Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray, it was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. In simpler terms, vector quantization chooses a set of points to represent a larger set of points. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model and to sparse coding models used in deep learning algorithms such as autoencoder. == Training == One simple training algorithm for vector quantization is: Pick a sample point at random Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance Repeat A more sophisticated algorithm reduces the bias in the density matching estimation and ensures that all points are used, by including an extra sensitivity parameter: Increase each centroid's sensitivity s i {\displaystyle s_{i}} by a small amount Pick a sample point P {\displaystyle P} at random For each quantization vector centroid c i {\displaystyle c_{i}} , let d ( P , c i ) {\displaystyle d(P,c_{i})} denote the distance of P {\displaystyle P} and c i {\displaystyle c_{i}} Find the centroid c i {\displaystyle c_{i}} for which d ( P , c i ) − s i {\displaystyle d(P,c_{i})-s_{i}} is the smallest Move c i {\displaystyle c_{i}} towards P {\displaystyle P} by a small fraction of the distance Set s i {\displaystyle s_{i}} to zero Repeat It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another simple method is LBG, which is based on k-means. The algorithm can be iteratively updated with "live" data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples. == Applications == Vector quantization is used for lossy data compression, lossy data correction, pattern recognition, density estimation and clustering. Lossy data correction, or prediction, is used to recover data missing from some dimensions. It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid. For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm). === Use in data compression === Vector quantization, also called "block quantization" or "pattern matching quantization" is often used in lossy data compression. It works by encoding values from a multidimensional vector space into a finite set of values from a discrete subspace of lower dimension. A lower-space vector requires less storage space, so the data is compressed. Due to the density matching property of vector quantization, the compressed data has errors that are inversely proportional to density. The transformation is usually done by projection or by using a codebook. In some cases, a codebook can be also used to entropy code the discrete value in the same step, by generating a prefix coded variable-length encoded value as its output. The set of discrete amplitude levels is quantized jointly rather than each sample being quantized separately. Consider a k-dimensional vector [ x 1 , x 2 , . . . , x k ] {\displaystyle [x_{1},x_{2},...,x_{k}]} of amplitude levels. It is compressed by choosing the nearest matching vector from a set of n-dimensional vectors [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} , with n < k. All possible combinations of the n-dimensional vector [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} form the vector space to which all the quantized vectors belong. Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression. Twin vector quantization (VQF) is part of the MPEG-4 standard dealing with time domain weighted interleaved vector quantization. === Video codecs based on vector quantization === Bink video Cinepak Daala is transform-based but uses pyramid vector quantization on transformed coefficients Digital Video Interactive: Production-Level Video and Real-Time Video Indeo Microsoft Video 1 QuickTime: Apple Video (RPZA) and Graphics Codec (SMC) Sorenson SVQ1 and SVQ3 Smacker video VQA format, used in many games The usage of video codecs based on vector quantization has declined significantly in favor of those based on motion compensated prediction combined with transform coding, e.g. those defined in MPEG standards, as the low decoding complexity of vector quantization has become less relevant. === Audio codecs based on vector quantization === AMR-WB+ CELP CELT (now part of Opus) is transform-based but uses pyramid vector quantization on transformed coefficients Codec 2 DTS G.729 iLBC Ogg Vorbis TwinVQ === Use in pattern recognition === VQ was also used in the eighties for speech and speaker recognition. Recently it has also been used for efficient nearest neighbor search and on-line signature recognition. In pattern recognition applications, one codebook is constructed for each class (each class being a user in biometric applications) using acoustic vectors of this user. In the testing phase the quantization distortion of a testing signal is worked out with the whole set of codebooks obtained in the training phase. The codebook that provides the smallest vector quantization distortion indicates the identified user. The main advantage of VQ in pattern recognition is its low computational burden when compared with other techniques such as dynamic time warping (DTW) and hidden Markov model (HMM). The main drawback when compared to DTW and HMM is that it does not take into account the temporal evolution of the signals (speech, signature, etc.) because all the vectors are mixed up. In order to overcome this problem a multi-section codebook approach has been proposed. The multi-section approach consists of modelling the signal with several sections (for instance, one codebook for the initial part, another one for the center and a last codebook for the ending part). === Use as clustering algorithm === As VQ is seeking for centroids as density points of nearby lying samples, it can be also directly used as a prototype-based clustering method: each centroid is then associated with one prototype. By aiming to minimize the expected squared quantization error and introducing a decreasing learning gain fulfilling the Robbins-Monro conditions, multiple iterations over the whole data set with a concrete but fixed number of prototypes converges to the solution of k-means clustering algorithm in an incremental manner. === Generative adversarial networks (GAN) === VQ has been used to quantize a feature representation layer in the discriminator of generative adversarial networks. The feature quantization (FQ) technique performs implicit feature matching. It improves the GAN training, and yields an improved performance on a variety of popular GAN models: BigGAN for image generation, StyleGAN for face synthesis, and U-GAT-IT for unsupervised image-to-image translation.
