AI For Business Hkbu

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  • Cloud Native Computing Foundation

    Cloud Native Computing Foundation

    The Cloud Native Computing Foundation (CNCF) is a subsidiary of the Linux Foundation founded in 2015 to support cloud-native computing. == History == It was announced alongside Kubernetes 1.0, an open source container cluster manager, which was contributed to the Linux Foundation by Google as a seed technology. Founding members include Google, CoreOS, Mesosphere, Red Hat, Twitter, Huawei, Intel, RX-M, Cisco, IBM, Docker, Univa, and VMware. Today, CNCF is supported by over 450 members. In August 2018 Google announced that it was handing over operational control of Kubernetes to the community. == Projects == Argo is a collection of tools for getting work done with Kubernetes. Among its main features are Workflows and Events. It was accepted to CNCF on March 26, 2020 at the Incubating maturity level and then moved to the Graduated maturity level on December 6, 2022. cert-manager provisions and manages TLS certificates in Kubernetes. It was accepted to CNCF on November 10, 2020, moved to the Incubating maturity level on September 19, 2022, and then moved to the Graduated maturity level on September 29, 2024. Cilium provides networking, security, and observability for Kubernetes deployments using eBPF technology. It joined the CNCF at incubation level in October 2021 and the CNCF announced its graduation in October 2023. containerd is an industry-standard core container runtime. It is currently available as a daemon for Linux and Windows, which can manage the complete container lifecycle of its host system. In 2015, Docker donated the OCI Specification to The Linux Foundation with a reference implementation called runc. Since February 28, 2019 it is an official CNCF project. Its general availability and intention to donate the project to CNCF was announced by Docker in 2017. CoreDNS is a DNS server that chains plugins. Its graduation was announced in 2019. Dapr, the distributed application runtime, provides APIs for building secure and reliable microservices and agentic AI systems. Dapr was donated to the CNCF in November 2021 and joined at incubation level. The CNCF announced its graduation in November 2024. Envoy: Originally built at Lyft to move their architecture away from a monolith, Envoy is a high-performance open source edge and service proxy that makes the network transparent to applications. Lyft contributed Envoy to Cloud Native Computing Foundation in September 2017. etcd is a distributed key value store, providing a method of storing data across a cluster of machines. It became a CNCF incubating project in 2018 at KubeCon+CloudNativeCon North America in Seattle that year. Falco is an open source and cloud native runtime security initiative. It is the "de facto Kubernetes threat detection engine". It became an incubating project in January 2020 and graduated in February 2024. Flux is an open source project for powering GitOps in Kubernetes clusters. It provides the GitOps Toolkit, a set of Kubernetes APIs that allow you to define how configuration source code is securely pulled into your cluster and deployed by popular Kubernetes manifests rendering engines like Kustomize and Helm. The most recommended source mechanism is the OCIRepository API, which provides enhanced security and benefits from container image tooling out there. Flux has also notification integrations with popular services like Prometheus Alertmanager, PagerDuty, Slack and so on. Flux has graduated in CNCF in 2022. Harbor is an "open source trusted cloud native registry project that stores, signs, and scans content." It became an incubating project in September 2019 and graduated in June 2020. Helm is a package manager that helps developers "easily manage and deploy applications onto the Kubernetes cluster." It joined the incubating level in June 2018 and graduated in April 2020. Istio is a service mesh technology. It was accepted by CNCF in September 2022 and graduated on July 12, 2023. Jaeger, Created by Uber Engineering, Jaeger is an open source distributed tracing system inspired by Google Dapper paper and OpenZipkin community. It can be used for tracing microservice-based architectures, including distributed context propagation, distributed transaction monitoring, root cause analysis, service dependency analysis, and performance/latency optimization. The Cloud Native Computing Foundation Technical Oversight Committee voted to accept Jaeger as the 12th hosted