Luminance HDR, formerly Qtpfsgui, is graphics software used for the creation and manipulation of high-dynamic-range images. Released under the terms of the GPL, it is available for Linux, Microsoft Windows, and Mac OS X (Intel only). Luminance HDR supports several High Dynamic Range (HDR) as well as Low Dynamic Range (LDR) file formats. == Functionality == Prerequisite of HDR photography are several narrow-range digital images with different exposures. Luminance HDR combines these images and calculates a high-contrast image. In order to view this image on a regular computer monitor, Luminance HDR can convert it into a displayable LDR image format using a variety of methods, such as tone mapping. Currently fifteen different tone mapping operators (algorithms) are available, each one with its tunable parameters. Different image processing techniques can be applied to the generated HDR images, such as resizing, cropping, rotating and a number of projective transformations. The software also provides batch processing functionality for creating HDR images and for tone mapping them in a non-interactive way. A module for copying Exif data among sets of images is also provided. For users who prefers the command line, a non-GUI, non-graphical interface is also available on all supported platforms. A common problem with HDR photography is that images need to be aligned exactly. If the subject is static, this can be achieved using a tripod or a stable surface on which the camera is placed. In the case of image data that does not align exactly, an automatic alignment can be performed using a tool provided by the Hugin project. If this automation doesn't provide the desired result, the user may improve it manually. == Supported formats == HDR images are images with a high dynamic range and, using Luminance HDR, they can be created as well as edited. The following HDR graphic formats are supported: OpenEXR Radiance HDR Tag Image File Format (TIFF) Format: 16 Bit, 32 Bit (Float) and LogLuv Raw PFS native Luminance HDR can create an HDR image from several LDR images and tonemap an HDR into an LDR. The following LDR formats are supported: JPG PNG Portable Pixmap (PPM) Portable Bitmap (PBM) TIFF (8 Bit)
Microsoft Whiteboard
Microsoft Whiteboard is a free multi-platform application, as well as an online service and a feature in Microsoft Teams, which simulates a virtual whiteboard and enables real-time collaboration between users. == Overview and features == Microsoft Whiteboard allows users to draw on a virtual whiteboard using input methods such as a stylus pen or a mouse and keyboard, and write down notes, draw connections between shareable ideas, and interact in real time. Microsoft Whiteboard is available to download on the following platforms and devices: Microsoft Windows (on Windows 10 or above) Android Apple iOS Surface Hub devices It is also available on the web and as a feature in Microsoft Teams. Microsoft Whiteboard allows users with Microsoft accounts to view, edit, and share whiteboards using the provided tools and options. The feature set includes tools for drawing, shapes, and media. Drawing in Microsoft Whiteboard is called inking. It works both on mobile devices and computers. The inking toolbar has customizable pencils, a ruler, a highlighter, an eraser, and an object selector. Whiteboard can recognize shapes drawn by hand and straighten them. Holding the Shift key on a computer while inking draws straight lines. Microsoft Whiteboard has keyboard shortcuts for some functions. Additional features include inserting sticky notes, text boxes, stickers, as well as images. Grid lines and colors are adjustable. Different templates can be inserted into the whiteboard. Users can also share their reactions. A feature limited to boards created in Microsoft Teams, is the ability to make them read-only; other participants from the meeting cannot edit them. == Reviews == PC Magazine gave Microsoft Whiteboard a score of 3.5 out of 5, praising the app's free availability and plentiful templates. It compared it to other, paid whiteboarding solutions, and concluded that Microsoft offers the best free one. Some of the cons, described by PCMag, include the inability to view boards without a Microsoft account and the inability to create custom templates.
