Waikato Environment for Knowledge Analysis (Weka) is a collection of machine learning and data analysis free software licensed under the GNU General Public License. It was developed at the University of Waikato, New Zealand, and is the companion software to the book "Data Mining: Practical Machine Learning Tools and Techniques". == Description == Weka contains a collection of visualization tools and algorithms for data analysis and predictive modeling, together with graphical user interfaces for easy access to these functions. The original non-Java version of Weka was a Tcl/Tk front-end to (mostly third-party) modeling algorithms implemented in other programming languages, plus data preprocessing utilities in C, and a makefile-based system for running machine learning experiments. This original version was primarily designed as a tool for analyzing data from agricultural domains, but the more recent fully Java-based version (Weka 3), for which development started in 1997, is now used in many different application areas, in particular for educational purposes and research. Advantages of Weka include: Free availability under the GNU General Public License. Portability, since it is fully implemented in the Java programming language and thus runs on almost any modern computing platform. A comprehensive collection of data preprocessing and modeling techniques. Ease of use due to its graphical user interfaces. Weka supports several standard data mining tasks, more specifically, data preprocessing, clustering, classification, regression, visualization, and feature selection. Input to Weka is expected to be formatted according the Attribute-Relational File Format and with the filename bearing the .arff extension. All of Weka's techniques are predicated on the assumption that the data is available as one flat file or relation, where each data point is described by a fixed number of attributes (normally, numeric or nominal attributes, but some other attribute types are also supported). Weka provides access to SQL databases using Java Database Connectivity and can process the result returned by a database query. Weka provides access to deep learning with Deeplearning4j. It is not capable of multi-relational data mining, but there is separate software for converting a collection of linked database tables into a single table that is suitable for processing using Weka. Another important area that is currently not covered by the algorithms included in the Weka distribution is sequence modeling. == Extension packages == In version 3.7.2, a package manager was added to allow the easier installation of extension packages. Some functionality that used to be included with Weka prior to this version has since been moved into such extension packages, but this change also makes it easier for others to contribute extensions to Weka and to maintain the software, as this modular architecture allows independent updates of the Weka core and individual extensions. == History == In 1993, the University of Waikato in New Zealand began development of the original version of Weka, which became a mix of Tcl/Tk, C, and makefiles. In 1997, the decision was made to redevelop Weka from scratch in Java, including implementations of modeling algorithms. In 2005, Weka received the SIGKDD Data Mining and Knowledge Discovery Service Award. In 2006, Pentaho Corporation acquired an exclusive licence to use Weka for business intelligence. It forms the data mining and predictive analytics component of the Pentaho business intelligence suite. Pentaho has since been acquired by Hitachi Vantara, and Weka now underpins the PMI (Plugin for Machine Intelligence) open source component. == Related tools == Auto-WEKA is an automated machine learning system for Weka. Environment for DeveLoping KDD-Applications Supported by Index-Structures (ELKI) is a similar project to Weka with a focus on cluster analysis, i.e., unsupervised methods. H2O.ai is an open-source data science and machine learning platform KNIME is a machine learning and data mining software implemented in Java. Massive Online Analysis (MOA) is an open-source project for large scale mining of data streams, also developed at the University of Waikato in New Zealand. Neural Designer is a data mining software based on deep learning techniques written in C++. Orange is a similar open-source project for data mining, machine learning and visualization based on scikit-learn. RapidMiner is a commercial machine learning framework implemented in Java which integrates Weka. scikit-learn is a popular machine learning library in Python.