project in September 2017 and became a graduated project in 2019. In 2020 it became an approved and fully integrated part of the CNCF ecosystem. Kubernetes is an open source framework for automating deployment and managing applications in a containerized and clustered environment. "It aims to provide better ways of managing related, distributed components across the varied infrastructure." It was originally designed by Google and donated to The Linux Foundation to form the Cloud Native Computing Foundation with Kubernetes as the seed technology. The "large and diverse" community supporting the project has made its staying power more robust than other, older technologies of the same ilk. In January 2020, the CNCF annual report showed significant growth in interest, training, event attendance and investment related to Kubernetes. Linkerd is CNCF's fifth member project, and the project that coined the term "service mesh". Linkerd adds observability, security, and reliability features to applications by adding them to the platform rather than the application layer, and features a "micro-proxy" to maximize speed and security of its data plane. Linkerd graduated from CNCF in July 2021. Open Policy Agent (OPA) is "an open source general-purpose policy engine and language for cloud infrastructure." It became a CNCF incubating project in April 2019. OPA graduated from CNCF in February 2021. Prometheus is a cloud monitoring tool sponsored by SoundCloud in early iterations. In August 2018, the tool was designated a graduated project by the Cloud Native Computing Foundation. It is now a Cloud Native Computing Foundation member project. Rook is CNCF's first cloud native storage project. It became an incubation level project in 2018 and graduated in October 2020. SPIFFE is an open standard and framework for workload identity, much the same way that OAuth is an open standard and framework for human identity. It is built from the ground up to accommodate modern computing environments, which operate with systems scale and velocity (as opposed to human scale and velocity), while still maintaining interoperability with existing technologies like OAuth and X.509 Public key infrastructure. Unlike other identity standards, SPIFFE supports multiple credential types for a single identity, ensuring that the highly varied needs of production environments are consistently met without compromise. SPIFFE joined the CNCF as a sandbox project in 2018, was accepted to incubation in 2020, and graduated in 2022. SPIRE is an open source identity provider for workloads based on the SPIFFE framework. It is highly pluggable, and fills the attestation and issuance needs required by any workload identity solution. The plugin interfaces it exposes allows users to write integrations with in-house systems, build internal self-service portals, and more. It is a very powerful building block for issuing short-lived identity credentials to dynamic cloud workloads. SPIRE became a CNCF Graduated project in 2022. The Update Framework (TUF) helps developers to secure new or existing software update systems, which are often found to be vulnerable to many known attacks. TUF addresses this widespread problem by providing a comprehensive, flexible security framework that developers can integrate with any software update system. TUF was CNCF's first security-focused project and the ninth project overall to graduate from the foundation's hosting program. TiKV provides a distributed key–value database. Vitess is a database clustering system for horizontal scaling of MySQL, first created for internal use by YouTube. It became a CNCF project in 2018 and graduated in November 2019. Contour is a management server for Envoy that can direct the management of Kubernetes' traffic. Contour also provides routing features that are more advanced than Kubernetes' out-of-the-box Ingress specification. VMWare contributed the project to CNCF in July 2020. Cortex offers horizontally scalable, multi-tenant, long-term storage for Prometheus and works alongside Amazon DynamoDB, Google Bigtable, Cassandra, S3, GCS, and Microsoft Azure. It was introduced into the ecosystem incubator alongside Thanos in August 2020. CRI-O is an Open Container Initiative (OCI) based "implementation of Kubernetes Container Runtime Interface". CRI-O allows Kubernetes to be container runtime-agnostic. It became an incubating project in 2019. gRPC is a "modern open source high performance RPC framework that can run in any environment." The project was formed in 2015 when Google decided to open sou

