Critical data studies is the exploration of and engagement with social, cultural, and ethical challenges that arise when working with big data. It is through various unique perspectives and taking a critical approach that this form of study can be practiced. As its name implies, critical data studies draws heavily on the influence of critical theory, which has a strong focus on addressing the organization of power structures. This idea is then applied to the study of data. Interest in this unique field of critical data studies began in 2011 with scholars danah boyd and Kate Crawford posing various questions for the critical study of big data and recognizing its potential threatening impacts on society and culture. It was not until 2014, and more exploration and conversations, that critical data studies was officially coined by scholars Craig Dalton and Jim Thatcher. They put a large emphasis on understanding the context of big data in order to approach it more critically. Researchers such as David Ribes, Robert Soden, Seyram Avle, Sarah E. Fox, and Phoebe Sengers focus on understanding data as a historical artifact and taking an interdisciplinary approach towards critical data studies. Other key scholars in this discipline include Rob Kitchin and Tracey P. Lauriault who focus on reevaluating data through different spheres. Various critical frameworks that can be applied to analyze big data include Feminist, Anti-Racist, Queer, Indigenous, Decolonial, Anti-Ableist, as well as Symbolic and Synthetic data science. These frameworks help to make sense of the data by addressing power, biases, privacy, consent, and underrepresentation or misrepresentation concerns that exist in data as well as how to approach and analyze this data with a more equitable mindset. == Motivation == In their article in which they coin the term 'critical data studies,' Dalton and Thatcher also provide several justifications as to why data studies is a discipline worthy of a critical approach. First, 'big data' is an important aspect of twenty-first century society, and the analysis of 'big data' allows for a deeper understanding of what is happening and for what reasons. Big data is important to critical data studies because it is the type of data used within this field. Big data does not necessarily refer to a large data set, it can have a data set with millions of rows, but also a data set that just has a wide variety and expansive scope of data with a smaller type of dataset. As well as having whole populations in the data set and not just sample sizes. Furthermore, big data as a technological tool and the information that it yields are not neutral, according to Dalton and Thatcher, making it worthy of critical analysis in order to identify and address its biases. Building off this idea, another justification for a critical approach is that the relationship between big data and society is an important one, and therefore worthy of study. Ribes et. al. argue there is a need for an interdisciplinary understanding of data as a historical artifact as a motivating aspect of critical data studies.The overarching consensus in the Computer-Supported Cooperative Work (CSCW) field, is that people should speak for the data, and not let the data speak for itself. The sources of big data and it’s relationship to varied metadata can be a complicated one, which leads to data disorder and a need for an ethical analysis. Additionally, Iliadis and Russo (2016) have called for studying data assemblages. This is to say, data has innate technological, political, social, and economic histories that should be taken into consideration. Kitchin argues data is almost never raw, and it is almost always cooked, meaning that it is always spoken for by the data scientists utilizing it. Thus, Big Data should be open to a variety of perspectives, especially those of cultural and philosophical nature. Further, data contains hidden histories, ideologies, and philosophies. Big data technology can cause significant changes in society's structure and in the everyday lives of people, and, being a product of society, big data technology is worthy of sociological investigation. Moreover, data sets are almost never completely without any influence. Rather, data are shaped by the vision or goals of those gathering the data, and during the data collection process, certain things are quantified, stored, sorted and even discarded by the research team. A critical approach is thus necessary in order to understand and reveal the intent behind the information being presented.One of these critical approaches has been through feminist data studies. This method applies feminist principles to critical studies and data collecting and analysis. The goal of this is to address the power imbalance in data science and society. According to Catherine D’Ignazio and Lauren F. Klein, a power analysis can be performed by examining power, challenging power, evaluating emotion and embodiment, rethinking binaries and hierarchies, embracing pluralism, considering context, and making labor visible. Feminist data studies is part of the movement towards making data to benefit everyone and not to increase existing inequalities. Moreover, data alone cannot speak for themselves; in order to possess any concrete meaning, data must be accompanied by theoretical insight or alternative quantitative or qualitative research measures. Based on different social topics such as anti-racist data studies, critical data studies give a focus on those social issues concerning data. Specifically in anti-racist data studies they use a classification approach to get representation for those within that community. Desmond Upton Patton and others used their own classification system in the communities of Chicago to help target and reduce violence with young teens on twitter. They had students in those communities help them to decipher the terminology and emojis of these teens to target the language used in tweets that followed with violence outside of the computer screens. This is just one real world example of critical data studies and its application. Dalton and Thatcher argue that if one were to only think of data in terms of its exploitative power, there is no possibility of using data for revolutionary, liberatory purposes. Finally, Dalton and Thatcher propose that a critical approach in studying data allows for 'big data' to be combined with older, 'small data,' and thus create more thorough research, opening up more opportunities, questions and topics to be explored. == Issues and concerns for critical data scholars == Data plays a pivotal role in the emerging knowledge economy, driving productivity, competitiveness, efficiency, sustainability, and capital accumulation. The ethical, political, and economic dimensions of data dynamically evolve across space and time, influenced by changing regimes, technologies, and priorities. Technically, the focus lies on handling, storing, and