Mutation (evolutionary algorithm)
Mutation is a genetic operator used to maintain genetic diversity of the chromosomes of a population of an evolutionary algorithm (EA), including genetic algorithms in particular. It is analogous to biological mutation. The classic example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be flipped. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types of mutation operators are commonly used for representations other than binary, such as floating-point encodings or representations for combinatorial problems. The purpose of mutation in EAs is to introduce diversity into the sampled population. Mutation operators are used in an attempt to avoid local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even stopping convergence to the global optimum. This reasoning also leads most EAs to avoid only taking the fittest of the population in generating the next generation, but rather selecting a random (or semi-random) set with a weighting toward those that are fitter. The following requirements apply to all mutation operators used in an EA: every point in the search space must be reachable by one or more mutations. there must be no preference for parts or directions in the search space (no drift). small mutations should be more probable than large ones. For different genome types, different mutation types are suitable. Some mutations are Gaussian, Uniform, Zigzag, Scramble, Insertion, Inversion, Swap, and so on. An overview and more operators than those presented below can be found in the introductory book by Eiben and Smith or in. == Bit string mutation == The mutation of bit strings ensue through bit flips at random positions. Example: The probability of a mutation of a bit is 1 l {\displaystyle {\frac {1}{l}}} , where l {\displaystyle l} is the length of the binary vector. Thus, a mutation rate of 1 {\displaystyle 1} per mutation and individual selected for mutation is reached. == Mutation of real numbers == Many EAs, such as the evolution strategy or the real-coded genetic algorithms, work with real numbers instead of bit strings. This is due to the good experiences that have been made with this type of coding. The value of a real-valued gene can either be changed or redetermined. A mutation that implements the latter should only ever be used in conjunction with the value-changing mutations and then only with comparatively low probability, as it can lead to large changes. In practical applications, the respective value range of the decision variables to be changed of the optimisation problem to be solved is usually limited. Accordingly, the values of the associated genes are each restricted to an interval [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} . Mutations may or may not take these restrictions into account. In the latter case, suitable post-treatment is then required as described below. === Mutation without consideration of restrictions === A real number x {\displaystyle x} can be mutated using normal distribution N ( 0 , σ ) {\displaystyle {\mathcal {N}}(0,\sigma )} by adding the generated random value to the old value of the gene, resulting in the mutated value x ′ {\displaystyle x'} : x ′ = x + N ( 0 , σ ) {\displaystyle x'=x+{\mathcal {N}}(0,\sigma )} In the case of genes with a restricted range of values, it is a good idea to choose the step size of the mutation σ {\displaystyle \sigma } so that it reasonably fits the range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} of the gene to be changed, e.g.: σ = x max − x min 6 {\displaystyle \sigma ={\frac {x_{\text{max}}-x_{\text{min}}}{6}}} The step size can also be adjusted to the smaller permissible change range depending on the current value. In any case, however, it is likely that the new value x ′ {\displaystyle x'} of the gene will be outside the permissible range