NCSA Brown Dog is a research project to develop a method for easily accessing historic research data stored in order to maintain the long-term viability of large bodies of scientific research. It is supported by the National Center for Supercomputing Applications (NCSA) that is funded by the National Science Foundation (NSF). == History == Brown Dog is part of the DataNet partners program funded by NSF in 2008. DataNet was conceived to address the increasingly digital and data-intensive nature of science, engineering and education. Brown Dog is part of a follow-on effort called Data Infrastructure Building Blocks (DIBBs), focused on building software to support DataNet. The project was proposed by researchers at NCSA and the University of Illinois Urbana-Champaign as well as researchers from Boston University and the University of North Carolina at Chapel Hill. == Unstructured, uncurated, long tail data == Much scientific data is smaller, unstructured and uncurated and thus not easily shared. Such data is sometimes referred to as "long tail" data. This borrows a term from statistics and refers to the tail of the distribution of project sizes. The majority of smaller projects lack the resources to properly steward the data they produce. This so-called "long tail" data, both past and present, has the potential to inform future research in many study areas. Much of this data has become inaccessible due to obsolete software and file formats. The resulting impossibility of reviewing data from older research disrupts the overall scientific research project. == Approach == Brown Dog describes itself as the "super mutt" of software (thus the name "Brown Dog"), serving as a low-level data infrastructure to interface digital data content across the internet. Its approach is to use every possible source of automated help (i.e., software) in existence in a robust and provenance-preserving manner to create a service that can deal with as much of this data as possible. The project sees the broader impact of its work in its potential to serve the general public as a sort of "DNS for data", with the goal of making all data and all file formats as accessible as webpages are today. == Technology == Brown Dog seeks to address problems involving the use of uncurated and unstructured data collections through the development of two services: the Data Access Proxy (DAP) to aid in the conversion of file formats and the Data Tilling Services (DTS) for the automatic extraction of metadata from file contents. Once developed, researchers and general public users will be able to download browser plugins and other tools from the Brown Dog tool catalog. === Data Tilling Service === Data Tilling Service (DTS) will allow users to search data collections using an existing file to discover other similar files in a collection. A DTS search field will be appended to configured browsers where example files can be dropped. This tells DTS to search all the files under a given URL for files similar to the dropped file. For example, while browsing an online image collection, a user could drop an image of three people into the search field, and the DTS would return all images in the collection that also contain three people. If DTS encounters a foreign file format, it will utilize DAP to make the file accessible. DTS also indexes the data and extract and appends metadata to files and collections enabling users to gain some sense of the type of data they are encountering. This service runs on port 9443. === Data Access Proxy === Data Access Proxy (DAP) allows users to access data files that would otherwise be unreadable. Similar to an internet gateway or Domain Name Service, the DAP configuration would be entered into a user's machine and browser settings. Data requests over HTTP would first be examined by DAP to determine if the native file format is readable on the client device. If not, DAP converts the file into the best available format readable by the client machine. Alternatively, the user could specify the desired format themselves. This service runs on port 8184. == Use cases == Brown Dog targets three use cases proposed by groups within the EarthCube research communities. Developers and researchers from these communities will work together on use cases that span geoscience, engineering, biology and social science. === Long tail vegetation data in ecology and global change biology === This use case is led by Michael Dietze, Boston University Data on the abundance, species composition, and size structure of vegetation is critically important for a wide array of sub-disciplines in ecology, conservation, natural resource management, and global change biology. However, addressing many of the pressing questions in these disciplines will require that terrestrial