analyzing vast data sets, utilizing machine learning-based data mining and analytics. This technological advancement raises concerns about data quality, encompassing validity, reliability, authenticity, usability, and lineage. The use of data in modern society brings about new ways of understanding and measuring the world, but also brings with it certain concerns or issues. Data scholars attempt to bring some of these issues to light in their quest to be critical of data. Technical and organizational issues could include the scope of the data set, meaning there is too little or too much data to work with, leading to inaccurate results. It becomes crucial for critical data scholars to carefully consider the adequacy of data volume for their analyses. The quality of the data itself is another facet of concern. The data itself could be of poor quality, such as an incomplete or messy data set with missing or inaccurate data values. This would lead researchers to have to make edits and assumptions about the data itself. Addressing these issues often requires scholars to make edits and assumptions about the data to ensure its reliability and relevance. Data scientists could have improper access to the actual data set, limiting their abilities to analyze it. Linnet Taylor explains how gaps in data can arise when people of varying levels of power have certain rights to their data sources. These people in power can control what data is collected, how it is displayed and how it is analyzed. The capabilities of the research team also play a crucial role in the quality of data analytics. The research team may have inadequate skills or organizational capabilities which leads to the actual analytics performed on the dataset to be biased. This can also lead to ecological fallacies, meaning an assumption is made about an individual based on data or results from a larger group of people. These technical and organizational challenges highlight the complexity of working with data and
Text Database and Dictionary of Classic Mayan
The project Text Database and Dictionary of Classic Mayan (abbr. TWKM) promotes research on the writing and language of pre-Hispanic Maya culture. It is housed in the Faculty of Arts at the University of Bonn and was established with funding from the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts. The project has a projected run-time of fifteen years and is directed by Nikolai Grube from the Department of Anthropology of the Americas at the University of Bonn. The goal of the project is to conduct computer-based studies of all extant Maya hieroglyphic texts from an epigraphic and cultural-historical standpoint, and to produce and publish a database and a comprehensive dictionary of the Classic Mayan language. == Subject of the Project == The text database, as well as the dictionary that will be compiled by the conclusion of the project, will be assembled based on all known texts from the pre-Hispanic Maya culture. These texts were produced and used between approximately the third century B.C. through A.D. 1500, in a region that today includes parts of the countries of Mexico, Guatemala, Belize, and Honduras. The thousands of hieroglyphic inscriptions on monuments, ceramics, or daily objects that have survived into the present offer insight into the language's vocabulary and structure. The project's database and dictionary will digitally represent original spellings using the logo-syllabic Maya hieroglyphs, as well as their transcription and transliteration in the Roman alphabet. The data will be additionally annotated with various epigraphic analyses, translations, and further object-specific information. == Project Partners == TWKM will employ digital technologies in order to compile and make available the data and metadata, as well as to publish the project's research results. The project thereby methodologically positions itself in the field of the digital humanities. The project will be conducted in cooperation with the project partners (below), the research association for the eHumanities TextGrid, as well as the University and Regional Library of Bonn (ULB). The working environment that is currently under construction, in which the data and metadata will be compiled and annotated, will be realized in theTextGrid Laboratory, a software of the virtual research environment. A further component of this software, the TextGrid Repository, will make the data that are authorized for publication freely available online and ensure their long-term storage. The tools for data compilation and annotation attained from the modularly constructed and extended TextGrid lab thereby provide all the necessary materials for facilitating the research team's the typical epigraphic workflow. The workflow usually begins by documenting the texts and the objects on which they are preserved, and by compiling descriptive data. It then continues with the various levels of epigraphic and linguistic analysis, and concludes in the best case scenario with a translation of the analyzed inscription and a corresponding publication. In cooperation with the ULB, selected data will additionally be made available. The project's Virtual Inscription Archive will present online, in the Digital Collections of the ULB, hieroglyphic inscriptions selected from the published data in the repository, including an image of and brief information about the texts and the objects on which they are written, epigraphic analysis, and translation. == Project Goal == One of the project's goals is to produce a dictionary of Classic Mayan, in both digital and print form, towards the end of the project run-time. Additionally, a database with a corpus of inscriptions, including their translations and epigraphic analyses, will be made freely available online. The database furthermore will provide an ontology-like link of the contextual object data with the inscriptions and with each other, thereby allowing a cultural-historical arrangement of all contents within the periods of pre-Hispanic Maya culture. The contents of the database are additionally linked to citations of relevant literature. As a result, the database will also make freely available to both the scientific community and other interested parties a bibliography representing the research history and a base of knowledge concerning ancient Maya culture and script. In addition, the Classic Maya script, in its temporally defined stages of language development, will be gathered into and documented in a comprehensive language corpus with the aid of the information gathered by the project. In collaboration with all project participants, the corpus data can be used, together with the aid of various comparable analyses and also computational linguistic methods, such as inference-based methods, to confirm readings of some hieroglyphs that are currently only partially confirmed, and to eventually completely decipher the Classic Maya script.