EM algorithm and GMM model
In statistics, EM (expectation maximization) algorithm handles latent variables, while GMM is the Gaussian mixture model. == Background == In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the control group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red blood cell hemoglobin concentration than those without Anemia. x {\displaystyle x} is a random vector such as x := ( red blood cell volume , red blood cell hemoglobin concentration ) {\displaystyle x:={\big (}{\text{red blood cell volume}},{\text{red blood cell hemoglobin concentration}}{\big )}} , and from medical studies it is known that x {\displaystyle x} are normally distributed in each group, i.e. x ∼ N ( μ , Σ ) {\displaystyle x\sim {\mathcal {N}}(\mu ,\Sigma )} . z {\displaystyle z} is denoted as the group where x {\displaystyle x} belongs, with z i = 0 {\displaystyle z_{i}=0} when x i {\displaystyle x_{i}} belongs to the Anemia group and z i = 1 {\displaystyle z_{i}=1} when x i {\displaystyle x_{i}} belongs to the control group. Also z ∼ Categorical ( k , ϕ ) {\displaystyle z\sim \operatorname {Categorical} (k,\phi )} where k = 2 {\displaystyle k=2} , ϕ j ≥ 0 , {\displaystyle \phi _{j}\geq 0,} and ∑ j = 1 k ϕ j = 1 {\displaystyle \sum _{j=1}^{k}\phi _{j}=1} . See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } . A maximum likelihood estimation can be applied: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ( p ( x ( i ) ; ϕ , μ , Σ ) ) = ∑ i = 1 m log ∑ z ( i ) = 1 k p ( x ( i ) ∣ z ( i ) ; μ , Σ ) p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log(p(x^{(i)};\phi ,\mu ,\Sigma ))=\sum _{i=1}^{m}\log \sum _{z^{(i)}=1}^{k}p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)p(z^{(i)};\phi )} As the z i {\displaystyle z_{i}} for each x i {\displaystyle x_{i}} are known, the log likelihood function can be simplified as below: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log p ( x ( i ) ∣ z ( i ) ; μ , Σ ) + log p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)+\log p\left(z^{(i)};\phi \right)} Now the likelihood function can be maximized by making partial derivative over μ , Σ , ϕ {\displaystyle \mu ,\Sigma ,\phi } , obtaining: ϕ j = 1 m ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \phi _{j}={\frac {1}{m}}\sum _{i=1}^{m}1\{z^{(i)}=j\}} μ j = ∑ i = 1 m 1 { z ( i ) = j } x ( i ) ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \mu _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}x^{(i)}}{\sum _{i=1}^{m}1\left\{z^{(i)}=j\right\}}}} Σ j = ∑ i = 1 m 1 { z ( i ) = j } ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \Sigma _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}(x^{(i)}-\mu _{j})(x^{(i)}-\mu _{j})^{T}}{\sum _{i=1}^{m}1\{z^{(i)}=j\}}}} If z i {\displaystyle z_{i}} is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if z i {\displaystyle z_{i}} is unknown it is much more complicated. Being z {\displaystyle z} a latent variable (i.e. not observed), with unlabeled scenario, the expectation maximization algorithm is needed to estimate z {\displaystyle z} as well as other parameters. Generally, this problem is set as a GMM since the data in each group is normally distributed. In machine learning, the latent variable z {\displaystyle z} is considered as a latent pattern lying under the data, which the observer is not able to see very directly. x i {\displaystyle x_{i}} is the known data, while ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } are the parameter of the model. With the EM algorithm, some underlying pattern z {\displaystyle z} in the data x i {\displaystyle x_{i}} can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important. == EM algorithm in GMM == The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z ( i ) {\displaystyle z^{(i)}} can be randomly initialized. In the E-step, the algorithm tries to guess the value of z ( i ) {\displaystyle z^{(i)}} based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of z ( i ) {\displaystyle z^{(i)}} of the E-step. These two steps are repeated until convergence is reached. The algorithm in GMM is: Repeat until convergence: 1. (E-step) For each i , j {\displaystyle i,j} , set w j ( i ) := p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) {\displaystyle w_{j}^{(i)}:=p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)} 2. (M-step) Update the parameters ϕ j := 1 m ∑ i = 1 m w j ( i ) {\displaystyle \phi _{j}:={\frac {1}{m}}\sum _{i=1}^{m}w_{j}^{(i)}} μ j := ∑ i = 1 m w j ( i ) x ( i ) ∑ i = 1 m w j ( i ) {\displaystyle \mu _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}x^{(i)}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} Σ j := ∑ i = 1 m w j ( i ) ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m w j ( i ) {\displaystyle \Sigma _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}\left(x^{(i)}-\mu _{j}\right)\left(x^{(i)}-\mu _{j}\right)^{T}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} With Bayes' rule, the following result is obtained by the E-step: p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) = p ( x ( i ) | z ( i ) = j ; μ , Σ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) | z ( i ) = l ; μ , Σ ) p ( z ( i ) = l ; ϕ ) {\displaystyle p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)={\frac {p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)p\left(z^{(i)}=j;\phi \right)}{\sum _{l=1}^{k}p\left(x^{(i)}|z^{(i)}=l;\mu ,\Sigma \right)p\left(z^{(i)}=l;\phi \right)}}} According to GMM setting, these following formulas are obtained: p ( x ( i ) | z ( i ) = j ; μ , Σ ) = 1 ( 2 π ) n / 2 | Σ j | 1 / 2 exp ( − 1 2 ( x ( i ) − μ j ) T Σ j − 1 ( x ( i ) − μ j ) ) {\displaystyle p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)={\frac {1}{(2\pi )^{n/2}\left|\Sigma _{j}\right|^{1/2}}}\exp \left(-{\frac {1}{2}}\left(x^{(i)}-\mu _{j}\right)^{T}\Sigma _{j}^{-1}\left(x^{(i)}-\mu _{j}\right)\right)} p ( z ( i ) = j ; ϕ ) = ϕ j {\displaystyle p\left(z^{(i)}=j;\phi \right)=\phi _{j}} In this way, a switch between the E-step and the M-step is possible, according to the randomly initialized parameters.