biosphere and hydrologic models are able to assimilate the large amount of long-tail data that exists but is largely inaccessible. The Brown Dog team in cooperation with researches from Dietze's lab will facilitate the capture of a huge body of smaller research-oriented vegetation data sets collected over many decades and historical vegetation data embedded in Public Land Survey data dating back to 1785. This data will be used as initial conditions for models, to make sense of other large data sets and for model calibration and validation. === Designing green infrastructure considering storm water and human requirements === This use case is led by Barbara Minsker], University of Illinois at Urbana-Champaign]; William Sullivan, University of Illinois at Urbana-Champaign; Arthur Schmidt, University of Illinois at Urbana-Champaign. This case study involves developing novel green infrastructure design criteria and models that integrate requirements for storm water management and ecosystem and human health and well being. To address the scientific and social problems associated with the design of green spaces, data accessibility and availability is a major challenge. This study will focus on identified areas of the Green Healthy Neighborhood Planning region within the City of Chicago where existing local sewer performance is most deficient and where changes in impervious area through green infrastructure would be beneficial to under served neighborhoods. Brown Dog will be used to extract long-tail experimental data on human landscape preferences and health impacts. This data will be used to develop a human health impacts model that will then be linked together with a terrestrial biosphere model and a storm water model using Brown Dog technology. === Development and application for critical zone studies === This use case is led by Praveen Kumar, University of Illinois at Urbana-Champaign Critical Zone (CZ) is the "skin" of the earth that extends from the treetops to the bedrock that is created by life processes working at scales from microbes to biomes. The Critical Zone supports all terrestrial living systems. Its upper part is the bio-mantle. This is where terrestrial biota live, reproduce, use and expend energy, and where their wastes and remains accumulate and decompose. It encompasses the soil, which acts as a geomembrane through which water and solutes, energy, gases, solids, and organisms interact with the atmosphere, biosphere, hydrosphere, and lithosphere. A variety of drivers affect this bio-dynamic zone, ranging from climate and deforestation to agriculture, grazing and human development. Understanding and predicting these effects is central to managing and sustaining vital ecosystem services such as soil fertility, water purification, and production of food resources, and, at larger scales, global carbon cycling and carbon sequestration. The CZ provides a unifying framework for integrating terrestrial surface and near-surface environments, and reflects an intricate web of biological and chemical processes and human impacts occurring at vastly different temporal and spatial scales. The nature of these data create significant challenges for inter-disciplinary studies of the CZ because integration of the variety and number of data products and models has been a barrier. On the other hand, CZ data provides an excellent opportunity for defining, testing and implementing Brown Dog technologies. In this context "unstructured" data is viewed broadly as consisting of a collection of heterogeneous data with formats that reflect temporal and disciplinary legacies, data from emerging low cost open hardware based sensors and embedded sensor networks that lack well defined metadata and sensor characteristics, as well as data that are available as maps, images and text. == NSF Award == CIF21 DIBBs: Brown Dog was awarded in the winter of 2013 with a start date of October 1, 2013. Estimated expiration date is September 30, 2018. The award amount was $10,519,716.00, the largest DIBB award. The principal investigator is Kenton McHenry of NCSA at the University of Illinois at Urbana-Champaign. Coleaders are Jong Lee NCSA/UIU
Apache Pig