Actor-critic algorithm
The actor-critic algorithm (AC) is a family of reinforcement learning (RL) algorithms that combine policy-based RL algorithms such as policy gradient methods, and value-based RL algorithms such as value iteration, Q-learning, SARSA, and TD learning. An AC algorithm consists of two main components: an "actor" that determines which actions to take according to a policy function, and a "critic" that evaluates those actions according to a value function. Some AC algorithms are on-policy, some are off-policy. Some apply to either continuous or discrete action spaces. Some work in both cases. == Overview == The actor-critic methods can be understood as an improvement over pure policy gradient methods like REINFORCE via introducing a baseline. === Actor === The actor uses a policy function π ( a | s ) {\displaystyle \pi (a|s)} , while the critic estimates either the value function V ( s ) {\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or any combination thereof. The actor is a parameterized function π θ {\displaystyle \pi _{\theta }} , where θ {\displaystyle \theta } are the parameters of the actor. The actor takes as argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ | s ) {\displaystyle \pi _{\theta }(\cdot |s)} . If the action space is discrete, then ∑ a π θ ( a | s ) = 1 {\displaystyle \sum _{a}\pi _{\theta }(a|s)=1} . If the action space is continuous, then ∫ a π θ ( a | s ) d a = 1 {\displaystyle \int _{a}\pi _{\theta }(a|s)da=1} . The goal of policy optimization is to improve the actor. That is, to find some θ {\displaystyle \theta } that maximizes the expected episodic reward J ( θ ) {\displaystyle J(\theta )} : J ( θ ) = E π θ [ ∑ t = 0 T γ t r t ] {\displaystyle J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\gamma ^{t}r_{t}\right]} where γ {\displaystyle \gamma } is the discount factor, r t {\displaystyle r_{t}} is the reward at step t {\displaystyle t} , and T {\displaystyle T} is the time-horizon (which can be infinite). The goal of policy gradient method is to optimize J ( θ ) {\displaystyle J(\theta )} by gradient ascent on the policy gradient ∇ J ( θ ) {\displaystyle \nabla J(\theta )} . As detailed on the policy gradient method page, there are many unbiased estimators of the policy gradient: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ j ≤ T ∇ θ ln π θ ( A j | S j ) ⋅ Ψ j | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{0\leq j\leq T}\nabla _{\theta }\ln \pi _{\theta }(A_{j}|S_{j})\cdot \Psi _{j}{\Big |}S_{0}=s_{0}\right]} where Ψ j {\textstyle \Psi _{j}} is a linear sum of the following: ∑ 0 ≤ i ≤ T ( γ i R i ) {\textstyle \sum _{0\leq i\leq T}(\gamma ^{i}R_{i})} . γ j ∑ j ≤ i ≤ T ( γ i − j R i ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})} : the REINFORCE algorithm. γ j ∑ j ≤ i ≤ T ( γ i − j R i ) − b ( S j ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})-b(S_{j})} : the REINFORCE with baseline algorithm. Here b {\displaystyle b} is an arbitrary function. γ j ( R j + γ V π θ ( S j + 1 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma V^{\pi _{\theta }}(S_{j+1})-V^{\pi _{\theta }}(S_{j})\right)} : TD(1) learning. γ j Q π θ ( S j , A j ) {\textstyle \gamma ^{j}Q^{\pi _{\theta }}(S_{j},A_{j})} . γ j A π θ ( S j , A j ) {\textstyle \gamma ^{j}A^{\pi _{\theta }}(S_{j},A_{j})} : Advantage Actor-Critic (A2C). γ j ( R j + γ R j + 1 + γ 2 V π θ ( S j + 2 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma R_{j+1}+\gamma ^{2}V^{\pi _{\theta }}(S_{j+2})-V^{\pi _{\theta }}(S_{j})\right)} : TD(2) learning. γ j ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(n) learning. γ j ∑ n = 1 ∞ λ n − 1 1 − λ ⋅ ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\sum _{n=1}^{\infty }{\frac {\lambda ^{n-1}}{1-\lambda }}\cdot \left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(λ) learning, also known as GAE (generalized advantage estimate). This is obtained by an exponentially decaying sum of the TD(n) learning