Safe and Secure Innovation for Frontier Artificial Intelligence Models Act
The Safe and Secure Innovation for Frontier Artificial Intelligence Models Act, or SB 1047, was a failed 2024 California bill intended to "mitigate the risk of catastrophic harms from AI models so advanced that they are not yet known to exist". Specifically, the bill would have applied to models which cost more than $100 million to train and were trained using a quantity of computing power greater than 1026 integer or floating-point operations. SB 1047 would have applied to all AI companies doing business in California—the location of the company would not matter. The bill would have created protections for whistleblowers and required developers to perform risk assessments of their models prior to release, with guidance from the Government Operations Agency. It would also have established CalCompute, a University of California public cloud computing cluster for startups, researchers and community groups. == Background == The rapid increase in capabilities of AI systems in the 2020s, including the release of ChatGPT in November 2022, caused some researchers and members of the public to become concerned about the existential risks associated with increasingly powerful AI systems. Hundreds of tech executives and AI researchers, including two of the so-called "Godfathers of AI", Geoffrey Hinton and Yoshua Bengio, signed a statement in May 2023 calling for the mitigation of the "risk of extinction from AI" to be a global priority alongside "pandemics and nuclear war". However, the plausibility of these risks is still widely debated. Strong regulation of AI has been criticized for purportedly causing regulatory capture by large AI companies like OpenAI, a phenomenon in which regulation advances the interest of larger companies at the expense of smaller competition and the public in general, although OpenAI ended up opposing the bill. Other advocates of AI regulation aim to prevent bias and privacy violations, rather than existential risks. For example, some experts who view existential concerns as overblown and unrealistic view them as a distraction from near-term harms of AI like discriminatory automated decision making. In the face of existential concerns, technology companies have made voluntary commitments to conduct safety testing, for example at the AI Safety Summit and AI Seoul Summit. In 2023, not long before the bill was proposed, Governor Newsom of California and President Biden issued executive orders on artificial intelligence. State Senator Wiener said SB 1047 draws heavily on the Biden executive order, and is motivated by the absence of unified federal legislation on AI safety. Historically, California has passed regulation on several tech issues itself, including consumer privacy and net neutrality, in the absence of action by Congress. == History == === Proposal and voting === The bill was authored by State Senator Scott Wiener. Wiener first proposed AI legislation for California through an intent bill called SB 294, the Safety in Artificial Intelligence Act, in September 2023. On February 7, 2024, Wiener introduced SB 1047. On May 21, SB 1047 passed the Senate 32–1. The bill was significantly amended by Wiener on August 15, 2024, in response to industry advice. Amendments included adding clarifications, and removing the creation of a "Frontier Model Division" and the penalty of perjury. On August 28, the bill passed the State Assembly 48–16. Then, due to the amendments, the bill was once again voted on by the Senate, passing 30–9. === Veto by governor === On September 29, Governor Gavin Newsom vetoed the bill. The deadline for California lawmakers to overrule Newsom's veto was November 30, 2024. Newsom cited concerns over the bill's regulatory framework targeting only large AI models based on their computational size, while not taking into account whether the models are deployed in high-risk environments. Newsom emphasized that this approach could create a false sense of security, overlooking smaller models that might present equally significant risks. He acknowledged the need for AI safety protocols but stressed the importance of adaptability in regulation as AI technology continues to evolve rapidly. Governor Newsom also committed to working with technology experts, federal partners, and research institutions, including the Carnegie Endowment for International Peace, led by former California Supreme Court Justice Mariano-Florentino Cuéllar; and Stanford University's Human-Centered AI (HAI) Institute, led by Dr. Fei-Fei Li. He announced plans to collaborate with these entities to advance responsible AI development, aiming to protect the public while fostering innovation. == Provisions == SB 1047 would have covered AI models with training compute over 1026 integer or floating-point operations and a cost