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  • System of record

    System of record

    A system of record (SOR) or source system of record (SSoR) is a data management term for an information storage system (commonly implemented on a computer system running a database management system) that is the authoritative data source for a given data element or piece of information, like for example a row (or record) in a table. In data vault it is referred to as the record source. == Background == The need to identify systems of record can become acute in organizations where management information systems have been built by taking output data from multiple source systems, re-processing this data, and then re-presenting the result for a new business use. In these cases, multiple information systems may disagree about the same piece of information. These disagreements may stem from semantic differences, differences in opinion, use of different sources, differences in the timing of the extract, transform, load processes that create the data they report against, or may simply be the result of bugs. == Use == The integrity and validity of any data set is open to question when there is no traceable connection to a good source, and listing a source system of record is a solution to this. Where the integrity of the data is vital, if there is an agreed system of record, the data element must either be linked to, or extracted directly from it. In other cases, the provenance and estimated data quality should be documented. The "system of record" approach is a good fit for environments where both: there is a single authority over all data consumers, and all consumers have similar needs == Trade-offs == In diverse environments, one instead needs to support the presence of multiple opinions. Consumers may accept different authorities or may differ on what constitutes an authoritative source—researchers may prefer carefully vetted data, while tactical military systems may require the most recent credible report.

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  • Knowledge organization system

    Knowledge organization system

    Knowledge organization system (KOS), concept system, or concept scheme is the generic term used in knowledge organization (KO) for the selection of concepts with an indication of selected semantic relations. Despite their differences in type, coverage, and application, all KOS aim to support the organization of knowledge and information to facilitate their management and retrieval. KOS vary in complexity from simple sorted lists to complex relational networks. They represent both structural and functional features, and serve to eliminate ambiguity, control synonyms, establish relationships, and present properties. From their origins in library and information science (LIS), KOS have been applied to other domains and disciplines within science and industry, although scholarly research and debate remain primarily within the KO field. Challenges of KOS include ambiguity of terminology, repercussions of biased systems, and potential obsolescence. KOS can be expressed in RDF and RDFS as per the Simple Knowledge Organization System (SKOS) recommendation by W3C, which aims to enable the sharing and linking of KOS via the Web. One of the largest collections of KOS is the BARTOC registry. == Types == While different schema of KOS have been proposed, most are generally arranged in terms of the complexity of their construction and maintenance. Some scholars argue that organizing KOS on a spectrum oversimplifies the shared characteristics among them, and may even result in a non-ideal structure being chosen. The following types are not exhaustive, and are often not mutually-exclusive in practice. === Term lists === Term lists are the least structured form of KOS. They include lists, glossaries, dictionaries, and synonym rings. Authority files and gazetteers may also be considered term lists, however other scholars categorize them and directories as "metadata-like models". Examples include the Union List of Artist Names name authority file and the GeoNames gazetteer. === Categorization and classification === KOS that emphasize specific (and often hierarchical) structures include subject headings, taxonomies, categorization schema, and classification schema & systems. Despite inconsistent use of the terms "categorization" and "classification" in some literature, categorization is generally loosely-assembled grouping schema and may include attributes that are not mutually exclusive (or having fuzzy boundaries), while classification is related to the arrangement of non-overlapping and mutually-exclusive classes. Classification schema may be universal (such as Dewey Decimal Classification and Information Coding Classification) or domain-specific (such as the National Library of Medicine Classification). === Relationship models === The types of KOS with greatest complexity and which utilize connections between concepts include thesauri, semantic networks, and ontologies. One of the most prominent examples of a semantic network is WordNet. === Others === Certain structures proposed to be considered types of KOS—but are not consistently included in schema—include folksonomies, topic maps, web directory structures, publication organization systems, and bibliometric maps. Some KOS organize other KOS themselves—for instance, PeriodO is a gazetteer of periodization categories. == Applications == Some early KOS were developed as a support system for abstracting and indexing services to be used by specially-trained searchers. With the growth of information digitization, usability became increasingly accessible, and more complex structures were developed. Prominent examples of KOS outside of LIS include organism taxonomy in biology, the periodic table of elements in chemistry, SIC and NAICS classification systems for industry & business, and AGROVOC agricultural controlled vocabulary. == Challenges == The study and design of KOS is an ongoing topic of discussion among KO scholars. === Terminology === [There is] a serious lack of vocabulary control in the literature on controlled vocabulary. Inconsistency of terminology within the study of KOS is a common issue. For instance, "ontology" is used for both a specific type of KOS as well as a generic term for any KOS. The terms "taxonomy", "classification", and "categorization" are also sometimes used interchangeably. === Bias === As knowledge can be historically and culturally biased, scholars have also discussed how KOS themselves can perpetuate harmful practices or stereotypes. For example, a number of concerns and criticisms about the classification of mental disorders in the Diagnostic and Statistical Manual of Mental Disorders have been raised, contributing to ongoing revisions. Ethical and intentional design approaches have been proposed for multi-perspective KOS in efforts to mitigate bias and other harmful practices. === Obsolescence === The possible obsolescence of the thesaurus and other simpler KOS has been the topic of debate, especially in the face of increasingly complex ontologies, the growing usage of "Google-like retrieval systems", and the move of KO theory and research away from LIS and toward computer science. Supporters of thesauri argue its continued usefulness for metadata enrichment, vocabulary mapping, and web services, as well as its usage in specific domains such as corporate intranets and digital image libraries.

