis. Text detection and classification in images Unsafe visual content detection === Algorithms that a user can train on a custom dataset === SearchFaces enables users to import a database of images with pre-labeled faces, to train a machine learning model on this database, and to expose the model as a cloud service with an API. Then, the user can post new images to the API and receive information about the faces in the image. The API can be used to expose a number of capabilities, including identifying faces of known people, comparing faces, and finding similar faces in a database. Face-based user verification == History and use == === 2017 === In late 2017, the Washington County, Oregon Sheriff's Office began using Rekognition to identify suspects' faces. Rekognition was marketed as a general-purpose computer vision tool, and an engineer working for Washington County decided to use the tool for facial analysis of suspects. Rekognition was offered to the department for free, and Washington County became the first US law enforcement agency known to use Rekognition. In 2018, the agency logged over 1,000 facial searches. The county, according to the Washington Post, by 2019 was paying about $7 a month for all of its searches. The relationship was unknown to the public until May 2018. In 2018, Rekognition was also used to help identify celebrities during a royal wedding telecast. === 2018 === In April 2018, it was reported that FamilySearch was using Rekognition to enable their users to "see which of their ancestors they most resemble based on family photographs". In early 2018, the FBI also began using it as a pilot program for analyzing video surveillance. In May 2018, it was reported by the ACLU that Orlando, Florida was running a pilot using Rekognition for facial analysis in law enforcement, with that pilot ending in July 2019. After the report, on June 22, 2018, Gizmodo reported that Amazon workers had written a letter to CEO Jeff Bezos requesting he cease selling Rekognition to US law enforcement, particularly ICE and Homeland Security. A letter was also sent to Bezos by the ACLU. On June 26, 2018, it was reported that the Orlando police force had ceased using Rekognition after their trial contract expired, reserving the right to use it in the future. The Orlando Police Department said that they had "never gotten to the point to test images" due to old infrastructure and low bandwidth. In July 2018, the ACLU released a test showing that Rekognition had falsely matched 28 members of Congress with mugshot photos, particularly Congresspeople of color. 25 House members afterwards sent a letter to Bezos, expressing concern about Rekognition. Amazon responded saying the Rekognition test had generated 80 percent confidence, while it recommended law enforcement only use matches rated at 99 percent confidence. The Washington Post states that Oregon instead has officers pick a "best of five" result, instead of adhering to the recommendation. In September 2018, it was reported that Mapillary was using Rekognition to read the text on parking signs (e.g. no stopping, no parking, or specific parking hours) in cities. In October 2018, it was reported that Amazon had earlier that year pitched Rekognition to U.S. Immigration and Customs Enforcement agency. Amazon defended government use of Rekognition. On December 1, 2018, it was reported that 8 Democratic lawmakers had said in a letter that Amazon had "failed to provide sufficient answers" about Rekognition, writing that they had "serious concerns that this type of product has significant accuracy issues, places disproportionate burdens on communities of color, and could stifle Americans' willingness to exercise their First Amendment rights in public." === 2019 === In January 2019, MIT researchers published a peer-reviewed study asserting that Rekognition had more difficulty in identifying dark-skinned females than competitors such as IBM and Microsoft. In the study, Rekognition misidentified darker-skinned women as men 31% of the time, but made no mistakes for light-skinned men. Amazon called the report "misinterpreted results" of the research with an improper "default confidence threshold." In January 2019, Amazon's shareholders "urged Amazon to stop selling Rekognition software to law enforcement agencies." Amazon in response defended its use of Rekognition, but supported new federal oversight and guidelines to "make sure facial recognition technology cannot be used to discriminate." In February 2019, it was reported that Amazon was collaborating with the National Institute of Standards and Technology (NIST) on developing standardized tests to improve accuracy and remove bias with facial recognition. In March 