of values. Such a case must be considered a lethal mutation, since the obvious repair by using the respective violated limit as the new value of the gene would lead to a drift. This is because the limit value would then be selected with the entire probability of the values beyond the limit of the value range. The evolution strategy works with real numbers and mutation based on normal distribution. The step sizes are part of the chromosome and are subject to evolution together with the actual decision variables. === Mutation with consideration of restrictions === One possible form of changing the value of a gene while taking its value range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} into account is the mutation relative parameter change of the evolutionary algorithm GLEAM (General Learning Evolutionary Algorithm and Method), in which, as with the mutation presented earlier, small changes are more likely than large ones. First, an equally distributed decision is made as to whether the current value x {\displaystyle x} should be increased or decreased and then the corresponding total change interval is determined. Without loss of generality, an increase is assumed for the explanation and the total change interval is then [ x , x max ] {\displaystyle [x,x_{\max }]} . It is divided into k {\displaystyle k} sub-areas of equal size with the width δ {\displaystyle \delta } , from which k {\displaystyle k} sub-change intervals of different size are formed: i {\displaystyle i} -th sub-change interval: [ x , x + δ ⋅ i ] {\displaystyle [x,x+\delta \cdot i]} with δ = ( x max − x ) k {\displaystyle \delta ={\frac {(x_{\text{max}}-x)}{k}}} and i = 1 , … , k {\displaystyle i=1,\dots ,k} Subsequently, one of the k {\displaystyle k} sub-change intervals is selected in equal distribution and a random number, also equally distributed, is drawn from it as the new value x ′ {\displaystyle x'} of the gene. The resulting summed probabilities of the sub-change intervals result in the probability distribution of the k {\displaystyle k} sub-areas shown in the adjacent figure for the exemplary case of k = 10 {\displaystyle k=10} . This is not a normal distribution as before, but this distribution also clearly favours small changes over larger ones. This mutation for larger values of k {\displaystyle k} , such as 10, is less well suited for tasks where the optimum lies on one of the value range boundaries. This can be remedied by significantly reducing k {\displaystyle k} when a gene value approaches its limits very closely. === Common properties === For both mutation operators for real-valued numbers, the probability of an increase and decrease is independent of the current value and is 50% in each case. In addition, small changes are considerably more likely than large ones. For mixed-integer optimization problems, rounding is usually used. == Mutation of permutations == Mutations of permutations are specially designed for genomes that are themselves permutations of a set. These are often used to solve combinatorial tasks. In the two mutations presented, parts of the genome are rotated or inverted. === Rotation to the right === The presentation of the procedure is illustrated by an example on the right: === Inversion === The presentation of the procedure is illustrated by an example on the right: === Variants with preference for smaller changes === The requirement raised at the beginning for mutations, according to which small changes should be more probable than large ones, is only inadequately fulfilled by the two permutation mutations presented, since the lengths of the partial lists and the number of shift positions are determined in an equally distributed manner. However, the longer the partial list and the shift, the greater the change in gene order. This can be remedied by the following