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  • AlphaTensor

    AlphaTensor

    AlphaTensor is an artificial intelligence system developed by DeepMind for discovering efficient matrix multiplication algorithms using reinforcement learning. Introduced in 2022, the system was based on AlphaZero and formulated the search for matrix multiplication algorithms as a single-player game called TensorGame. AlphaTensor was designed to search for new ways to multiply matrices with fewer scalar multiplication operations. Matrix multiplication is a fundamental operation in linear algebra, numerical analysis, scientific computing, computer graphics, and machine learning. The system discovered thousands of matrix multiplication algorithms, including algorithms that rediscovered known human-designed methods and others that improved on previously known results for particular matrix sizes and mathematical settings. == Background == Matrix multiplication is one of the basic operations in numerical computing. The standard algorithm for multiplying two square matrices has cubic time complexity, while faster algorithms such as the Strassen algorithm reduce the number of multiplication operations by using more complex algebraic decompositions. Finding optimal matrix multiplication algorithms can be difficult because it involves searching through a large space of possible tensor decompositions. AlphaTensor approached this problem by representing algorithm discovery as TensorGame, in which each move corresponds to an operation that reduces a tensor representing matrix multiplication. The goal of the game is to find a low-rank decomposition of the matrix multiplication tensor, corresponding to an efficient multiplication algorithm. == Development == AlphaTensor was developed by DeepMind and described in a paper published in Nature in October 2022. The system built on the reinforcement-learning approach used in AlphaZero, which had previously been applied to games such as Go, chess, and shogi. Unlike those games, TensorGame involved a very large search space, requiring changes to the AlphaZero-style search method and neural network architecture. DeepMind released source code and discovered algorithms associated with the publication through a public GitHub repository. == Results == AlphaTensor discovered matrix multiplication algorithms over both standard arithmetic and finite fields. One widely reported result was a method for multiplying 4 × 4 matrices over the field with two elements using 47 multiplication operations, improving on the 49 operations required by applying Strassen's algorithm recursively in that setting. The system also found algorithms optimized for particular computer hardware, including algorithms designed for graphics processing units and Tensor Processing Units. DeepMind stated that some of the hardware-specific algorithms improved practical execution time compared with commonly used algorithms on the tested hardware. == Significance == AlphaTensor was described as an example of using machine learning not only to apply existing algorithms, but to assist in discovering new ones. The work was connected to broader research in algorithm discovery, automated machine learning, program synthesis, and computational complexity theory, especially the open problem of determining the optimal complexity of matrix multiplication. AlphaTensor later became part of a broader group of Google DeepMind systems for algorithm and mathematical discovery, alongside systems such as AlphaDev and AlphaEvolve.