Apache Pig is a high-level platform for creating programs that run on Apache Hadoop. The language for this platform is called Pig Latin. Pig can execute its Hadoop jobs in MapReduce, Apache Tez, or Apache Spark. Pig Latin abstracts the programming from the Java MapReduce idiom into a notation which makes MapReduce programming high level, similar to that of SQL for relational database management systems. Pig Latin can be extended using user-defined functions (UDFs) which the user can write in Java, Python, JavaScript, Ruby or Groovy and then call directly from the language. == History == Apache Pig was originally developed at Yahoo Research around 2006 for researchers to have an ad hoc way of creating and executing MapReduce jobs on very large data sets. In 2007, it was moved into the Apache Software Foundation. === Naming === Regarding the naming of the Pig programming language, the name was chosen arbitrarily and stuck because it was memorable, easy to spell, and for novelty. The story goes that the researchers working on the project initially referred to it simply as 'the language'. Eventually they needed to call it something. Off the top of his head, one researcher suggested Pig, and the name stuck. It is quirky yet memorable and easy to spell. While some have hinted that the name sounds coy or silly, it has provided us with an entertaining nomenclature, such as Pig Latin for the language, Grunt for the shell, and PiggyBank for the CPAN-like shared repository. == Example == Below is an example of a "Word Count" program in Pig Latin: The above program will generate parallel executable tasks which can be distributed across multiple machines in a Hadoop cluster to count the number of words in a dataset such as all the webpages on the internet. == Pig vs SQL == In comparison to SQL, Pig has a nested relational model, uses lazy evaluation, uses extract, transform, load (ETL), is able to store data at any point during a pipeline, declares execution plans, supports pipeline splits, thus allowing workflows to proceed along DAGs instead of strictly sequential pipelines. On the other hand, it has been argued DBMSs are substantially faster than the MapReduce system once the data is loaded, but that loading the data takes considerably longer in the database systems. It has also been argued RDBMSs offer out of the box support for column-storage, working with compressed data, indexes for efficient random data access, and transaction-level fault tolerance. Pig Latin is procedural and fits very naturally in the pipeline paradigm while SQL is instead declarative. In SQL users can specify that data from two tables must be joined, but not what join implementation to use (You can specify the implementation of JOIN in SQL, thus "... for many SQL applications the query writer may not have enough knowledge of the data or enough expertise to specify an appropriate join algorithm."). Pig Latin allows users to specify an implementation or aspects of an implementation to be used in executing a script in several ways. In effect, Pig Latin programming is similar to specifying a query execution plan, making it easier for programmers to explicitly control the flow of their data processing task. SQL is oriented around queries that produce a single result. SQL handles trees naturally, but has no built in mechanism for splitting a data processing stream and applying different operators to each sub-stream. Pig Latin script describes a directed acyclic graph (DAG) rather than a pipeline. Pig Latin's ability to include user code at any point in the pipeline is useful for pipeline development. If SQL is used, data must first be imported into the database, and then the cleansing and transformation process can begin.
ID3 algorithm
In decision tree learning, ID3 (Iterative Dichotomiser 3) is a greedy algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm. The 3 in the name is meant to signify that this was Quinlan's third attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split on multi-valued attributes. == Algorithm == The ID3 algorithm begins with the original set S {\displaystyle S} as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S {\displaystyle S} and calculates the entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} or the information gain I G ( S ) {\displaystyle IG(S)} of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S {\displaystyle S} is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm continues to recurse on each subset, considering only attributes never selected before. Recursion on a subset may stop in one of these cases: every element in the subset belongs to the same class; in which case the node is turned into a leaf node and labelled with the class of the examples. there are no more attributes to be selected, but the examples still do not belong to the same class. In this case, the node is made a leaf node and labelled with the most common class of the examples in the subset. there are no examples in the subset, which happens when no example in the parent set was found to match a specific value of the selected attribute. An example could be the absence of a person among the population with age over 100 years. Then a leaf node is created and labelled with the most common class of the examples in the parent node's set. Throughout the algorithm, the decision tree is constructed with each non-terminal node (internal