Information schema
In relational databases, the information schema (information_schema) is an ANSI-standard set of read-only views that provide information about all of the tables, views, columns, and procedures in a database. It can be used as a source of the information that some databases make available through non-standard commands, such as: the SHOW command of MySQL the DESCRIBE command of Oracle's SQLPlus the \d command in psql (PostgreSQL's default command-line program). => SELECT count(table_name) FROM information_schema.tables; count ------- 99 (1 row) => SELECT column_name, data_type, column_default, is_nullable FROM information_schema.columns WHERE table_name='alpha'; column_name | data_type | column_default | is_nullable -------------+-----------+----------------+------------- foo | integer | | YES bar | character | | YES (2 rows) => SELECT FROM information_schema.information_schema_catalog_name; catalog_name -------------- johnd (1 row) == Implementation == As a notable exception among major database systems, Oracle does not as of 2015 implement the information schema. An open-source project exists to address this. RDBMSs that support information_schema include: Amazon Redshift Apache Hive Microsoft SQL Server MonetDB Snowflake MySQL PostgreSQL H2 Database HSQLDB InterSystems Caché MariaDB SingleStore (formerly MemSQL) Mimer SQL Snowflake Trino Presto CrateDB ClickHouse CockroachDB Kinetica DB TiDB RDBMSs that do not support information_schema include: Apache Derby Apache Ignite Firebird Microsoft Access IBM Informix Ingres IBM Db2 Oracle Database SAP HANA SQLite Sybase ASE Sybase SQL Anywhere Teradata Vertica
Big Mechanism
Big Mechanism is a $45 million DARPA research program, begun in 2014, aimed at developing software that will read cancer research papers, integrate them into a cancer model and frame new hypotheses by the end of 2017 through the automated collection of big data and integrating across various disciplines such as knowledge-based NLP, curation and ontology, systems and mathematical biology by reading research abstracts and papers to extract pieces of causal mechanisms. == Ras gene == The program focuses on mutations in the Ras gene family, which underlie some one-third of human cancers. Currently, a rough road map shows interaction sequences among proteins affecting cell replication and death. However, the causal relations are poorly understood. == Plan == The program is to occur in three stages. The first is to read literature and convert it into formal representations. Second is to integrate the knowledge into computational models. Third is to produce experimentally testable explanations and predictions. Research teams are developing four separate systems targeting all three tasks. In February 2015, an evaluation meeting reviewed progress on the first stage. Multiple tasks were considered. One was extraction of experimental procedure details and evaluating statements such as "we demonstrate" and "we suggest." Another worked to map sentence meaning and relationships. The best machine-reading system extracted 40% of relevant information from a small corpus and correctly determined how each passage related to the model. The second stage is to become active in summer 2015, when members attempt to produce a single reference model. The third stage is the most challenging, because the artificial intelligence community has had limited success at developing hypothesis generators. Molecular biology may be more amenable, because most domain knowledge is technical and available in written form.
Argument Web
The Argument Web is a large-scale Web of interconnected arguments created by individuals as they express their opinions and interact with the opinions of others. The Argument Web aims to make online debate intuitive for participants such as mediators, students, academics, broadcasters and bloggers, to create a Web infrastructure that allows for the storage, automatic retrieval and analysis of linked argument data, and to improve the quality of online argument and debate. The Argument Web can be described as a portion of a larger Semantic Web. == AIFdb == AIFdb is a database implementation or ‘reification’ of the Argument Interchange Format (AIF), which allows for the storage and retrieval of AIF compliant argument structures. This database solution was provided as a foundation for an open, integrated Argument Web. It offers an extensive range of web services for interacting with stored argument data, while also offering search and argument visualisation features that are all consistent with the formal ontology of AIF. At a basic level, the AIFdb web services allow for the insertion and querying of basic components of an AIF argument, such as nodes, edges and schemes. Building upon this basis, it also facilitates more complex interactions with these AIF argument structures. Such complex queries could make it possible, for example, to determine all the statements made by a particular person in support a given I-Node. While, at its highest level of interaction, AIFdb can handle the import and export of many standard file formats, including SVG, DOT, RDF/XML and other formats of argument theory tools, like Carneades, Rationale and Araucaria. == Argument blogging == ArguBlogging is software which allows its users to select portions of hypertext on webpages in their Web browsers and to agree or disagree with the selected content, posting their arguments to their blogs with linked argument data. It is implemented as a bookmarklet, adding functionality to Web browsers and interoperating with blogging platforms such as Blogger and Tumblr.