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  • Diia

    Diia

    Diia (Ukrainian: Дія [ˈd⁽ʲ⁾ijɐ] , lit. 'Action'; also an acronym for Держава і Я, Derzhava i Ya, IPA: [derˈʒɑwɐ i ˈjɑ], lit. 'State and Me') is a mobile app, a web portal and a brand of e-governance in Ukraine. Launched in 2020, the Diia app allows Ukrainian citizens to use digital documents on their smartphones instead of physical ones for identification and sharing purposes. The Diia portal allows access to over 130 government services. Eventually, the government plans to make all kinds of state-person interactions available through Diia. Diia was built in partnership with the United States and is poised to be shared with other countries. On the sidelines of the 2023 World Economic Forum in Davos, USAID Administrator Samantha Power said the US hopes to replicate the success of Diia in other countries. == History == Diia was first presented on September 27, 2019, by the Ministry of Digital Transformation of Ukraine as a brand of the State in a Smartphone project. Vice Prime Minister and Minister of Digital Transformation Mykhailo Fedorov announced the creation of a mobile app and a web portal that would unite in a single place all the services provided by the state to citizens and businesses. On February 6, 2020, the mobile app Diia was officially launched. During the presentation, Ukrainian President Volodymyr Zelensky said that 9 million Ukrainians now have access to their driver's license and car registration documents on their phones, while Prime Minister Oleksiy Honcharuk called the implementation of the State in a Smartphone project a priority for the government. In April 2020, the Ukrainian government approved a resolution for experimental usage of digital ID-cards and passports which would be issued to all Ukrainians via the Diia. On October 5, 2020, during the Diia Summit, the government presented a first major update of the app and web portal branded "Diia 2.0". More types of documents were added to the app as well as the ability to share documents with others via a single tap on a push-message. The web portal in turn expanded the number of available services to 27, including the ability to register a private limited company in half an hour. President Zelensky who opened the summit, announced that in 2021 Ukraine will enter the "paper less" mode by prohibiting civil servants from demanding paper documents. By the end of 2020, the app had more than six million users, while the portal had 50 available services. In March 2021, the Ukrainian parliament adopted a bill equating digital identity documents with their physical analogues. Starting on August 23, Ukrainian citizens can use digital ID-cards and passports for all purposes while in Ukraine. According to Minister of Digital Transformation Mykhailo Fedorov, Ukraine will become the first country in the world where digital identity documents are considered legally equivalent to ordinary ones. In September 2024, Diia launched an online marriage registration service, which can be beneficial especially for military personnel who spend much time on the frontline separated from their partners. In October 2024, Diia's online marriage service appeared in Time's Inventions of the 2024 list. In the first month of its operations over 1.1 million Ukrainians tried to make proposals using the technology, and 435 couples got married. == Benefits and challenges == The first and most obvious benefit is the convenience of such a platform. Citizens can have many documents on their smartphones at once, without concern about losing or damaging them. Whenever needed, they can just open an app on their smartphones and show/check the document they need. The idea is that Diia will help cut the bureaucracy associated with public services, which in turn will help fight corruption and increase government savings. Fewer people are needed to be employed in the public sector and fewer human to human interactions are supposed to happen. With the start of the program, already 10% of government employees were reduced, which contributes to hundreds of millions of dollars in savings, but besides this, the initiative also improves the speed, efficiency, and transparency of government services. In addition, the digitalization of the government sector helps to develop the whole IT industry in the country, people become more digitally aware and educated, this affects other sectors as well, increasing the spread of digital infrastructure and expediting the speed of overall digitalization. The UN E-government Development Index, which assesses the capabilities of governments to integrate its functions electronically, such as the use of internet and mobile devices, ranked Ukraine 69th in 193 countries surveyed in 2020. Despite its low ranking in the e-government development index, Ukraine made a big jump on the e-participation index, which they ranked 43rd out of 193 countries from 0.66 in 2018 to 0.81 in 2020 (un.org, 2020), suggesting that the government and its citizens are adapting the IT-based government functions. The main goal of e-government according to Perez-Morote et.al. (2020) is to have accountability and transparency among the countries involved. But to do so, there are several challenges that a country should assess first prior to implementing e-government. In the research written by Heeks (2001), the author identified 2 main challenges that countries face in the development of e-government, first is the strategic challenge which involves the preparedness (e-readiness) of the entire government system for electronic transformation, and second challenge is the tactical challenge where the government must design (e-governance design) a system where it can be understood by every user, it's important that the information that needs to be communicated to the consumers is received clearly. For the first challenge (e-readiness), Ukraine had an internet penetration rate of 76% in 2020 and is expected to grow to 82%, it is important that consumers have the internet access for it to enable the consumers to utilize the service. Another factor is the readiness of its institutional infrastructure, which means that the government has its own organization which is solely focused on implementing the e-government project. In the case of Ukraine, the e-governance team is led by Oleksandr Ryzhenko, and the country's e-governance initiative is even further strengthened by ensuring that the data and legal infrastructure are already prepared. Ukraine has done this by modernizing their legislation that is more appropriate in the digital service, and the data exchange solution used by Ukraine is called Trembita. The human infrastructure is also being updated, as competent individuals must be the one doing the task, hence, EGOV4UKRAINE was launched, this aims to get IT developers for developing a system for administrative services. These efforts by the Ukrainian government did not go unnoticed, and they received an award from the e-Governance Academy as "partner of the year 2017". For the second challenge, which deals with the system design, the success of Ukraine can be seen on the latest data of UNDP, where it shows a high increase in the E-participation index. In 2018, Ukraine ranked 75th it ranked 46th in 2020 (un.org, 2020). Despite visible success, the implementation of the e-government was accompanied by problems. Data leakage became the main one. In May 2020, the data of 26 million driver's licenses appeared in the public domain on the Internet. The Ukrainian government said the Diia app was not linked to a data breach, but it is impossible to say for certain. Any storage of official documents in electronic format is associated with the risk of their leakage. In addition, the Diia application still has data protection issues, as the required protection system has not been implemented. This is also compounded by the country's weak data protection legal regime. In addition, since 2023, Ukrainians are able to register their cars with this app. Issued license plates are not using regional codes, but they are using special codes starting with DI or PD. == Diia City == In May 2020, the government presented Diia City headed by Oleksandr Borniakov, a large-scale project which would establish a virtual model of a free economic zone for representatives of the creative economy. It would provide for special digital residency with a particular taxation regime, intellectual property protection and simplified regulations. Diia City concurrently imposes certain constraints on contracts involving individual entrepreneurs (FOPs). It also offers the benefit of tax rebates. Diia City garners endorsement from the Ukrainian government, believing it will support the country's position in the IT market. As of July 30, 2023, the program had more than 600 residents, including companies like iGama, Avenga, SBRobotiks, and Intellectsoft.