node) representing the selected attribute on which the data was split, and terminal nodes (leaf nodes) representing the class label of the final subset of this branch. === Summary === Calculate the entropy of every attribute a {\displaystyle a} of the data set S {\displaystyle S} . Partition ("split") the set S {\displaystyle S} into subsets using the attribute for which the resulting entropy after splitting is minimized; or, equivalently, information gain is maximum. Make a decision tree node containing that attribute. Recurse on subsets using the remaining attributes. === Properties === ID3 does not guarantee an optimal solution. It can converge upon local optima. It uses a greedy strategy by selecting the locally best attribute to split the dataset on each iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking longer. ID3 can overfit the training data. To avoid overfitting, smaller decision trees should be preferred over larger ones. This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time-consuming. === Usage === The ID3 algorithm is used by training on a data set S {\displaystyle S} to produce a decision tree which is stored in memory. At runtime, this decision tree is used to classify new test cases (feature vectors) by traversing the decision tree using the features of the datum to arrive at a leaf node. == The ID3 metrics == === Entropy === Entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} is a measure of the amount of uncertainty in the (data) set S {\displaystyle S} (i.e. entropy characterizes the (data) set S {\displaystyle S} ). H ( S ) = ∑ x ∈ X − p ( x ) log 2 p ( x ) {\displaystyle \mathrm {H} {(S)}=\sum _{x\in X}{-p(x)\log _{2}p(x)}} Where, S {\displaystyle S} – The current dataset for which entropy is being calculated This changes at each step of the ID3 algorithm, either to a subset of the previous set in the case of splitting on an attribute or to a "sibling" partition of the parent in case the recursion terminated previously. X {\displaystyle X} – The set of classes in S {\displaystyle S} p ( x ) {\displaystyle p(x)} – The proportion of the number of elements in class x {\displaystyle x} to the number of elements in set S {\displaystyle S} When H ( S ) = 0 {\displaystyle \mathrm {H} {(S)}=0} , the set S {\displaystyle S} is perfectly classified (i.e. all elements in S {\displaystyle S} are of the same class). In ID3, entropy is calculated for each remaining attribute. The attribute with the smallest entropy is used to split the set S {\displaystyle S} on this iteration. Entropy in information theory measures how much information is expected to be gained upon measuring a random variable; as such, it can also be used to quantify the amount to which the distribution of the quantity's values is unknown. A constant quantity has zero entropy, as its distribution is perfectly known. In contrast, a uniformly distributed random variable (discretely or continuously uniform) maximizes entropy. Therefore, the greater the entropy at a node, the less information is known about the classification of data at this stage of the tree; and therefore, the greater the potential to improve the classification here. As such, ID3 is a greedy heuristic performing a best-first search for locally optimal entropy values. Its accuracy can be improved by preprocessing the data. === Information gain === Information gain I G ( A ) {\displaystyle IG(A)} is the measure of the difference in entropy from before to after the set S {\displaystyle S} is split on an attribute A {\displaystyle A} . In other words, how much uncertainty in S {\displaystyle S} was reduced after splitting set S {\displaystyle S} on attribute A {\displaystyle A} . I G ( S , A ) = H ( S ) − ∑ t ∈ T p ( t ) H ( t ) = H ( S ) − H ( S | A ) . {\displaystyle IG(S,A)=\mathrm {H} {(S)}-\sum _{t\in T}p(t)\mathrm {H} {(t)}=\mathrm {H} {(S)}-\mathrm {H} {(S|A)}.} Where, H ( S ) {\displaystyle \mathrm {H} (S)} – Entropy of set S {\displaystyle S} T {\displaystyle T} – The subsets created from splitting set S {\displaystyle S} by attribute A {\displaystyle A} such that S = ⋃ t ∈ T t {\displaystyle S=\bigcup _{t\in T}t} p ( t ) {\displaystyle p(t)} – The proportion of the number of elements in t {\displaystyle t} to the number of elements in set S {\displaystyle S} H ( t ) {\displaystyle \mathrm {H} (t)} – Entropy of subset t {\displaystyle t} In ID3, information gain can be calculated (instead of entropy) for each remaining attribute. The attribute with the largest information gain is used to split the set S {\displaystyle S} on this iteration.
Variational message passing