modifications. The end index j {\displaystyle j} of the partial lists is determined as the distance d {\displaystyle d} to the start index i {\displaystyle i} : j = ( i + d ) mod | P 0 | {\displaystyle j=(i+d){\bmod {\left|P_{0}\right|}}} where d {\displaystyle d} is determined randomly according to one of the two procedures for the mutation of real numbers from the interval [ 0 , | P 0 | − 1 ] {\displaystyle \left[0,\left|P_{0}\right|-1\right]} and rounded. For the rotation, k {\displaystyle k} is determined similarly to the distance d {\displaystyle d} , but the value 0 {\displaystyle 0} is forbidden. For the inversion, note that i ≠ j {\displaystyle i\neq j} must hold, so for d {\displaystyle d} the value 0 {\displaystyle 0} must be excluded.
Low-rank approximation
In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to numerous other techniques, including principal component analysis, factor analysis, total least squares, latent semantic analysis, orthogonal regression, and dynamic mode decomposition. == Definition == Given structure specification S : R n p → R m × n {\displaystyle {\mathcal {S}}:\mathbb {R} ^{n_{p}}\to \mathbb {R} ^{m\times n}} , vector of structure parameters p ∈ R n p {\displaystyle p\in \mathbb {R} ^{n_{p}}} , norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} , and desired rank r {\displaystyle r} , minimize over p ^ ‖ p − p ^ ‖ subject to rank ( S ( p ^ ) ) ≤ r . {\displaystyle {\text{minimize}}\quad {\text{over }}{\widehat {p}}\quad \|p-{\widehat {p}}\|\quad {\text{subject to}}\quad \operatorname {rank} {\big (}{\mathcal {S}}({\widehat {p}}){\big )}\leq r.} == Applications == Linear system identification, in which case the approximating matrix is Hankel structured. Machine learning, in which case the approximating matrix is nonlinearly structured. Recommender systems, in which cases the data matrix has missing values and the approximation is categorical. Distance matrix completion, in which case there is a positive definiteness constraint. Natural language processing, in which case the approximation is nonnegative. Computer algebra, in which case the approximation is Sylvester structured. Matrix product states, in which case the approximation is usually rescaled to have fixed Frobenius norm. == Basic low-rank approximation problem == The unstructured problem with fit measured by the Frobenius norm, i.e., minimize over D ^ ‖ D − D ^ ‖ F subject to rank ( D ^ ) ≤ r {\displaystyle {\text{minimize}}\quad {\text{over }}{\widehat {D}}\quad \|D-{\widehat {D}}\|_{\text{F}}\quad {\text{subject to}}\quad \operatorname {rank} {\big (}{\widehat {D}}{\big )}\leq r} has an analytic solution in terms of the singular value decomposition of the data matrix. The result is referred to as the matrix approximation lemma or Eckart–Young–Mirsky theorem. This problem was originally solved by Erhard Schmidt in the infinite dimensional context of integral operators (although his methods easily generalize to arbitrary compact operators on Hilbert spaces) and later rediscovered by C. Eckart and G. Young. L. Mirsky generalized the result to arbitrary unitarily invariant norms. Let D = U Σ V ⊤ ∈ R m × n , m ≥ n {\displaystyle D=U\Sigma V^{\top }\in \mathbb {R} ^{m\times n},\quad m\geq n} be the singular value decomposition of D {\displaystyle D} , where Σ =: diag ( σ 1 , … , σ r ) {\displaystyle \Sigma =:\operatorname {diag} (\sigma _{1},\ldots ,\sigma _{r})} , where r ≤ min { m , n } = n {\displaystyle r\leq \min\{m,n\}=n} , is the m × n {\displaystyle m\times n} rectangular diagonal matrix with r {\displaystyle r} non-zero singular values σ 1 ≥ … ≥ σ r > σ r + 1 = … = σ n = 0 {\displaystyle \sigma _{1}\geq \ldots \geq \sigma _{r}>\sigma _{r+1}=\ldots =\sigma _{n}=0} . For a given k ∈ { 1 , … , r } {\displaystyle k\in \{1,\dots ,r\}} , partition U {\displaystyle U} , Σ {\displaystyle \Sigma } , and V {\displaystyle V} as follows: U =: [ U 1 U 2 ] , Σ =: [ Σ 1 0 0 Σ 2 ] , and V =: [ V 1 V 2 ] , {\displaystyle U=:{\begin{bmatrix}U_{1}&U_{2}\end{bmatrix}},\quad \Sigma =:{\begin{bmatrix}\Sigma _{1}&0\\0&\Sigma _{2}\end{bmatrix}},\quad {\text{and}}\quad V=:{\begin{bmatrix}V_{1}&V_{2}\end{bmatrix}},} where U 1 {\displaystyle U_{1}} is m × k {\displaystyle m\times k} , Σ 1 {\displaystyle \Sigma _{1}} is k × k {\displaystyle k\times k} , and V 1 {\displaystyle V_{1}} is n × k {\displaystyle n\times k} . Then the rank k {\displaystyle k} matrix D ^ ∗ := U 1 Σ 1 V 1 ⊤ , {\displaystyle {\widehat {D}}^{}:=U_{1}\Sigma _{1}V_{1}^{\top },} obtained from the truncated singular value decomposition is such that ‖ D − D ^ ∗ ‖ F = min rank ( D ^ ) ≤ k ‖ D − D ^ ‖ F = σ k + 1 2 + ⋯ + σ r 2 . {\displaystyle \|D-{\widehat {D}}^{}\|_{\text{F}}=\min _{\operatorname {rank} ({\widehat {D}})\leq k}\|D-{\widehat {D}}\|_{\text{F}}={\sqrt {\sigma _{k+1}^{2}+\cdots +\sigma _{r}^{2}}}.} The minimizer D ^ ∗ {\displaystyle {\widehat {D}}^{}} is unique if and only if σ k > σ k + 1 {\displaystyle \sigma _{k}>\sigma _{k+1}} . == Proof of Eckart–Young–Mirsky theorem (for spectral norm) == Let A ∈ R m × n {\displaystyle A\in \mathbb {R} ^{m\times n}} be a real (possibly rectangular) matrix with m ≤ n {\displaystyle m\leq n} . Suppose that A = U Σ V ⊤ {\displaystyle A=U\Sigma V^{\top }} is the singular value decomposition of A {\displaystyle A} . Recall that U {\displaystyle U} and V {\displaystyle V} are orthogonal matrices, and Σ {\displaystyle \Sigma } is an m × n {\displaystyle m\times n} diagonal matrix with entries ( σ 1 , σ 2 , ⋯ , σ m ) {\displaystyle (\sigma _{1},\sigma _{2},\cdots ,\sigma _{m})} such that σ 1 ≥ σ 2 ≥ ⋯ ≥ σ m ≥ 0 {\displaystyle \sigma _{1}\geq \sigma _{2}\geq \cdots \geq \sigma _{m}\geq 0} . We claim that the best rank- k {\displaystyle k} approximation to A {\displaystyle A} in the spectral norm, denoted by ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} , is given by A k := ∑ i = 1 k σ i u i v i ⊤ {\displaystyle A_{k}:=\sum _{i=1}^{k}\sigma _{i}u_{i}v_{i}^{\top }} where u i {\displaystyle u_{i}} and v i {\displaystyle v_{i}} denote the i {\displaystyle i} th column of U {\displaystyle U} and V {\displaystyle V} , respectively. First, note that we have ‖ A − A k ‖ 2 = ‖ ∑ i = 1 n σ i u i v i ⊤ − ∑ i = 1 k σ i u i v i ⊤ ‖ 2 = ‖ ∑ i = k + 1 n σ i u i v i ⊤ ‖ 2 = σ k + 1 {\displaystyle \|A-A_{k}\|_{2}=\left\|\sum _{i=1}^{\color {red}{n}}\sigma _{i}u_{i}v_{i}^{\top }-\sum _{i=1}^{\color {red}{k}}\sigma _{i}u_{i}v_{i}^{\top }\right\|_{2}=\left\|\sum _{i=\color {red}{k+1}}^{n}\sigma _{i}u_{i}v_{i}^{\top }\right\|_{2}=\sigma _{k+1}} Therefore, we need to show that if B k = X Y ⊤ {\displaystyle B_{k}=XY^{\top }} where X {\displaystyle X} and Y {\displaystyle Y} have k {\displaystyle k} columns then ‖ A − A k ‖ 2 = σ k + 1 ≤ ‖ A − B k ‖ 2 {\displaystyle \|A-A_{k}\|_{2}=\sigma _{k+1}\leq \|A-B_{k}\|_{2}} . Since Y {\displaystyle Y} has k {\displaystyle k} columns, then there must be a nontrivial linear combination of the first k + 1 {\displaystyle k+1} columns of V {\displaystyle V} , i.e., w = γ 1 v 1 + ⋯ + γ k + 1 v k + 1 , {\displaystyle w=\gamma _{1}v_{1}+\cdots +\gamma _{k+1}v_{k+1},} such that Y ⊤ w = 0 {\displaystyle Y^{\top }w=0} . Without loss of generality, we can scale w {\displaystyle w} so that ‖ w ‖ 2 = 1 {\displaystyle \|w\|_{2}=1} or (equivalently) γ 1 2 + ⋯ + γ k + 1 2 = 1 {\displaystyle \gamma _{1}^{2}+\cdots +\gamma _{k+1}^{2}=1} . Therefore, ‖ A − B k ‖ 2 2 ≥ ‖ ( A − B k ) w ‖ 2 2 = ‖ A w ‖ 2 2 = γ 1 2 σ 1 2 + ⋯ + γ k + 1 2 σ k + 1 2 ≥ σ k + 1 2 . {\displaystyle \|A-B_{k}\|_{2}^{2}\geq \|(A-B_{k})w\|_{2}^{2}=\|Aw\|_{2}^{2}=\gamma _{1}^{2}\sigma _{1}^{2}+\cdots +\gamma _{k+1}^{2}\sigma _{k+1}^{2}\geq \sigma _{k+1}^{2}.