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  • Master data

    Master data

    Master data represents "data about the business entities that provide context for business transactions". The most commonly found categories of master data are parties (individuals and organisations, and their roles, such as customers, suppliers, employees), products, financial structures (such as ledgers and cost centres) and locational concepts. Master data should be distinguished from reference data. While both provide context for business transactions, reference data is concerned with classification and categorisation, while master data is concerned with business entities. Master data is, by its nature, almost always non-transactional in nature. There exist edge cases where an organization may need to treat certain transactional processes and operations as "master data". This arises, for example, where information about master data entities, such as customers or products, is only contained within transactional data such as orders and receipts and is not housed separately. ISO 8000 is the international standard for data quality and data portability in master data. == Alternative definition == An alternative definition of the term master data is that it represents the business objects that contain the most valuable, agreed upon information shared across an organization. In this sense, it gives context to business activities and transactions, answering questions like who, what, when and how as well as expanding the ability to make sense of these activities through categorizations, groupings and hierarchies. It can cover relatively static reference data, transactional, unstructured, analytical, hierarchical and metadata. What constitutes master data under this definition is therefore not about an essential quality of the data (e.g. it is a business entity that provides context for business transactions), but rather about the context in which the organisation has decided to treat the data. == Externally-defined master data == For most organisations, most or all master data is defined and managed within that organisation. Some master data, however, may be externally defined and managed. This represents the single source of basic business data used across a marketplace, regardless of organisation or location. Thus, it can be used by multiple enterprises within a value chain, facilitating "integration of multiple data sources and literally [putting] everyone in the market on the same page." An example of market master data is the Universal Product Code (UPC) found on consumer products. == Master data management == Curating and managing master data is key to ensuring its quality and thus fitness for purpose. All aspects of an organisation, operational and analytical, are greatly dependent on the quality of an organization's master data. Master Data is therefore the focus of the information technology (IT) discipline of master data management (MDM). Without this discipline in place, organisations commonly encounter difficulties with having multiple versions of "the truth" about a business entity, both within individual applications, and distributed across applications.