Variational message passing (VMP) is an approximate inference technique for continuous- or discrete-valued Bayesian networks, with conjugate-exponential parents, developed by John Winn. VMP was developed as a means of generalizing the approximate variational methods used by such techniques as latent Dirichlet allocation, and works by updating an approximate distribution at each node through messages in the node's Markov blanket. == Likelihood lower bound == Given some set of hidden variables H {\displaystyle H} and observed variables V {\displaystyle V} , the goal of approximate inference is to maximize a lower-bound on the probability that a graphical model is in the configuration V {\displaystyle V} . Over some probability distribution Q {\displaystyle Q} (to be defined later), ln P ( V ) = ∑ H Q ( H ) ln P ( H , V ) P ( H | V ) = ∑ H Q ( H ) [ ln P ( H , V ) Q ( H ) − ln P ( H | V ) Q ( H ) ] {\displaystyle \ln P(V)=\sum _{H}Q(H)\ln {\frac {P(H,V)}{P(H|V)}}=\sum _{H}Q(H){\Bigg [}\ln {\frac {P(H,V)}{Q(H)}}-\ln {\frac {P(H|V)}{Q(H)}}{\Bigg ]}} . So, if we define our lower bound to be L ( Q ) = ∑ H Q ( H ) ln P ( H , V ) Q ( H ) {\displaystyle L(Q)=\sum _{H}Q(H)\ln {\frac {P(H,V)}{Q(H)}}} , then the likelihood is simply this bound plus the relative entropy between P {\displaystyle P} and Q {\displaystyle Q} . Because the relative entropy is non-negative, the function L {\displaystyle L} defined above is indeed a lower bound of the log likelihood of our observation V {\displaystyle V} . The distribution Q {\displaystyle Q} will have a simpler character than that of P {\displaystyle P} because marginalizing over P {\displaystyle P} is intractable for all but the simplest of graphical models. In particular, VMP uses a factorized distribution Q ( H ) = ∏ i Q i ( H i ) , {\displaystyle Q(H)=\prod _{i}Q_{i}(H_{i}),} where H i {\displaystyle H_{i}} is a disjoint part of the graphical model. == Determining the update rule == The likelihood estimate needs to be as large as possible; because it's a lower bound, getting closer log P {\displaystyle \log P} improves the approximation of the log likelihood. By substituting in the factorized version of Q {\displaystyle Q} , L ( Q ) {\displaystyle L(Q)} , parameterized over the hidden nodes H i {\displaystyle H_{i}} as above, is simply the negative relative entropy between Q j {\displaystyle Q_{j}} and Q j ∗ {\displaystyle Q_{j}^{}} plus other terms independent of Q j {\displaystyle Q_{j}} if Q j ∗ {\displaystyle Q_{j}^{}} is defined as Q j ∗ ( H j ) = 1 Z e E − j { ln P ( H , V ) } {\displaystyle Q_{j}^{}(H_{j})={\frac {1}{Z}}e^{\mathbb {E} _{-j}\{\ln P(H,V)\}}} , where E − j { ln P ( H , V ) } {\displaystyle \mathbb {E} _{-j}\{\ln P(H,V)\}} is the expectation over all distributions Q i {\displaystyle Q_{i}} except Q j {\displaystyle Q_{j}} . Thus, if we set Q j {\displaystyle Q_{j}} to be Q j ∗ {\displaystyle Q_{j}^{}} , the bound L {\displaystyle L} is maximized. == Messages in variational message passing == Parents send their children the expectation of their sufficient statistic while children send their parents their natural parameter, which also requires messages to be sent from the co-parents of the node. == Relationship to exponential families == Because all nodes in VMP come from exponential families and all parents of nodes are conjugate to their children nodes, the expectation of the sufficient statistic can be computed from the normalization factor. == VMP algorithm == The algorithm begins by computing the expected value of the sufficient statistics for that vector. Then, until the likelihood converges to a stable value (this is usually accomplished by setting a small threshold value and running the algorithm until it increases by less than that threshold value), do the following at each node: Get all messages from parents. Get all messages from children (this might require the children to get messages from the co-parents). Compute the expected value of the nodes sufficient statistics. == Constraints == Because every child must be conjugate to its parent, this has limited the types of distributions that can be used in the model. For example, the parents of a Gaussian distribution must be a Gaussian distribution (corresponding to the Mean) and a gamma distribution (corresponding to the precision, or one over σ {\displaystyle \sigma } in more common parameterizations). Discrete variables can have Dirichlet parents, and Poisson and exponential nodes must have gamma parents. More recently, VMP has been extended to handle models that violate this conditional conjugacy constraint. == Literature == John Winn; Christopher M. Bishop (2005). "Variational Message Passing" (PDF). Journal of Machine Learning Research. 6: 661–694. ISSN 1533-7928. Wikidata Q139488859. Beal, M.J. (2003). Variational Algorithms for Approximate Bayesian Inference (PDF) (PhD). Gatsby Computational Neuroscience Unit, University College London. Archived from the original (PDF) on 2005-04-28. Retrieved 2007-02-15.