} The result follows by taking the square root of both sides of the above inequality. == Proof of Eckart–Young–Mirsky theorem (for Frobenius norm) == Let A ∈ R m × n {\displaystyle A\in \mathbb {R} ^{m\times n}} be a real (possibly rectangular) matrix with m ≤ n {\displaystyle m\leq n} . Suppose that A = U Σ V ⊤ {\displaystyle A=U\Sigma V^{\top }} is the singular value decomposition of A {\displaystyle A} . We claim that the best rank k {\displaystyle k} approximation to A {\displaystyle A} in the Frobenius norm, denoted by ‖ ⋅ ‖ F {\displaystyle \|\cdot \|_{F}} , is given by A k = ∑ i = 1 k σ i u i v i ⊤ {\displaystyle A_{k}=\sum _{i=1}^{k}\sigma _{i}u_{i}v_{i}^{\top }} where u i {\displaystyle u_{i}} and v i {\displaystyle v_{i}} denote the i {\displaystyle i} th column of U {\displaystyle U} and V {\displaystyle V} , respectively. First, note that we have ‖ A − A k ‖ F 2 = ‖ ∑ i = k + 1 n σ i u i v i ⊤ ‖ F 2 = ∑ i = k + 1 n σ i 2 {\displaystyle \|A-A_{k}\|_{F}^{2}=\left\|\sum _{i=k+1}^{n}\sigma _{i}u_{i}v_{i}^{\top }\right\|_{F}^{2}=\sum _{i=k+1}^{n}\sigma _{i}^{2}} Therefore, we need to show that if B k = X Y ⊤ {\displaystyle B_{k}=XY^{\top }} where X {\displaystyle X} and Y {\displaystyle Y} have k {\displaystyle k} columns then ‖ A − A k ‖ F 2 = ∑ i = k + 1 n σ i 2 ≤ ‖ A − B k ‖ F 2 . {\displaystyle \|A-A_{k}\|_{F}^{2}=\sum _{i=k+1}^{n}\sigma _{i}^{2}\leq \|A-B_{k}\|_{F}^{2}.} By the triangle inequality with the spectral norm
Soft independent modelling of class analogies
Soft independent modelling by class analogy (SIMCA) is a statistical method for supervised classification of data. The method requires a training data set consisting of samples (or objects) with a set of attributes and their class membership. The term soft refers to the fact the classifier can identify samples as belonging to multiple classes and not necessarily producing a classification of samples into non-overlapping classes. == Method == In order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis (PCA); only the significant components are retained. For a given class, the resulting model then describes either a line (for one Principal Component or PC), plane (for two PCs) or hyper-plane (for more than two PCs). For each modelled class, the mean orthogonal distance of training data samples from the line, plane, or hyper-plane (calculated as the residual standard deviation) is used to determine a critical distance for classification. This critical distance is based on the F-distribution and is usually calculated using 95% or 99% confidence intervals. New observations are projected into each PC model and the residual distances calculated. An observation is assigned to the model class when its residual distance from the model is below the statistical limit for the class. The observation may be found to belong to multiple classes and a measure of goodness of the model can be found from the number of cases where the observations are classified into multiple classes. The classification efficiency is usually indicated by Receiver operating characteristics. In the original SIMCA method, the ends of the hyper-plane of each class are closed off by setting statistical control limits along the retained principal components axes (i.e., score value between plus and minus 0.5 times score standard deviation). More recent adaptations of the SIMCA method close off the hyper-plane by construction of ellipsoids (e.g. Hotelling's T2 or Mahalanobis distance). With such modified SIMCA methods, classification of an object requires both that its orthogonal distance from the model and its projection within the model (i.e. score value within the region defined by the ellipsoid) are not significant. == Application == SIMCA as a method of classification has gained widespread use especially in applied statistical fields such as chemometrics and spectroscopic data analysis.