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  • Skyline operator

    Skyline operator

    The skyline operator is the subject of an optimization problem and computes the Pareto optimum on tuples with multiple dimensions. This operator is an extension to SQL proposed by Börzsönyi et al. to filter results from a database to keep only those objects that are not dominated by any other point on all dimensions. The name skyline comes from the view on Manhattan from the Hudson River, where those buildings can be seen that are not hidden by any other. A building is visible if it is not dominated by a building that is taller or closer to the river (two dimensions, distance to the river minimized, height maximized). Another application of the skyline operator involves selecting a hotel for a holiday. The user wants the hotel to be both cheap and close to the beach. However, hotels that are close to the beach may also be expensive. In this case, the skyline operator would only present those hotels that are not worse than any other hotel in both price and distance to the beach. == Formal specification == The skyline operator returns tuples that are not dominated by any other tuple. A tuple dominates another if it is at least as good in all dimensions and better in at least one dimension. Formally, we can think of each tuple as a vector p , q ∈ R n {\displaystyle p,q\in \mathbb {R} ^{n}} . p {\displaystyle p} dominates q {\displaystyle q} (written: p ≻ q {\displaystyle p\succ q} ) if p {\displaystyle p} is at least as good as q {\displaystyle q} in every dimension, and superior in at least one: p ≻ q ⇔ ∀ i ∈ [ n ] . p [ i ] ⪰ q [ i ] ∧ ∃ j ∈ [ n ] . p [ j ] ≻ q [ j ] . {\displaystyle p\succ q\Leftrightarrow \forall i\in [n].p[i]\succeq q[i]\wedge \exists j\in [n].p[j]\succ q[j].} Dominance ( p ≻ q {\displaystyle p\succ q} ) can be defined as any strict partial ordering, for example greater (with ≻:=> {\displaystyle \succ :=>} and ⪰:=≥ {\displaystyle \succeq :=\geq } ) or less (with ≻:=< {\displaystyle \succ :=<} and ⪰:=≤ {\displaystyle \succeq :=\leq } ). Assuming two dimensions and defining dominance in both dimensions as greater, we can compute the skyline in SQL-92 as follows: == Proposed syntax == As an extension to SQL, Börzsönyi et al. proposed the following syntax for the skyline operator: where d1, ... dm denote the dimensions of the skyline and MIN, MAX and DIFF specify whether the value in that dimension should be minimised, maximised or simply be different. Without an SQL extension, the SQL query requires an antijoin with not exists: == Implementation == The skyline operator can be implemented directly in SQL using current SQL constructs, but this has been shown to be very slow in disk-based database systems. Other algorithms have been proposed that make use of divide and conquer, indices, MapReduce and general-purpose computing on graphics cards. Skyline queries on data streams (i.e. continuous skyline queries) have been studied in the context of parallel query processing on multicores, owing to their wide diffusion in real-time decision making problems and data streaming analytics. Exasol features a native implementation.

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  • Information flow

    Information flow

    In discourse-based grammatical theory, information flow is any tracking of referential information by speakers. Information may be new, i.e., just introduced into the conversation; given, i.e., already active in the speakers' consciousness; or old, i.e., no longer active. The various types of activation, and how these are defined, are model-dependent. Information flow affects grammatical structures such as: Word order (topic, focus, and afterthought constructions). Active, passive, or middle voice. Choice of deixis, such as articles; "medial" deictics such as Spanish ese and Japanese sore are generally determined by the familiarity of a referent rather than by physical distance. Overtness of information, such as whether an argument of a verb is indicated by a lexical noun phrase, a pronoun, or not mentioned at all. Clefting: Splitting a single clause into two clauses, each with its own verb, e.g. ‘The chicken turtles tasted like chicken.’ becomes ‘It was the chicken turtle | that tasted like chicken.’ In this case, clefting is used to shift the focus of the sentence to the subject, the chicken turtle. Front focus: Placing at the start (front) of a sentence information that would normally occur later in the sentence, to give it extra prominence. For example, in pop culture, Yoda's speech often utilizes such syntactic construction, such as when he says 'much to learn you still have' to Luke Skywalker. End focus (or end weight): Given or familiar information followed by new information. This gives prominence to the final part of the sentences and can enable suspense to build, e.g. ‘Through the door came a gigantic wolf’.(Umer Prince)

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  • Manifold regularization

    Manifold regularization

    In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm

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