terms. === Critic === In the unbiased estimators given above, certain functions such as V π θ , Q π θ , A π θ {\displaystyle V^{\pi _{\theta }},Q^{\pi _{\theta }},A^{\pi _{\theta }}} appear. These are approximated by the critic. Since these functions all depend on the actor, the critic must learn alongside the actor. The critic is learned by value-based RL algorithms. For example, if the critic is estimating the state-value function V π θ ( s ) {\displaystyle V^{\pi _{\theta }}(s)} , then it can be learned by any value function approximation method. Let the critic be a function approximator V ϕ ( s ) {\displaystyle V_{\phi }(s)} with parameters ϕ {\displaystyle \phi } . The simplest example is TD(1) learning, which trains the critic to minimize the TD(1) error: δ i = R i + γ V ϕ ( S i + 1 ) − V ϕ ( S i ) {\displaystyle \delta _{i}=R_{i}+\gamma V_{\phi }(S_{i+1})-V_{\phi }(S_{i})} The critic parameters are updated by gradient descent on the squared TD error: ϕ ← ϕ − α ∇ ϕ ( δ i ) 2 = ϕ + α δ i ∇ ϕ V ϕ ( S i ) {\displaystyle \phi \leftarrow \phi -\alpha \nabla _{\phi }(\delta _{i})^{2}=\phi +\alpha \delta _{i}\nabla _{\phi }V_{\phi }(S_{i})} where α {\displaystyle \alpha } is the learning rate. Note that the gradient is taken with respect to the ϕ {\displaystyle \phi } in V ϕ ( S i ) {\displaystyle V_{\phi }(S_{i})} only, since the ϕ {\displaystyle \phi } in γ V ϕ ( S i + 1 ) {\displaystyle \gamma V_{\phi }(S_{i+1})} constitutes a moving target, and the gradient is not taken with respect to that. This is a common source of error in implementations that use automatic differentiation, and requires "stopping the gradient" at that point. Similarly, if the critic is estimating the action-value function Q π θ {\displaystyle Q^{\pi _{\theta }}} , then it can be learned by Q-learning or SARSA. In SARSA, the critic maintains an estimate of the Q-function, parameterized by ϕ {\displaystyle \phi } , denoted as Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} . The temporal difference error is then calculated as δ i = R i + γ Q θ ( S i + 1 , A i + 1 ) − Q θ ( S i , A i ) {\displaystyle \delta _{i}=R_{i}+\gamma Q_{\theta }(S_{i+1},A_{i+1})-Q_{\theta }(S_{i},A_{i})} . The critic is then updated by θ ← θ + α δ i ∇ θ Q θ ( S i , A i ) {\displaystyle \theta \leftarrow \theta +\alpha \delta _{i}\nabla _{\theta }Q_{\theta }(S_{i},A_{i})} The advantage critic can be trained by training both a Q-function Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} and a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then let A ϕ ( s , a ) = Q ϕ ( s , a ) − V ϕ ( s ) {\displaystyle A_{\phi }(s,a)=Q_{\phi }(s,a)-V_{\phi }(s)} . Although, it is more common to train just a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then estimate the advantage by A ϕ ( S i , A i ) ≈ ∑ j ∈ 0 : n − 1 γ j R i + j + γ n V ϕ ( S i + n ) − V ϕ ( S i ) {\displaystyle A_{\phi }(S_{i},A_{i})\approx \sum _{j\in 0:n-1}\gamma ^{j}R_{i+j}+\gamma ^{n}V_{\phi }(S_{i+n})-V_{\phi }(S_{i})} Here, n {\displaystyle n} is a positive integer. The higher n {\displaystyle n} is, the more lower is the bias in the advantage estimation, but at the price of higher variance. The Generalized Advantage Estimation (GAE) introduces a hyperparameter λ {\displaystyle \lambda } that smoothly interpolates between Monte Carlo returns ( λ = 1 {\displaystyle \lambda =1} , high variance, no bias) and 1-step TD learning ( λ = 0 {\displaystyle \lambda =0} , low variance, high bias). This hyperparameter can be adjusted to pick the optimal bias-variance trade-off in advantage estimation. It uses an exponentially decaying average of n-step returns with λ {\displaystyle \lambda } being the decay strength. == Variants == Asynchronous Advantage Actor-Critic (A3C): Parallel and asynchronous version of A2C. Soft Actor-Critic (SAC): Incorporates entropy maximization for improved exploration. Deep Deterministic Policy Gradient (DDPG): Specialized for continuous action spaces.