Collaboration-oriented architecture
Collaboration Oriented Architecture (COA) is a computer system that is designed to collaborate, or use services, from systems that are outside of the operators control. Collaboration Oriented Architecture will often use Service Oriented Architecture to deliver the technical framework. Collaboration Oriented Architecture is the ability to collaborate between systems that are based on the Jericho Forum principles or "Commandments". Bill Gates and Craig Mundie (Microsoft) clearly articulated the need for people to work outside of their organizations in a secure and collaborative manner in their opening keynote to the RSA Security Conference in February 2007. Successful implementation of a Collaboration Oriented Architecture implies the ability to successfully inter-work securely over the Internet and will typically mean the resolution of the problems that come with de-perimeterisation. == Etymology == The term Collaboration Oriented Architectures was defined and developed in a meeting of the Jericho Forum at a meeting held at HSBC on 6 July 2007. == Definition == The key elements that qualify a security architecture as a Collaboration Oriented Architecture are as follows; Protocol: Systems use appropriately secure protocols to communicate. Authentication: The protocol is authenticated with user and/or system credentials. Federation: User and/or systems credentials are accepted and validated by systems that are not under your (locus of) control. Network Agnostic: The design does not rely on a secure network, thus it will operate securely from an Intranet to raw-Internet Trust: The collaborating system have the capacity to be able to confirm to a specified degree of confidence that the components in a transaction chain have. Risk: The collaborating systems can make a risk assessment on any transaction based on the communicated levels of required trust, based on the required degree of identity, confidentiality, integrity, availability. == Authentication == Working in a collaborative multi-sourced environment implies the need for authentication, authorization and accountability which must interoperate / exchange outside of your locus / area of control. People/systems must be able to manage permissions of resources and rights of users they don't control There must be capability of trusting an organization, which can authenticate individuals or groups, thus eliminating the need to create separate identities In principle, only one instance of person / system / identity may exist, but privacy necessitates the support for multiple instances, or one instance with multiple facets, often referred to as personas Systems must be able to pass on security credentials /assertions Multiple loci (areas) of control must be supported
IDistance
In pattern recognition, iDistance is an indexing and query processing technique for k-nearest neighbor queries on point data in multi-dimensional metric spaces. The kNN query is one of the hardest problems on multi-dimensional data, especially when the dimensionality of the data is high. iDistance is designed to process kNN queries in high-dimensional spaces efficiently and performs extremely well for skewed data distributions, which usually occur in real-life data sets. iDistance employs a two-phase search strategy involving an initial filtering of candidate regions and a subsequent refinement of results, an approach aligned with the Filter and Refine Principle (FRP). This means that the index first prunes the search space to eliminate unlikely candidates, then verifies the true nearest neighbors in a refinement step, following the general FRP paradigm used in database search algorithms. The iDistance index can also be augmented with machine learning models to learn data distributions for improved searching and storage of multi-dimensional data. == Indexing == Building the iDistance index has two steps: A number of reference points in the data space are chosen. There are various ways of choosing reference points. Using cluster centers as reference points is the most efficient way. The data points are partitioned into Voronoi cells based on well-chosen reference points. The distance between a data point and its closest reference point is calculated. This distance plus a scaling value is called the point's iDistance. By this means, points in a multi-dimensional space are mapped to one-dimensional values, and then a B+-tree can be adopted to index the points using the iDistance as the key. The figure on the right shows an example where three reference points (O1, O2, O3) are chosen. The data points are then mapped to a one-dimensional space and indexed in a B+-tree. Various extensions have been proposed to make the selection of reference points for effective query performance, including employing machine learning to learn the identification of reference points. == Query processing == To process a kNN query, the query is mapped to a number of one-dimensional range queries, which can be processed efficiently on a B+-tree. In the above figure, the query Q is mapped to a value in the B+-tree while the kNN search ``sphere" is mapped to a range in the B+-tree. The search sphere expands gradually until the k NNs are found. This corresponds to gradually expanding range searches in the B+-tree. The iDistance technique can be viewed as a way of accelerating the sequential scan. Instead of scanning records from the beginning to the end of the data file, the iDistance starts the scan from spots where the nearest neighbors can be obtained early with a very high probability. == Applications == The iDistance has been used in many applications including Image retrieval Video indexing Similarity search in P2P systems Mobile computing Recommender system == Historical background == The iDistance was first proposed by Cui Yu, Beng Chin Ooi, Kian-Lee Tan and H. V. Jagadish in 2001. Later, together with Rui Zhang, they improved the technique and performed a more comprehensive study on it in 2005.