Scale-invariant feature operator
In the fields of computer vision and image analysis, the scale-invariant feature operator (or SFOP) is an algorithm to detect local features in images. The algorithm was published by Förstner et al. in 2009. == Algorithm == The scale-invariant feature operator (SFOP) is based on two theoretical concepts: spiral model feature operator Desired properties of keypoint detectors: Invariance and repeatability for object recognition Accuracy to support camera calibration Interpretability: Especially corners and circles, should be part of the detected keypoints (see figure). As few control parameters as possible with clear semantics Complementarity to known detectors scale-invariant corner/circle detector. == Theory == === Maximize the weight === Maximize the weight w {\displaystyle w} = 1/variance of a point p {\displaystyle p} w ( p , α , τ , σ ) = ( N ( σ ) − 2 ) λ m i n ( M ( p , α , τ , σ ) ) Ω ( p , α , τ , σ ) {\displaystyle w(\mathbf {p} ,\alpha ,\tau ,\sigma )=\left(N(\sigma )-2\right){\frac {\lambda _{min}(M(\mathbf {p} ,\alpha ,\tau ,\sigma ))}{\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )}}} comprising: 1. the image model Ω ( p , α , τ , σ ) = ∑ n = 1 N ( σ ) [ ( q n − p ) T R α ∇ T g ( q n ) ] 2 G σ ( q n − p ) = N ( σ ) t r { R α ∇ τ ∇ τ T R α T ∗ p p T G σ ( p ) } {\displaystyle {\begin{aligned}\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )&=\sum _{n=1}^{N(\sigma )}[(\mathbf {q} _{n}-\mathbf {p} )^{T}\mathbf {R} _{\alpha }\mathbf {\nabla } _{T}g(\mathbf {q} _{n})]^{2}G_{\sigma }(\mathbf {q} _{n}-\mathbf {p} )\\&=N(\sigma )\mathbf {tr} \left\{R_{\alpha }\mathbf {\nabla } _{\tau }\mathbf {\nabla } _{\tau }^{T}R_{\alpha }^{T}\mathbf {p} \mathbf {p} ^{T}G_{\sigma }(\mathbf {p} )\right\}\end{aligned}}} 2. the smaller eigenvalue of the structure tensor M ( p , α , τ , σ ) ⏟ structure tensor = G σ ( p ) ⏟ weighted summation ∗ ( R σ ∇ τ ∇ τ T R σ T ) ⏟ squared rotated gradients {\displaystyle \underbrace {M(\mathbf {p} ,\alpha ,\tau ,\sigma )} _{\text{structure tensor}}=\underbrace {G_{\sigma }(\mathbf {p} )} _{\text{weighted summation}}\underbrace {(R_{\sigma }\nabla _{\tau }\nabla _{\tau }^{T}R_{\sigma }^{T})} _{\text{squared rotated gradients}}} === Reduce the search space === Reduce the 5-dimensional search space by linking the differentiation scale τ {\displaystyle \tau } to the integration scale τ = σ / 3 {\displaystyle \tau =\sigma /3} solving for the optimal α ^ {\displaystyle {\hat {\alpha }}} using the model Ω ( α ) = a − b cos ( 2 α − 2 α 0 ) {\displaystyle \Omega (\alpha )=a-b\cos(2\alpha -2\alpha _{0})} and determining the parameters from three angles, e. g. Ω ( 0 ∘ ) , Ω ( 60 ∘ ) , Ω ( 120 ∘ ) → a , b , α 0 → α ^ {\displaystyle \Omega (0^{\circ }),\Omega (60^{\circ }),\Omega (120^{\circ })\quad \rightarrow \quad a,b,\alpha _{0}\quad \rightarrow \quad {\hat {\alpha }}} pre-selection possible: α = 0 ∘ → junctions , α = 90 ∘ → circular features {\displaystyle \alpha =0^{\circ }\,\rightarrow \,{\mbox{junctions}},\quad \alpha =90^{\circ }\,\rightarrow \,{\mbox{circular features}}} === Filter potential keypoints === non-maxima suppression over scale, space and angle thresholding the isotropy λ 2 ( M ) {\displaystyle \lambda _{2(M)}} :eigenvalues characterize the shape of the keypoint, smallest eigenvalue has to be larger than threshold T λ {\displaystyle T_{\lambda }} derived from noise variance V ( n ) {\displaystyle V(n)} and significance level S {\displaystyle S} : T λ ( V ( n ) , τ , σ , S ) = N ( σ ) 16 π τ 4 V ( n ) χ 2 , S 2 {\displaystyle T_{\lambda }(V(n),\tau ,\sigma ,S)={\frac {N(\sigma )}{16\pi \tau ^{4}}}V(n)\chi _{2,S}^{2}} == Algorithm == == Results == === Interpretability of SFOP keypoints ===
IBM ALP
IBM Assembly Language Processor (ALP) is an assembler written by IBM for 32-bit OS/2 Warp (OS/2 3.0), which was released in 1994. ALP accepts source programs compatible with Microsoft Macro Assembler (MASM) version 5.1, which was originally used to build many of the device drivers included with OS/2. For OS/2 versions 3 and 4, ALP was distributed, along with other tools and documentation, as part of the Device Driver Kit (DDK). The DDK was withdrawn in 2004 as part of IBM's discontinuance of OS/2.