AI nationalism
AI nationalism is the idea that nations should develop and control their own artificial intelligence technologies to advance their own interests and ensure technological sovereignty. This concept is gaining traction globally, leading countries to implement new laws, form strategic alliances, and invest significantly in domestic AI capabilities. == Global trends and national strategies == In 2018, British technology investor Ian Hogarth published an influential essay titled AI Nationalism. He argued that as AI gains more power and its economic and military significance expands, governments will take measures to bolster their own domestic AI industries, and predicted that the advancement of machine learning systems would lead to what he termed "AI nationalism." He anticipated that this rise in AI would accelerate a global arms race, resulting in more closed economies, restrictions on foreign acquisitions, and limitations on the movement of talent. Hogarth predicted that AI policy would become a central focus of government agendas. He also criticized Britain’s approach to AI strategy, citing the sale of London-based DeepMind—one of the leading AI laboratories, acquired by Google for a relatively modest £400 million in 2014—as a significant misstep. AI nationalism is chiefly reflected in the escalating rhetoric of an artificial intelligence arms race, portraying AI development as a zero-sum game where the winner gains significant economic, political, and military advantages. This mindset, as highlighted in a 2017 Pentagon report, warns that sharing AI technology could erode technological supremacy and enhance rivals' capabilities. The winner-takes-all mentality of AI nationalism poses risks including unsafe AI development, increased geopolitical tension, and potential military aggression (such as cyberattacks or targeting AI professionals). Several countries, including Canada, France, and India, have formulated national strategies to advance their positions in AI. In the United States, a leading player in the global AI arena, trade policies have been enacted to restrict China's access to critical microchips, reflecting a strategic effort to maintain a technological edge. The United States’ National Security Commission on Artificial Intelligence (NSCAI) frames AI development as a critical aspect of a broader technology competition crucial for national success. It emphasizes the need to outpace China in AI to maintain strategic advantage, reflecting AI nationalism by linking geopolitical power directly to advancements in AI. France has seen notable governmental support for local AI startups, particularly those specializing in language technologies that cater to French and other non-English languages. In Saudi Arabia, Crown Prince Mohammed bin Salman is investing billions in AI research and development. The country has actively collaborated with major technology firms such as Amazon, IBM, and Microsoft to establish itself as a prominent AI hub. == Historical and cultural context == AI nationalism is seen as deeply connected to historical racism and imperialism. It is viewed not merely as a technological competition but as a contest over racial and civilizational superiority. Historically, technological achievements were often used to justify colonialism and racial hierarchies, with Western societies perceiving their advancements as evidence of superiority. In the context of AI, this historical context continues to shape views on intelligence and development. Some argue that AI nationalism reinforces the idea of fundamental civilizational divides, especially between the Western world and China. This perspective often frames China's progress in AI as a direct challenge to Western values, presenting the AI competition as a struggle over values. AI nationalism is said to draw from long-standing anti-Asian stereotypes, such as the "Yellow Peril," which portray Asian nations as threats to Western civilization. This viewpoint links Asian technological advances with dehumanization and artificiality, reflecting persistent anxieties about China's growing role in the global tech landscape. == Implications == AI nationalism is seen as a component of a broader trend towards the fragmentation of the internet, where digital services are increasingly influenced by local regulations and national interests. This shift is creating a new technological landscape in which the impact of artificial intelligence on individuals' lives can vary significantly depending on their geographic location. J. Paul Goode argues that AI nationalism may exacerbate existing societal divisions by promoting the development of systems that embed cultural biases, thereby privileging certain groups while disadvantaging others.
Similarity learning
Similarity learning is an area of supervised machine learning in artificial intelligence. It is closely related to regression and classification, but the goal is to learn a similarity function that measures how similar or related two objects are. It has applications in ranking, in recommendation systems, visual identity tracking, face verification, and speaker verification. == Learning setup == There are four common setups for similarity and metric distance learning. Regression similarity learning In this setup, pairs of objects are given ( x i 1 , x i 2 ) {\displaystyle (x_{i}^{1},x_{i}^{2})} together with a measure of their similarity y i ∈ R {\displaystyle y_{i}\in R} . The goal is to learn a function that approximates f ( x i 1 , x i 2 ) ∼ y i {\displaystyle f(x_{i}^{1},x_{i}^{2})\sim y_{i}} for every new labeled triplet example ( x i 1 , x i 2 , y i ) {\displaystyle (x_{i}^{1},x_{i}^{2},y_{i})} . This is typically achieved by minimizing a regularized loss min W ∑ i l o s s ( w ; x i 1 , x i 2 , y