of over $100 million. If a covered model is fine-tuned using more than $10 million, the resulting model would also have been covered. The bill would have defined critical harms with respect to four categories: Creation or use of a chemical, biological, radiological, or nuclear weapon Cyberattacks on critical infrastructure causing mass casualties or at least $500 million of damage Autonomous crimes causing mass casualties or at least $500 million of damage Other harms of comparable severity Developers would have needed to create a "safety and security protocol" before training covered models. Before deployment, they would have submitted a statement of compliance, confirming they took reasonable care to take measures to prevent covered models that pose an unreasonable risk of critical harms. The statement would have included risk assessments and descriptions of their compliance process. These rules would have applied to both covered models and their derivatives, including post-training modifications, with annual third-party audits required starting in 2026. Safeguards to reduce risk included the ability to shut down the model, which has been variously described as a "kill switch" and "circuit breaker". Whistleblowing provisions would have protected employees who report safety problems and incidents. Additionally, SB 1047 would have created a public cloud computing cluster called CalCompute, associated with the University of California, to support startups, researchers, and community groups that lack large-scale computing resources. === Compliance and supervision === SB 1047 would have required developers, beginning January 1, 2026, to annually retain a third-party auditor to perform an independent audit of compliance with the requirements of the bill, as provided. The Government Operations Agency would have reviewed the results of safety tests and incidents, and issue guidance, standards, and best practices. The bill would have created a Board of Frontier Models to supervise the application of the bill by the Government Operations Agency. It is would be composed of 9 members. == Reception == === Subjects of debate === Proponents of the bill described its provisions as simple and narrowly focused, with Sen. Scott Weiner describing it as a "light-touch, basic safety bill". This was disputed by critics of the bill, who described the bill's language as vague and criticized it as consolidating power in the largest AI companies at the expense of smaller ones. Proponents, in turn, argued that the bill only applies to models trained using more than 1026 FLOPS and with over $100 million, or fine-tuned with more than $10 million, and that the threshold could be increased if needed. The penalty of perjury was also a subject of debate, and was eventually removed through an amendment. The scope of the "kill switch" requirement was also reduced, following concerns from open-source developers. The use of the term "reasonable assurance" in the bill was also controversial, and it was eventually amended to "reasonable care". Critics then argued that "reasonable care" imposed an excessive burden by requiring confidence that models could not be used to cause catastrophic harm; proponents claimed that the standard did not require certainty and that it already applied to AI developers under existing law. === Support and opposition === Individual supporters of the bill included Turing Award recipients Yoshua Bengio and Geoffrey Hinton, Elon Musk, Bill de Blasio, Kevin Esvelt, Dan Hendrycks, Vitalik Buterin, OpenAI whistleblowers Daniel Kokotajlo and William Saunders, Lawrence Lessig, Sneha Revanur, Stuart Russell, Jan Leike, actors Mark Ruffalo, Sean Astin, and Rosie Perez, Scott Aaronson, and Max Tegmark. Over 120 Hollywood celebrities, including Mark Hamill, Jane Fonda, and J. J. Abrams, also signed a statement in support of the bill. Max Tegmark likened the bill's focus on holding companies responsible for the harms caused by their models to the FDA requiring clinical trials before a company can release a drug to the market. Organizations sponsoring the bill included the Center for AI Safety, Economic Security California and Encode. The la
Trustworthy AI