2019, an open letter regarding Rekognition was sent by a group of prominent AI researchers to Amazon, criticizing its sale to law enforcement with around 50 signatures. In April 2019, Amazon was told by the Securities and Exchange Commission that they had to vote on two shareholder proposals seeking to limit Rekognition. Amazon argued that the proposals were an "insignificant public policy issue for the Company" not related to Amazon's ordinary business, but their appeal was denied. The vote was set for May. The first proposal was tabled by shareholders. On May 24, 2019, 2.4% of shareholders voted to stop selling Rekognition to government agencies, while a second proposal calling for a study into Rekognition and civil rights had 27.5% support. In August 2019, the ACLU again used Rekognition on members of government, with 26 of 120 lawmakers in California flagged as matches to mugshots. Amazon stated the ACLU was "misusing" the software in the tests, by not dismissing results that did not meet Amazon's recommended accuracy threshold of 99%. By August 2019, there had been protests against ICE's use of Rekognition to surveil immigrants. In March 2019, Amazon announced a Rekognition update that would improve emotional detection, and in August 2019, "fear" was added to emotions that Rekognition could detect. === 2020 === In June 2020, Amazon announced it was implementing a one-year moratorium on police use of Rekognition, in response to the George Floyd protests. === 2024 === The Department of Justice disclosed that the FBI is initiating the use of Amazon Rekognition. The DOJ's AI inventory revealed the FBI's "Project Tyr" aims to customize Rekognition to identify nudity, weapons, explosives, and other information from lawfully acquired media. === 2025 === In late 2025, the New York Times reported that scientist, Dr. Jürgen Matthäus, retired from as the head of research at the U.S. Holocaust Memorial Museum in Washington, D.C., used Amazon Rekognition to identify the shooter in the Holocaust photograph known as The Last Jew in Vinnitsa "with more than 99 percent certainty" — as Jakobus Onnen (1906–1943), a teacher from Tichelwarf near Weener in East Frisia who had been a member of the SS since 1934 and was later killed in action near Zhitomir in 1943. The photographer and victim remain unidentified. == Controversy regarding facial analysis == === Racial and gender bias === In 2018, MIT researchers Joy Buolamwini and Timnit Gebru published a study called Gender Shades. In this study, a set of images was collected, and faces in the images were labeled with face position, gender, and skin tone information. The images were run through SaaS facial recognition platforms from Face++, IBM, and Microsoft. In all three of these platforms, the classifiers performed best on male faces (with error rates on female faces being 8.1% to 20.6% higher than error rates on male faces), and they performed worst on dark female faces (with error rates ranging from 20.8% to 30.4%). The authors hypothesized that this discr
Autoencoder
An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning). An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation. The autoencoder learns an efficient representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine learning algorithms. Variants exist which aim to make the learned representations assume useful properties. Examples are regularized autoencoders (sparse, denoising and contractive autoencoders), which are effective in learning representations for subsequent classification tasks, and variational autoencoders, which can be used as generative models. Autoencoders are applied to many problems, including facial recognition, feature detection, anomaly detection, and learning the meaning of words. In terms of data synthesis, autoencoders can also be used to randomly generate new data that is similar to the input (training) data. == Mathematical principles == === Definition === An autoencoder is defined by the following components: Two sets: the space of encoded messages Z {\displaystyle {\mathcal {Z}}} ; the space of decoded messages X {\displaystyle {\mathcal {X}}} . Typically X {\displaystyle {\mathcal {X}}} and Z {\displaystyle {\mathcal {Z}}} are Euclidean spaces, that is, X = R m , Z = R n {\displaystyle {\mathcal {X}}=\mathbb {R} ^{m},{\mathcal {Z}}=\mathbb {R} ^{n}} with m > n . {\displaystyle m>n.