i ) + r e g ( w ) {\displaystyle \min _{W}\sum _{i}loss(w;x_{i}^{1},x_{i}^{2},y_{i})+reg(w)} . Classification similarity learning Given are pairs of similar objects ( x i , x i + ) {\displaystyle (x_{i},x_{i}^{+})} and non similar objects ( x i , x i − ) {\displaystyle (x_{i},x_{i}^{-})} . An equivalent formulation is that every pair ( x i 1 , x i 2 ) {\displaystyle (x_{i}^{1},x_{i}^{2})} is given together with a binary label y i ∈ { 0 , 1 } {\displaystyle y_{i}\in \{0,1\}} that determines if the two objects are similar or not. The goal is again to learn a classifier that can decide if a new pair of objects is similar or not. Ranking similarity learning Given are triplets of objects ( x i , x i + , x i − ) {\displaystyle (x_{i},x_{i}^{+},x_{i}^{-})} whose relative similarity obey a predefined order: x i {\displaystyle x_{i}} is known to be more similar to x i + {\displaystyle x_{i}^{+}} than to x i − {\displaystyle x_{i}^{-}} . The goal is to learn a function f {\displaystyle f} such that for any new triplet of objects ( x , x + , x − ) {\displaystyle (x,x^{+},x^{-})} , it obeys f ( x , x + ) > f ( x , x − ) {\displaystyle f(x,x^{+})>f(x,x^{-})} (contrastive learning). This setup assumes a weaker form of supervision than in regression, because instead of providing an exact measure of similarity, one only has to provide the relative order of similarity. For this reason, ranking-based similarity learning is easier to apply in real large-scale applications. Locality sensitive hashing (LSH) Hashes input items so that similar items map to the same "buckets" in memory with high probability (the number of buckets being much smaller than the universe of possible input items). It is often applied in nearest neighbor search on large-scale high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. A common approach for learning similarity is to model the similarity function as a bilinear form. For example, in the case of ranking similarity learning, one aims to learn a matrix W that parametrizes the similarity function f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . When data is abundant, a common approach is to learn a siamese network – a deep network model with parameter sharing. == Metric learning == Similarity learning is closely related to distance metric learning. Metric learning is the task of learning a distance function over objects. A metric or distance function has to obey four axioms: non-negativity, identity of indiscernibles, symmetry and subadditivity (or the triangle inequality). In practice, metric learning algorithms ignore the condition of identity of indiscernibles and learn a pseudo-metric. When the objects x i {\displaystyle x_{i}} are vectors in R d {\displaystyle R^{d}} , then any matrix W {\displaystyle W} in the symmetric positive semi-definite cone S + d {\displaystyle S_{+}^{d}} defines a distance pseudo-metric of the space of x through the form D W ( x 1 , x 2 ) 2 = ( x 1 − x 2 ) ⊤ W ( x 1 − x 2 ) {\displaystyle D_{W}(x_{1},x_{2})^{2}=(x_{1}-x_{2})^{\top }W(x_{1}-x_{2})} . When W {\displaystyle W} is a symmetric positive definite matrix, D W {\displaystyle D_{W}} is a metric. Moreover, as any symmetric positive semi-definite matrix W ∈ S + d {\displaystyle W\in S_{+}^{d}} can be decomposed as W = L ⊤ L {\displaystyle W=L^{\top }L} where L ∈ R e × d {\displaystyle L\in R^{e\times d}} and e ≥ r a n k ( W ) {\displaystyle e\geq rank(W)} , the distance function D W {\displaystyle D_{W}} can be rewritten equivalently D W ( x 1 , x 2 ) 2 = ( x 1 − x 2 ) ⊤ L ⊤ L ( x 1 − x 2 ) = ‖ L ( x 1 − x 2 ) ‖ 2 2 {\displaystyle D_{W}(x_{1},x_{2})^{2}=(x_{1}-x_{2})^{\top }L^{\top }L(x_{1}-x_{2})=\|L(x_{1}-x_{2})\|_{2}^{2}} . The distance D W ( x 1 , x 2 ) 2 = ‖ x 1 ′ − x 2 ′ ‖ 2 2 {\displaystyle D_{W}(x_{1},x_{2})^{2}=\|x_{1}'-x_{2}'\|_{2}^{2}} corresponds to the Euclidean distance between the transformed feature vectors x 1 ′ = L x 1 {\displaystyle x_{1}'=Lx_{1}} and x 2 ′ = L x 2 {\displaystyle x_{2}'=Lx_{2}} . Many formulations for metric learning have been proposed. Some well-known approaches for metric learning include learning from relative comparisons, which is based on the triplet loss, large margin nearest neighbor, and information theoretic metric learning (ITML). In statistics, the covariance matrix of the data is sometimes used to define a distance metric called Mahalanobis distance. == Applications == Similarity learning is used in information retrieval for learning to rank, in face verification or face identification, and in recommendation systems. Also, many machine learning approaches rely on some metric. This includes unsupervised learning such as clustering, which groups together close or similar objects. It also includes supervised approaches like K-nearest neighbor algorithm which rely on labels of nearby objects to decide on the label of a new object. Metric learning has been proposed as a preprocessing step for many of these approaches. == Scalability == Metric and similarity learning scale quadratically with the dimension of the input space, as can easily see when the learned metric has a bilinear form f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . Scaling to higher dimensions can be achieved by enforcing a sparseness structure over the matrix model, as done with HDSL, and with COMET. == Software == metric-learn is a free software Python library which offers efficient implementations of several supervised and weakly-supervised similarity and metric learning algorithms. The API of metric-learn is compatible with scikit-learn. OpenMetricLearning is a Python framework to train and validate the models producing high-quality embeddings. == Further information == For further information on this topic, see the surveys on metric and similarity learning by Bellet et al. and Kulis.