Trustworthy AI refers to artificial intelligence systems that are designed to have transparent reasoning, are explainable (XAI), accountable, robust, fair and honest, respectful of data privacy, and steerable or alignable with human goals. == Terminology == Recent work in AI ethics distinguishes trustworthiness and trustability as two different conditions relevant to trustworthy AI. Trustworthiness is concerned with whether an AI system or the institutions deploying it merit trust by being reliable, fair, and accountable. Trustability, on the other hand, is the prior question of whether a given entity is even the kind of thing to which interpersonal trust can coherently apply as opposed to mere instrumental reliance. Some philosophers argue that current AI systems are best understood as tools that are not genuine targets of interpersonal trust. They argue that trust should be directed toward the human and institutional arrangements that govern the systems' design, deployment, and oversight. This stance supports interpreting "trustworthy AI" as trustworthy governance and use of AI rather than trust in the artifacts themselves. Transparency in AI involves making the processes and decisions of such systems understandable to users and stakeholders. Accountability ensures that there are protocols for addressing adverse outcomes or biases that may arise, with designated responsibilities for oversight and remediation. Robustness and security aim to ensure that AI systems perform reliably under various conditions and are safeguarded against malicious attacks. Harmlessness can be achieved by refusal training: training the models to avoid problematic requests, and by adding filters to detect and prevent discussion on biased, unethical, or dangerous outputs. There is research on how to train AI so that it aligns with human goals. == Techniques and ITU standardization == Trustworthy AI creation is a goal of AI governance and policymaking. To achieve transparency and data privacy, several privacy-enhancing technologies (PETs) can be used. These include: Homomorphic encryption for computing with encrypted data without ever decrypting it. Federated learning and secure multi-party computation (MPC) for distributing the model training without sharing information between the learning centers and computing servers. Differential privacy for exposing statistical data while guaranteeing that no private information is exposed. Zero-knowledge proof - providing proven validity for statements without disclosing any extra information. A work programme for achieving Trustworthy AI was set up by the International Telecommunication Union, an agency of the United Nations, initiated under its AI for Good programme. Its origin lies with the ITU-WHO Focus Group on Artificial Intelligence for Health, where a strong need for both privacy and analytics created demand for a standard in these technologies. In 2020, AI for Good moved online, and the TrustworthyAI seminar series was established to initiate discussions on these topics. This eventually led to standardization activities. === Multi-party computation === Secure multi-party computation (MPC) is being standardized under "Question 5" (the incubator) of ITU-T Study Group 17. === Homomorphic encryption === Homomorphic encryption allows for computing on encrypted data, where the outcomes or result is still encrypted and unknown to those performing the computation, but can be deciphered by the original encryptor. It is often developed with the goal of enabling use in jurisdictions different from the data creation (under, for instance, GDPR). ITU has been collaborating since the early stage of the HomomorphicEncryption.org standardization meetings, which has developed a standard on homomorphic encryption. The fifth homomorphic encryption meeting was hosted at ITU HQ in Geneva. === Federated learning === Zero-sum masks as used by federated learning for privacy preservation are used extensively in the multimedia standards of ITU-T Study Group 16 (VCEG) such as JPEG, MP3, H.264, and H.265 (commonly known as MPEG). === Zero-knowledge proof === Previous pre-standardization work on the topic of zero-knowledge proof has been conducted in the ITU-T Focus Group on Digital Ledger Technologies. === Differential privacy === The application of differential privacy in the preservation of privacy was examined at several of the "Day 0" machine learning workshops at AI for Good Global Summits. == Mozilla "Rebel Alliance" == In January 2026, the Mozilla Foundation and its subsidiaries announced a strategic shift to deploy their entire $1.4 billion reserve into building what foundation president Mark Surman termed a "rebel alliance" for trustworthy AI. Framed by Surman as a mission-driven alternative to the market dominance of OpenAI and Anthropic, the initiative seeks to establish an open-source AI stack by 2028. The alliance includes several startups funded via Mozilla Ventures, specifically focusing on decentralized governance and transparency: Trail: A firm developing AI compliance frameworks for regulated industries. Transformer Lab: A developer of open-source tools for AI model management. Oumi: A platform for training and deploying open-source models. The "rebel alliance" terminology is a historical reference to Mozilla's efforts in 1998 to challenge Microsoft's browser monopoly. While the $1.4 billion in funding is significant, it has been contrasted with the tens of billions in capital raised by proprietary competitors like OpenAI.