A Very Fatal Murder
A Very Fatal Murder is a podcast produced by the satirical publication The Onion. A parody of true crime podcasts, A Very Fatal Murder is hosted by fictional New York City reporter David Pascall, who travels to the small town Bluff Springs, Nebraska to investigate the murder of prom queen Hayley Price. Pascall is voiced by David Sidorov, who also wrote for the podcast. The podcast premiered on January 23, 2018, and consists of 7 episodes. Season 2 was released in its entirety on May 11, 2019. == Production == A Very Fatal Murder satirizes popular true crime podcasts such as Serial, S-Town, and My Favorite Murder. According to head writer Katy Yeiser, the podcast is not meant as a take down of any particular podcast, but rather an ode to the genre. == Synopsis == The podcast follows fictional investigative reporter David Pascall (voiced by David Sidorov) who is searching for the perfect murder to create an award-winning podcast about. He is assisted by ETHL (the Extremely Timely Homicide Locator), an MIT-created computer programmed to find "the most interesting, violent, culturally relevant murder cases in America". == Episodes == === Season 1 === === Season 2 === == Reception == The podcast received mostly positive reviews, and was largely praised for attacking true-crime tropes such as the "hot dead girl" and the romanticization of small-town America. === Awards ===
IMazing
iMazing is mobile device management software that allows users to transfer files and data between iOS devices (iPhone, iPad and iPod Touch) and macOS or Windows computers, in addition to many other features beyond the scope of what Apple's own tools enable. == History == Developed by DigiDNA, iMazing was initially released in 2008 as DiskAid, enabling users to transfer data and files from the iPhone or iPod Touch to Mac or Windows computers. DiskAid was renamed iMazing in 2014. Version 2.0 was released on September 13, 2016. In August 2021, version 2.14 of iMazing added a spyware detection feature. The feature is based on Amnesty International’s Mobile Verification Toolkit to detect Pegasus Spyware following the publication of Pegasus Project. == Description == With iMazing, an iPhone or iPad can be used similarly to an external hard drive. It performs tasks that iTunes doesn’t offer, including incremental backups of iOS devices, browsing and exporting text and voicemail messages, managing apps, encryption, and migrating data from an old phone to a new one. The menu bar app iMazing Mini enables automatic, wireless and encrypted backups of iPhones. The iMazing HEIC Converter is a free desktop app for Mac and PC that lets users convert photos from HEIC format to JPG or PNG.
Fuzzy measure theory
In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures, possibility/necessity measures, and probability measures, which are a subset of classical measures. == Definitions == Let X {\displaystyle \mathbf {X} } be a universe of discourse, C {\displaystyle {\mathcal {C}}} be a class of subsets of X {\displaystyle \mathbf {X} } , and E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} . A function g : C → R {\displaystyle g:{\mathcal {C}}\to \mathbb {R} } where ∅ ∈ C ⇒ g ( ∅ ) = 0 {\displaystyle \emptyset \in {\mathcal {C}}\Rightarrow g(\emptyset )=0} E ⊆ F ⇒ g ( E ) ≤ g ( F ) {\displaystyle E\subseteq F\Rightarrow g(E)\leq g(F)} is called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . == Properties of fuzzy measures == A fuzzy measure is: additive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\geq g(E)+g(F)} ; submodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\geq g(E)+g(F)} ; subadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\leq g(E)+g(F)} ; symmetric if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have | E | = | F | {\displaystyle |E|=|F|} implies g ( E ) = g ( F ) {\displaystyle g(E)=g(F)} ; Boolean if for any E ∈ C {\displaystyle E\in {\mathcal {C}}} , we have g ( E ) = 0 {\displaystyle g(E)=0} or g ( E ) = 1 {\displaystyle g(E)=1} . Understanding the properties of fuzzy measures is useful in application. When a fuzzy measure is used to define a function such as the Sugeno integral or Choquet integral, these properties will be crucial in understanding the function's behavior. For instance, the Choquet integral with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted averaging (OWA) operator. Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral. == Möbius representation == Let g be a fuzzy measure. The Möbius representation of g is given by the set function M, where for every E , F ⊆ X {\displaystyle E,F\subseteq X} , M ( E ) = ∑ F ⊆ E ( − 1 ) | E ∖ F | g ( F ) . {\displaystyle M(E)=\sum _{F\subseteq E}(-1)^{|E\backslash F|}g(F).