Scale space implementation
In the areas of computer vision, image analysis and signal processing, the notion of scale-space representation is used for processing measurement data at multiple scales, and specifically enhance or suppress image features over different ranges of scale (see the article on scale space). A special type of scale-space representation is provided by the Gaussian scale space, where the image data in N dimensions is subjected to smoothing by Gaussian convolution. Most of the theory for Gaussian scale space deals with continuous images, whereas one when implementing this theory will have to face the fact that most measurement data are discrete. Hence, the theoretical problem arises concerning how to discretize the continuous theory while either preserving or well approximating the desirable theoretical properties that lead to the choice of the Gaussian kernel (see the article on scale-space axioms). This article describes basic approaches for this that have been developed in the literature, see also for an in-depth treatment regarding the topic of approximating the Gaussian smoothing operation and the Gaussian derivative computations in scale-space theory, and for a complementary treatment regarding hybrid discretization methods. == Statement of the problem == The Gaussian scale-space representation of an N-dimensional continuous signal, f C ( x 1 , ⋯ , x N , t ) , {\displaystyle f_{C}\left(x_{1},\cdots ,x_{N},t\right),} is obtained by convolving fC with an N-dimensional Gaussian kernel: g N ( x 1 , ⋯ , x N , t ) . {\displaystyle g_{N}\left(x_{1},\cdots ,x_{N},t\right).} In other words: L ( x 1 , ⋯ , x N , t ) = ∫ u 1 = − ∞ ∞ ⋯ ∫ u N = − ∞ ∞ f C ( x 1 − u 1 , ⋯ , x N − u N , t ) ⋅ g N ( u 1 , ⋯ , u N , t ) d u 1 ⋯ d u N . {\displaystyle L\left(x_{1},\cdots ,x_{N},t\right)=\int _{u_{1}=-\infty }^{\infty }\cdots \int _{u_{N}=-\infty }^{\infty }f_{C}\left(x_{1}-u_{1},\cdots ,x_{N}-u_{N},t\right)\cdot g_{N}\left(u_{1},\cdots ,u_{N},t\right)\,du_{1}\cdots du_{N}.} However, for implementation, this definition is impractical, since it is continuous. When applying the scale space concept to a discrete signal fD, different approaches can be taken. This article is a brief summary of some of the most frequently used methods. == Separability == Using the separability property of the Gaussian kernel g N ( x 1 , … , x N , t ) = G ( x 1 , t ) ⋯ G ( x N , t ) {\displaystyle g_{N}\left(x_{1},\dots ,x_{N},t\right)=G\left(x_{1},t\right)\cdots G\left(x_{N},t\right)} the N-dimensional convolution operation can be decomposed into a set of separable smoothing steps with a one-dimensional Gaussian kernel G along each dimension L ( x 1 , ⋯ , x N , t ) = ∫ u 1 = − ∞ ∞ ⋯ ∫ u N = − ∞ ∞ f C ( x 1 − u 1 , ⋯ , x N − u N , t ) G ( u 1 , t ) d u 1 ⋯ G ( u N , t ) d u N , {\displaystyle L(x_{1},\cdots ,x_{N},t)=\int _{u_{1}=-\infty }^{\infty }\cdots \int _{u_{N}=-\infty }^{\infty }f_{C}(x_{1}-u_{1},\cdots ,x_{N}-u_{N},t)G(u_{1},t)\,du_{1}\cdots G(u_{N},t)\,du_{N},} where G ( x , t ) = 1 2 π t e − x 2 2 t {\displaystyle G(x,t)={\frac {1}{\sqrt {2\pi t}}}e^{-{\frac {x^{2}}{2t}}}} and the standard deviation of the Gaussian σ is related to the scale parameter t according to t = σ2. Separability will be assumed in all that follows, even when the kernel is not exactly Gaussian, since separation of the dimensions is the most practical way to implement multidimensional smoothing, especially at larger scales. Therefore, the rest of the article focuses on the one-dimensional case. == The sampled Gaussian kernel == When implementing the one-dimensional smoothing step in practice, the presumably simplest approach is to convolve the discrete signal fD with a sampled Gaussian kernel: L ( x , t ) = ∑ n = − ∞ ∞ f ( x − n ) G ( n , t ) {\displaystyle L(x,t)=\sum _{n=-\infty }^{\infty }f(x-n)\,G(n,t)} where G ( n , t ) = 1 2 π t e − n 2 2 t {\displaystyle G(n,t)={\frac {1}{\sqrt {2\pi t}}}e^{-{\frac {n^{2}}{2t}}}} (with t = σ2) which in turn is truncated at the ends to give a filter with finite impulse response L ( x , t ) = ∑ n = − M M f ( x − n ) G ( n , t ) {\displaystyle L(x,t)=\sum _{n=-M}^{M}f(x-n)\,G(n,t)} for M chosen sufficiently large (see error function) such that 2 ∫ M ∞ G ( u , t ) d u = 2 ∫ M t ∞ G ( v , 1 ) d v < ε . {\displaystyle 2\int _{M}^{\infty }G(u,t)\,du=2\int _{\frac {M}{\sqrt {t}}}^{\infty }G(v,1)\,dv<\varepsilon .