} Two parametrized families of functions: the encoder family E ϕ : X → Z {\displaystyle E_{\phi }:{\mathcal {X}}\rightarrow {\mathcal {Z}}} , parametrized by ϕ {\displaystyle \phi } ; the decoder family D θ : Z → X {\displaystyle D_{\theta }:{\mathcal {Z}}\rightarrow {\mathcal {X}}} , parametrized by θ {\displaystyle \theta } .For any x ∈ X {\displaystyle x\in {\mathcal {X}}} , we usually write z = E ϕ ( x ) {\displaystyle z=E_{\phi }(x)} , and refer to it as the code, the latent variable, latent representation, latent vector, etc. Conversely, for any z ∈ Z {\displaystyle z\in {\mathcal {Z}}} , we usually write x ′ = D θ ( z ) {\displaystyle x'=D_{\theta }(z)} , and refer to it as the (decoded) message. Usually, both the encoder and the decoder are defined as multilayer perceptrons (MLPs). For example, a one-layer-MLP encoder E ϕ {\displaystyle E_{\phi }} is: E ϕ ( x ) = σ ( W x + b ) {\displaystyle E_{\phi }(\mathbf {x} )=\sigma (Wx+b)} where σ {\displaystyle \sigma } is an element-wise activation function, W {\displaystyle W} is a "weight" matrix, and b {\displaystyle b} is a "bias" vector. === Training an autoencoder === An autoencoder, by itself, is simply a tuple of two functions. To judge its quality, we need a task. A task is defined by a reference probability distribution μ r e f {\displaystyle \mu _{ref}} over X {\displaystyle {\mathcal {X}}} , and a "reconstruction quality" function d : X × X → [ 0 , ∞ ] {\displaystyle d:{\mathcal {X}}\times {\mathcal {X}}\to [0,\infty ]} , such that d ( x , x ′ ) {\displaystyle d(x,x')} measures how much x ′ {\displaystyle x'} differs from x {\displaystyle x} . With those, we can define the loss function for the autoencoder as L ( θ , ϕ ) := E x ∼ μ r e f [ d ( x , D θ ( E ϕ ( x ) ) ) ] {\displaystyle L(\theta ,\phi ):=\mathbb {\mathbb {E} } _{x\sim \mu _{ref}}[d(x,D_{\theta }(E_{\phi }(x)))]} The optimal autoencoder for the given task ( μ r e f , d ) {\displaystyle (\mu _{ref},d)} is then arg min θ , ϕ L ( θ , ϕ ) {\displaystyle \arg \min _{\theta ,\phi }L(\theta ,\phi )} . The search for the optimal autoencoder can be accomplished by any mathematical optimization technique, but usually by gradient descent. This search process is referred to as "training the autoencoder". In most situations, the reference distribution is just the empirical distribution given by a dataset { x 1 , . . . , x N } ⊂ X {\displaystyle \{x_{1},...,x_{N}\}\subset {\mathcal {X}}} , so that μ r e f = 1 N ∑ i = 1 N δ x i {\displaystyle \mu _{ref}={\frac {1}{N}}\sum _{i=1}^{N}\delta _{x_{i}}} where δ x i {\displaystyle \delta _{x_{i}}} is the Dirac measure, the quality function is just L 2 {\displaystyle L^{2}} loss: d ( x , x ′ ) = ‖ x − x ′ ‖ 2 2 {\displaystyle d(x,x')=\|x-x'\|_{2}^{2}} , and ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} is the Euclidean norm. Then the problem of searching for the optimal autoencoder is just a least-squares optimization: min θ , ϕ L ( θ , ϕ ) , where L ( θ , ϕ ) = 1 N ∑ i = 1 N ‖ x i − D θ ( E ϕ ( x i ) ) ‖ 2 2 {\displaystyle \min _{\theta ,\phi }L(\theta ,\phi ),\qquad {\text{where }}L(\theta ,\phi )={\frac {1}{N}}\sum _{i=1}^{N}\|x_{i}-D_{\theta }(E_{\phi }(x_{i}))\|_{2}^{2}} === Interpretation === An autoencoder has two main parts: an encoder that maps the message to a code, and a decoder that reconstructs the message from the code. An optimal autoencoder would perform as close to perfect reconstruction as possible, with "close to perfect" defined by the reconstruction quality function d {\displaystyle d} . The simplest way to perform the copying task perfectly would be to duplicate the signal. To suppress this behavior, the code space Z {\displaystyle {\mathcal {Z}}} usually has fewer dimensions than the message space X {\displaystyle {\mathcal {X}}} . Such an autoencoder is called undercomplete. It can be interpreted as compressing the message, or reducing its dimensionality. At the limit of an ideal undercomplete autoencoder, every possible code z {\displaystyle z} in the code space is used to encode a message x {\displaystyle x} that really appears in the distribution μ r e f {\displaystyle \mu _{ref}} , and the decoder is also perfect: D θ ( E ϕ ( x ) ) = x {\displaystyle D_{\theta }(E_{\phi }(x))=x} . This ideal autoencoder can then be used to generate messages indistinguishable from real messages, by feeding its decoder arbitrary code z {\displaystyle z} and obtaining D θ ( z ) {\displaystyle D_{\theta }(z)} , which is a message that really appears in the distribution μ r e f {\displaystyle \mu _{ref}} . If the code space Z {\displaystyle {\mathcal {Z}}} has dimension larger than (overcomplete), or equal to, the message space X {\displaystyle {\mathcal {X}}} , or the hidden units are given enough capacity, an autoencoder can learn the identity function and become useless. However, experimental results found that overcomplete autoencoders might still learn useful features. In the ideal setting, the code dimension and the model capacity could be set on the basis of the complexity of the data distribution to be