Region connection calculus
The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean space, or in a topological space) by their possible relations to each other. RCC8 consists of 8 basic relations that are possible between two regions: disconnected (DC) externally connected (EC) equal (EQ) partially overlapping (PO) tangential proper part (TPP) tangential proper part inverse (TPPi) non-tangential proper part (NTPP) non-tangential proper part inverse (NTPPi) From these basic relations, combinations can be built. For example, proper part (PP) is the union of TPP and NTPP. == Axioms == RCC is governed by two axioms. for any region x, x connects with itself for any region x, y, if x connects with y, y connects with x == Remark on the axioms == The two axioms describe two features of the connection relation, but not the characteristic feature of the connect relation. For example, we can say that an object is less than 10 meters away from itself and that if object A is less than 10 meters away from object B, object B will be less than 10 meters away from object A. So, the relation 'less-than-10-meters' also satisfies the above two axioms, but does not talk about the connection relation in the intended sense of RCC. == Composition table == The composition table of RCC8 are as follows: "" denotes the universal relation, no relation can be discarded. Usage example: if a TPP b and b EC c, (row 4, column 2) of the table says that a DC c or a EC c. == Examples == The RCC8 calculus is intended for reasoning about spatial configurations. Consider the following example: two houses are connected via a road. Each house is located on an own property. The first house possibly touches the boundary of the property; the second one surely does not. What can we infer about the relation of the second property to the road? The spatial configuration can be formalized in RCC8 as the following constraint network: house1 DC house2 house1 {TPP, NTPP} property1 house1 {DC, EC} property2 house1 EC road house2 { DC, EC } property1 house2 NTPP property2 house2 EC road property1 { DC, EC } property2 road { DC, EC, TPP, TPPi, PO, EQ, NTPP, NTPPi } property1 road { DC, EC, TPP, TPPi, PO, EQ, NTPP, NTPPi } property2 Using the RCC8 composition table and the path-consistency algorithm, we can refine the network in the following way: road { PO, EC } property1 road { PO, TPP } property2 That is, the road either overlaps (PO) property2, or is a tangential proper part of it. But, if the road is a tangential proper part of property2, then the road can only be externally connected (EC) to property1. That is, road PO property1 is not possible when road TPP property2. This fact is not obvious, but can be deduced once we examine the consistent "singleton-labelings" of the constraint network. The following paragraph briefly describes singleton-labelings. First, we note that the path-consistency algorithm will also reduce the possible properties between house2 and property1 from { DC, EC } to just DC. So, the path-consistency algorithm leaves multiple possible constraints on 5 of the edges in the constraint network. Since each of the multiple constraints involves 2 constraints, we can reduce the network to 32 (25) possible unique constraint networks, each containing only single labels on each edge ("singleton labelings"). However, of the 32 possible singleton labelings, only 9 are consistent. (See qualreas for details.) Only one of the consistent singleton labelings has the edge road TPP property2 and the same labeling includes road EC property1. Other versions of the region connection calculus include RCC5 (with only five basic relations - the distinction whether two regions touch each other are ignored) and RCC23 (which allows reasoning about convexity). == RCC8 use in GeoSPARQL == RCC8 has been partially implemented in GeoSPARQL as described below: == Implementations == GQR is a reasoner for RCC-5, RCC-8, and RCC-23 (as well as other calculi for spatial and temporal reasoning) qualreas is a Python framework for qualitative reasoning over networks of relation algebras, such as RCC-8, Allen's interval algebra and more.