} A common choice is to set M to a constant C times the standard deviation of the Gaussian kernel M = C σ + 1 = C t + 1 {\displaystyle M=C\sigma +1=C{\sqrt {t}}+1} where C is often chosen somewhere between 3 and 6. Using the sampled Gaussian kernel can, however, lead to implementation problems, in particular when computing higher-order derivatives at finer scales by applying sampled derivatives of Gaussian kernels. When accuracy and robustness are primary design criteria, alternative implementation approaches should therefore be considered. For small values of ε (10−6 to 10−8) the errors introduced by truncating the Gaussian are usually negligible. For larger values of ε, however, there are many better alternatives to a rectangular window function. For example, for a given number of points, a Hamming window, Blackman window, or Kaiser window will do less damage to the spectral and other properties of the Gaussian than a simple truncation will. Notwithstanding this, since the Gaussian kernel decreases rapidly at the tails, the main recommendation is still to use a sufficiently small value of ε such that the truncation effects are no longer important. == The discrete Gaussian kernel == A more refined approach is to convolve the original signal with the discrete Gaussian kernel T(n, t) L ( x , t ) = ∑ n = − ∞ ∞ f ( x − n ) T ( n , t ) {\displaystyle L(x,t)=\sum _{n=-\infty }^{\infty }f(x-n)\,T(n,t)} where T ( n , t ) = e − t I n ( t ) {\displaystyle T(n,t)=e^{-t}I_{n}(t)} and I n ( t ) {\displaystyle I_{n}(t)} denotes the modified Bessel functions of integer order, n. This is the discrete counterpart of the continuous Gaussian in that it is the solution to the discrete diffusion equation (discrete space, continuous time), just as the continuous Gaussian is the solution to the continuous diffusion equation. This filter can be truncated in the spatial domain as for the sampled Gaussian L ( x , t ) = ∑ n = − M M f ( x − n ) T ( n , t ) {\displaystyle L(x,t)=\sum _{n=-M}^{M}f(x-n)\,T(n,t)} or can be implemented in the Fourier domain using a closed-form expression for its discrete-time Fourier transform: T ^ ( θ , t ) = ∑ n = − ∞ ∞ T ( n , t ) e − i θ n = e t ( cos θ − 1 ) . {\displaystyle {\widehat {T}}(\theta ,t)=\sum _{n=-\infty }^{\infty }T(n,t)\,e^{-i\theta n}=e^{t(\cos \theta -1)}.} With this frequency-domain approach, the scale-space properties transfer exactly to the discrete domain, or with excellent approximation using periodic extension and a suitably long discrete Fourier transform to approximate the discrete-time Fourier transform of the signal being smoothed. Moreover, higher-order derivative approximations can be computed in a straightforward manner (and preserving scale-space properties) by applying small support central difference operators to the discrete scale space representation. As with the sampled Gaussian, a plain truncation of the infinite impulse response will in most cases be a sufficient approximation for small values of ε, while for larger values of ε it is better to use either a decomposition of the discrete Gaussian into a cascade of generalized binomial filters or alternatively to construct a finite approximate kernel by multiplying by a window function. If ε has been chosen too large such that effects of the truncation error begin to appear (for example as spurious extrema or spurious responses to higher-order derivative operators), then the options are to decrease the value of ε such that a larger finite kernel is used, with cutoff where the support is very small, or to use a tapered window. == Recursive filters == Since computational efficiency is often important, low-order recursive filters are often used for scale-space smoothing. For example, Young and van Vliet use a third-order recursive filter with one real pole and a pair of complex poles, applied forward and backward to make a sixth-order symmetric approximation to the Gaussian with low computational complexity for any smoothing scale. By relaxing a few of the axioms, Lindeberg concluded that good smoothing filters would be "normalized Pólya frequency sequences", a family of discrete kernels that includes all filters with real poles at 0 < Z < 1 and/or Z > 1, as well as with real zeros at Z < 0. For symmetry, which leads to approximate directional homogeneity, these filters must be further restricted to pairs of poles and zeros that lead to zero-phase filters. To match the transfer function curvature at zero frequency of the discrete Gaussian, which ensures an approximate semi-group property of additive t, two poles at Z = 1 + 2 t − ( 1 + 2 t ) 2 − 1 {\displaystyle
Symbol level
In knowledge-based systems, agents choose actions based on the principle of rationality to move closer to a desired goal. The agent is able to make decisions based on knowledge it has about the world (see knowledge level). But for the agent to actually change its state, it must use whatever means it has available. This level of description for the agent's behavior is the symbol level. The term was coined by Allen Newell in 1982. For example, in a computer program, the knowledge level consists of the information contained in its data structures that it uses to perform certain actions. The symbol level consists of the program's algorithms, the data structures themselves, and so on.