} The equivalent axioms in Möbius representation are: M ( ∅ ) = 0 {\displaystyle M(\emptyset )=0} . ∑ F ⊆ E | i ∈ F M ( F ) ≥ 0 {\displaystyle \sum _{F\subseteq E|i\in F}M(F)\geq 0} , for all E ⊆ X {\displaystyle E\subseteq \mathbf {X} } and all i ∈ E {\displaystyle i\in E} A fuzzy measure in Möbius representation M is called normalized if ∑ E ⊆ X M ( E ) = 1. {\displaystyle \sum _{E\subseteq \mathbf {X} }M(E)=1.} Möbius representation can be used to give an indication of which subsets of X interact with one another. For instance, an additive fuzzy measure has Möbius values all equal to zero except for singletons. The fuzzy measure g in standard representation can be recovered from the Möbius form using the Zeta transform: g ( E ) = ∑ F ⊆ E M ( F ) , ∀ E ⊆ X . {\displaystyle g(E)=\sum _{F\subseteq E}M(F),\forall E\subseteq \mathbf {X} .} == Simplification assumptions for fuzzy measures == Fuzzy measures are defined on a semiring of sets or monotone class, which may be as granular as the power set of X, and even in discrete cases the number of variables can be as large as 2|X|. For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that g ( E ) = ∑ i ∈ E g ( { i } ) {\displaystyle g(E)=\sum _{i\in E}g(\{i\})} and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or λ {\displaystyle \lambda } -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively. === Sugeno λ-measure === The Sugeno λ {\displaystyle \lambda } -measure is a special case of fuzzy measures defined iteratively. It has the following definition: ==== Definition ==== Let X = { x 1 , … , x n } {\displaystyle \mathbf {X} =\left\lbrace x_{1},\dots ,x_{n}\right\rbrace } be a finite set and let λ ∈ ( − 1 , + ∞ ) {\displaystyle \lambda \in (-1,+\infty )} . A Sugeno λ {\displaystyle \lambda } -measure is a function g : 2 X → [ 0 , 1 ] {\displaystyle g:2^{X}\to [0,1]} such that g ( X ) = 1 {\displaystyle g(X)=1} . if A , B ⊆ X {\displaystyle A,B\subseteq \mathbf {X} } (alternatively A , B ∈ 2 X {\displaystyle A,B\in 2^{\mathbf {X} }} ) with A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } then g ( A ∪ B ) = g ( A ) + g ( B ) + λ g ( A ) g ( B ) {\displaystyle g(A\cup B)=g(A)+g(B)+\lambda g(A)g(B)} . As a convention, the value of g at a singleton set { x i } {\displaystyle \left\lbrace x_{i}\right\rbrace } is called a density and is denoted by g i = g ( { x i } ) {\displaystyle g_{i}=g(\left\lbrace x_{i}\right\rbrace )} . In addition, we have that λ {\displaystyle \lambda } satisfies the property λ + 1 = ∏ i = 1 n ( 1 + λ g i ) {\displaystyle \lambda +1=\prod _{i=1}^{n}(1+\lambda g_{i})} . Tahani and Keller as well as Wang and Klir have shown that once the densities are known, it is possible to use the previous polynomial to obtain the values of λ {\displaystyle \lambda } uniquely. === k-additive fuzzy measure === The k-additive fuzzy measure limits the interaction between the subsets E ⊆ X {\displaystyle E\subseteq X} to size | E | = k {\displaystyle |E|=k} . This drastically reduces the number of variables needed to define the fuzzy measure, and as k can be anything from 1 (in which case the fuzzy measure is additive) to X, it allows for a compromise between modelling ability and simplicity. ==== Definition ==== A discrete fuzzy measure g on a set X is called k-additive ( 1 ≤ k ≤ | X | {\displaystyle 1\leq k\leq |\mathbf {X} |} ) if its Möbius representation verifies M ( E ) = 0 {\displaystyle M(E)=0} , whenever | E | > k {\displaystyle |E|>k} for any E ⊆ X {\displaystyle E\subseteq \mathbf {X} } , and there exists a subset F with k elements such that M ( F ) ≠ 0 {\displaystyle M(F)\neq 0} . == Shapley and interaction indices == In game theory, the Shapley value or Shapley index is used to indicate the weight of a game. Shapley values can be calculated for fuzzy measures in order to give some indication of the importance of each singleton. In the case of additive fuzzy measures, the Shapley value will be the same as each singleton. For a given fuzzy measure g, and | X | = n {\displaystyle |\mathbf {X} |=n} , the Shapley index for every i , … , n ∈ X {\displaystyle i,\dots ,n\in X} is: ϕ ( i ) = ∑ E ⊆ X ∖ { i } ( n − | E | − 1 ) ! | E | ! n ! [ g ( E ∪ { i } ) − g ( E ) ] . {\displaystyle \phi (i)=\sum _{E\subseteq \mathbf {X} \backslash \{i\}}{\frac {(n-|E|-1)!|E|!}{n!}}[g(E\cup \{i\})-g(E)].} The Shapley value is the vector ϕ ( g ) = ( ψ ( 1 ) , … , ψ ( n ) ) . {\displaystyle \mathbf {\phi } (g)=(\psi (1),\dots ,\psi (n)).}