Knowledge integration
Knowledge integration is the process of synthesizing multiple knowledge models (or representations) into a common model (representation). Compared to information integration, which involves merging information having different schemas and representation models, knowledge integration focuses more on synthesizing the understanding of a given subject from different perspectives. For example, multiple interpretations are possible of a set of student grades, typically each from a certain perspective. An overall, integrated view and understanding of this information can be achieved if these interpretations can be put under a common model, say, a student performance index. The Web-based Inquiry Science Environment (WISE), from the University of California at Berkeley has been developed along the lines of knowledge integration theory. Knowledge integration has also been studied as the process of incorporating new information into a body of existing knowledge with an interdisciplinary approach. This process involves determining how the new information and the existing knowledge interact, how existing knowledge should be modified to accommodate the new information, and how the new information should be modified in light of the existing knowledge. A learning agent that actively investigates the consequences of new information can detect and exploit a variety of learning opportunities; e.g., to resolve knowledge conflicts and to fill knowledge gaps. By exploiting these learning opportunities the learning agent is able to learn beyond the explicit content of the new information. The machine learning program KI, developed by Murray and Porter at the University of Texas at Austin, was created to study the use of automated and semi-automated knowledge integration to assist knowledge engineers constructing a large knowledge base. A possible technique which can be used is semantic matching. More recently, a technique useful to minimize the effort in mapping validation and visualization has been presented which is based on Minimal Mappings. Minimal mappings are high quality mappings such that i) all the other mappings can be computed from them in time linear in the size of the input graphs, and ii) none of them can be dropped without losing property i). The University of Waterloo operates a Bachelor of Knowledge Integration undergraduate degree program as an academic major or minor. The program started in 2008.
Cerebellar model articulation controller
The cerebellar model arithmetic computer (CMAC) is a type of neural network based on a model of the mammalian cerebellum. It is also known as the cerebellar model articulation controller. It is a type of associative memory. The CMAC was first proposed as a function modeler for robotic controllers by James Albus in 1975 (hence the name), but has been extensively used in reinforcement learning and also as for automated classification in the machine learning community. The CMAC is an extension of the perceptron model. It computes a function for n {\displaystyle n} input dimensions. The input space is divided up into hyper-rectangles, each of which is associated with a memory cell. The contents of the memory cells are the weights, which are adjusted during training. Usually, more than one quantisation of input space is used, so that any point in input space is associated with a number of hyper-rectangles, and therefore with a number of memory cells. The output of a CMAC is the algebraic sum of the weights in all the memory cells activated by the input point. A change of value of the input point results in a change in the set of activated hyper-rectangles, and therefore a change in the set of memory cells participating in the CMAC output. The CMAC output is therefore stored in a distributed fashion, such that the output corresponding to any point in input space is derived from the value stored in a number of memory cells (hence the name associative memory). This provides generalisation. == Building blocks == In the adjacent image, there are two inputs to the CMAC, represented as a 2D space. Two quantising functions have been used to divide this space with two overlapping grids (one shown in heavier lines). A single input is shown near the middle, and this has activated two memory cells, corresponding to the shaded area. If another point occurs close to the one shown, it will share some of the same memory cells, providing generalisation. The CMAC is trained by presenting pairs of input points and output values, and adjusting the weights in the activated cells by a proportion of the error observed at the output. This simple training algorithm has a proof of convergence. It is normal to add a kernel function to the hyper-rectangle, so that points falling towards the edge of a hyper-rectangle have a smaller activation than those falling near the centre. One of the major problems cited in practical use of CMAC is the memory size required, which is directly related to the number of cells used. This is usually ameliorated by using a hash function, and only providing memory storage for the actual cells that are activated by inputs. == One-step convergent algorithm == Initially least mean square (LMS) method is employed to update the weights of CMAC. The convergence of using LMS for training CMAC is sensitive to the learning rate and could lead to divergence. In 2004, a recursive least squares (RLS) algorithm was introduced to train CMAC online. It does not need to tune a learning rate. Its convergence has been proved theoretically and can be guaranteed to converge in one step. The computational complexity of this RLS algorithm is O(N3). == Hardware implementation infrastructure == Based on QR decomposition, an algorithm (QRLS) has been further simplified to have an O(N) complexity. Consequently, this reduces memory usage and time cost significantly. A parallel pipeline array structure on implementing this algorithm has been introduced. Overall by utilizing QRLS algorithm, the CMAC neural network convergence can be guaranteed, and the weights of the nodes can be updated using one step of training. Its parallel pipeline array structure offers its great potential to be implemented in hardware for large-scale industry usage. == Continuous CMAC == Since the rectangular shape of CMAC receptive field functions produce discontinuous staircase function approximation, by integrating CMAC with B-splines functions, continuous CMAC offers the capability of obtaining any order of derivatives of the approximate functions. == Deep CMAC == In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC. == Summary ==