Receptron
The receptron (short for "reservoir perceptron") is a neuromorphic data processing model — specifically neuromorphic computing — that generalizes the traditional perceptron, by incorporating non-linear interactions between inputs. Unlike classical perceptron, which rely on linearly independent weights, the receptron leverages complexity in physical substrates, such as the electric conduction properties of nanostructured materials or optical speckle fields, to perform classification tasks. The receptron bridges unconventional computing and neural network principles, enabling solutions that do not require the training approaches typical of artificial neural networks based on the perceptron model. == Algorithm == The receptron is an algorithm for supervised learning of binary classifiers, so a classification algorithm that makes its predictions based on a predictor function, combining a set of weights with the feature vector. The mathematical model is based on the sum of inputs with non-linear interactions: S = ∑ k = 1 n x j w ~ j ( x → ) | S ∈ R {\displaystyle S=\sum _{k=1}^{n}x_{j}{\widetilde {w}}_{j}({\vec {x}})|S\in R} (1) where j ∈ [ 1 , n ] {\displaystyle j\in [1,n]} and w ~ j {\displaystyle {\widetilde {w}}_{j}} are non-linear weight functions depending on the inputs, x → {\displaystyle {\vec {x}}} . Nonlinearity will typically make the system extremely complex, and allowing for the solution of problems not solvable through the simpler rules of a linear system, such as the perceptron or McCulloch Pitts neurons, which is based on the sum of linearly independent weights: S = ∑ k = 1 n x j w j p {\displaystyle S=\sum _{k=1}^{n}x_{j}w_{j}^{p}} (2) where w j {\displaystyle w_{j}} are constant real values. A consequence of this simplicity is the limitation to linearly separable functions, which necessitates multi-layer architectures and training algorithms like backpropagation As in the perceptron case, the summation in Eq. 1 origins the activation of the receptron output through the thresholding process, Y ( x 1 , . . . , x n ) = { 1 if S > th 0 if S ≤ th {\displaystyle Y(x_{1},...,x_{n})={\begin{cases}1&{\text{if }}S>{\text{th}}\\0&{\text{if }}S\leq {\text{th}}\end{cases}}} (3) where th is a constant threshold parameter. Equation 3 can be written by using the Heaviside step function. The weight functions w ~ ( x → ) {\displaystyle {\widetilde {w}}({\vec {x}})} can be written with a finite number of parameters w j 1 . . . j n {\displaystyle w_{j_{1}...j_{n}}} , simplifying the model representation. One can Taylor-expand w ~ ( x → ) {\displaystyle {\widetilde {w}}({\vec {x}})} and use the idempotency of Boolean variables ( x j ) q = x j ∀ q ≥ 1 {\displaystyle (x_{j})^{q}=x_{j}\forall q\geq 1} such that S ′ = b + ∑ k = 1 n x j w ~ j ( x → ) {\displaystyle S'=b+\sum _{k=1}^{n}x_{j}{\widetilde {w}}_{j}({\vec {x}})} can be written as S ′ ( x → ) = b + ∑ j w j x j + ∑ j < k w j k x j x k + ∑ j < k < l w j k l x j x k x l + . . . {\displaystyle S'({\vec {x}})=b+\sum _{j}w_{j}x_{j}+\sum _{j