modeled. A standard way to do so is to add modifications to the basic autoencoder, to be detailed below. == Variations == === Variational autoencoder (VAE) === Variational autoencoders (VAEs) belong to the families of variational Bayesian methods. Despite the architectural similarities with basic autoencoders, VAEs are architected with different goals and have a different mathematical formulation. The latent space is, in this case, composed of a mixture of distributions instead of fixed vectors. Given an input dataset x {\displaystyle x} characterized by an unknown probability function P ( x ) {\displaystyle P(x)} and a multivariate latent encoding vector z {\displaystyle z} , the objective is to model the data as a distribution p θ ( x ) {\displaystyle p_{\theta }(x)} , with θ {\displaystyle \theta } defined as the set of the network parameters so that p θ ( x ) = ∫ z p θ ( x , z ) d z {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }(x,z)dz} . === Sparse autoencoder (SAE) === Inspired by the sparse coding hypothesis in neuroscience, sparse autoencoders (SAE) are variants of autoencoders, such that the codes E ϕ ( x ) {\displaystyle E_{\phi }(x)} for messages tend to be sparse codes, that is, E ϕ ( x ) {\displaystyle E_{\phi }(x)} is close to zero in most entries. Sparse autoencoders may include more (rather than fewer) hidden units than inputs, but only a small number of the hidden units are allowed to be active at the same time. Encouraging sparsity improves performance on classification tasks. There are two main ways to enforce sparsity. One way is to simply clamp all but the highest-k activations of the latent code to zero. This is the k-sparse autoencoder. The k-sparse autoencoder inserts the following "k-sparse function" in the latent layer of a standard autoencoder: f k ( x 1 , . . . , x n ) = ( x 1 b 1 , . . . , x n b n ) {\displaystyle f_{k}(x_{1},...,x_{n})=(x_{1}b_{1},...,x_{n}b_{n})} where b i = 1 {\displaystyle b_{i}=1} if | x i | {\displaystyle |x_{i}|} ranks in the top k, and 0 otherwise. Backpropagating through f k {\displaystyle f_{k}} is simple: set gradient to 0 for b i = 0 {\displaystyle b_{i}=0} entries, and keep gradient for b i = 1 {\displaystyle b_{i}=1} entries. This is essentially a generalized ReLU function. The other way is a relaxed version of the k-
Unique negative dimension
Unique negative dimension (UND) is a complexity measure for the model of learning from positive examples. The unique negative dimension of a class C {\displaystyle C} of concepts is the size of the maximum subclass D ⊆ C {\displaystyle D\subseteq C} such that for every concept c ∈ D {\displaystyle c\in D} , we have ∩ ( D ∖ { c } ) ∖ c {\displaystyle \cap (D\setminus \{c\})\setminus c} is nonempty. This concept was originally proposed by M. Gereb-Graus in "Complexity of learning from one-side examples", Technical Report TR-20-89, Harvard University Division of Engineering and Applied Science, 1989.
PhotoWorks (ray tracing software)
PhotoWorks is a raytrace rendering program created by Dassault Systèmes SolidWorks Corporation, formerly supplied as a photorealistic rendering add-in for SolidWorks. The program is based on the Mental Ray rendering engine. It has a library of scenes and materials that can be used with user-created SolidWorks files to create still frame images within the SolidWorks GUI. Since the 2011 release of SolidWorks, PhotoWorks has been replaced by the PhotoView 360 rendering utility. A 2010 review comparing PhotoWorks with three other rendering programs for SolidWorks (including PhotoView 360) gave the program high marks for render speed and built-in materials, but low marks for realism and user interface. Appearance File Type: .p2m
Dendrogram
A dendrogram is a diagram representing a tree graph. This diagrammatic representation is frequently used in different contexts: in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses. in computational biology, it shows the clustering of genes or samples, sometimes in the margins of heatmaps. in phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree. The name dendrogram derives from the two ancient greek words δένδρον (déndron), meaning "tree", and γράμμα (grámma), meaning "drawing, mathematical figure". == Clustering example == For a clustering example, suppose that five taxa ( a {\displaystyle a} to e {\displaystyle e} ) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity). The distance between merged clusters is monotone, increasing with the level of the merger: the height of each node in the plot is proportional to the value of the intergroup dissimilarity between its two daughters (the nodes on the right representing individual observations all plotted at zero height).