National Cyber Security Policy is a policy framework by Department of Electronics and Information Technology (DeitY) It aims at protecting the public and private infrastructure from cyber attacks. The policy also intends to safeguard "information, such as personal information (of web users), financial and banking information and sovereign data". This was particularly relevant in the wake of US National Security Agency (NSA) leaks that suggested the US government agencies are spying on Indian users, who have no legal or technical safeguards against it. Ministry of Communications and Information Technology (India) defines Cyberspace as a complex environment consisting of interactions between people, software services supported by worldwide distribution of information and communication technology. == Reason for Cyber Security policies == India had no Cyber security policy before 2013. In 2013, The Hindu newspaper, citing documents leaked by NSA whistle-blower Edward Snowden, has alleged that much of the NSA surveillance was focused on India's domestic politics and its strategic and commercial interests. This sparked a furore among people. Under pressure, the government unveiled a National Cyber Security Policy 2013 on 2 July 2013. == Vision == To build a secure and resilient cyberspace for citizens, business, and government and also to protect anyone from intervening in user's privacy.It mentioned a five year target of training five lakh cyber security personnel by 2018. == Mission == To protect information and information infrastructure in cyberspace, build capabilities to prevent and respond to cyber threat, reduce vulnerabilities and minimize damage from cyber incidents through a combination of institutional structures, people, processes, technology, and cooperation. == Objective == Ministry of Communications and Information Technology (India) define objectives as follows: To create a secure cyber ecosystem in the country, generate adequate trust and confidence in IT system and transactions in cyberspace and thereby enhance adoption of IT in all sectors of the economy. To create an assurance framework for the design of security policies and promotion and enabling actions for compliance to global security standards and best practices by way of conformity assessment (Product, process, technology & people). To strengthen the Regulatory Framework for ensuring a SECURE CYBERSPACE ECOSYSTEM. To enhance and create National and Sectoral level 24x7 mechanism for obtaining strategic information regarding threats to ICT infrastructure, creating scenarios for response, resolution and crisis management through effective predictive, preventive, protective response and recovery actions. -To improve visibility of integrity of ICT products and services by establishing infrastructure for testing & validation of security of such product. To create workforce for 500,000 professionals skilled in next 5 years through capacity building skill development and training. To provide fiscal benefit to businesses for adoption of standard security practices and processes. To enable Protection of information while in process, handling, storage & transit so as to safeguard privacy of citizen's data and reducing economic losses due to cyber crime or data theft. To enable effective prevention, investigation and prosecution of cybercrime and enhancement of law enforcement capabilities through appropriate legislative intervention. == Strategies == Creating a secured Ecosystem. Creating an assurance framework. Encouraging Open Standards. Strengthening The regulatory Framework. Creating a mechanism for Security Threats Early Warning, Vulnerability management, and response to security threats. Securing E-Governance services. Protection and resilience of Critical Information Infrastructure. Promotion of Research and Development in cyber security. Reducing supply chain risks Human Resource Development (fostering education and training programs both in formal and informal sectors to Support the Nation's cyber security needs and build capacity. Creating cyber security awareness. Developing effective Public-Private partnerships. To develop bilateral and multilateral relationships in the area of cyber security with another country. (Information sharing and cooperation) a Prioritized approach for implementation.
SUPS
In computational neuroscience, SUPS (for Synaptic Updates Per Second) or formerly CUPS (Connections Updates Per Second) is a measure of a neuronal network performance, useful in fields of neuroscience, cognitive science, artificial intelligence, and computer science. == Computing == For a processor or computer designed to simulate a neural network SUPS is measured as the product of simulated neurons N {\displaystyle N} and average connectivity c {\displaystyle c} (synapses) per neuron per second: S U P S = c × N {\displaystyle SUPS=c\times N} Depending on the type of simulation it is usually equal to the total number of synapses simulated. In an "asynchronous" dynamic simulation if a neuron spikes at υ {\displaystyle \upsilon } Hz, the average rate of synaptic updates provoked by the activity of that neuron is υ c N {\displaystyle \upsilon cN} . In a synchronous simulation with step Δ t {\displaystyle \Delta t} the number of synaptic updates per second would be c N Δ t {\displaystyle {\frac {cN}{\Delta t}}} . As Δ t {\displaystyle \Delta t} has to be chosen much smaller than the average interval between two successive afferent spikes, which implies Δ t < 1 υ N {\displaystyle \Delta t<{\frac {1}{\upsilon N}}} , giving an average of synaptic updates equal to υ c N 2 {\displaystyle \upsilon cN^{2}} . Therefore, spike-driven synaptic dynamics leads to a linear scaling of computational complexity O(N) per neuron, compared with the O(N2) in the "synchronous" case. == Records == Developed in the 1980s Adaptive Solutions' CNAPS-1064 Digital Parallel Processor chip is a full neural network (NNW). It was designed as a coprocessor to a host and has 64 sub-processors arranged in a 1D array and operating in a SIMD mode. Each sub-processor can emulate one or more neurons and multiple chips can be grouped together. At 25 MHz it is capable of 1.28 GMAC. After the presentation of the RN-100 (12 MHz) single neuron chip at Seattle 1991 Ricoh developed the multi-neuron chip RN-200. It had 16 neurons and 16 synapses per neuron. The chip has on-chip learning ability using a proprietary backdrop algorithm. It came in a 257-pin PGA encapsulation and drew 3.0 W at a maximum. It was capable of 3 GCPS (1 GCPS at 32 MHz). In 1991–97, Siemens developed the MA-16 chip, SYNAPSE-1 and SYNAPSE-3 Neurocomputer. The MA-16 was a fast matrix-matrix multiplier that can be combined to form systolic arrays. It could process 4 patterns of 16 elements each (16-bit), with 16 neuron values (16-bit) at a rate of 800 MMAC or 400 MCPS at 50 MHz. The SYNAPSE3-PC PCI card contained 2 MA-16 with a peak performance of 2560 MOPS (1.28 GMAC); 7160 MOPS (3.58 GMAC) when using three boards. In 2013, the K computer was used to simulate a neural network of 1.73 billion neurons with a total of 10.4 trillion synapses (1% of the human brain). The simulation ran for 40 minutes to simulate 1 s of brain activity at a normal activity level (4.4 on average). The simulation required 1 Petabyte of storage.
European Conference on Computer Vision
The European Conference on Computer Vision (ECCV) is a biennial research conference with the proceedings published by Springer Science+Business Media. Similar to ICCV in scope and quality, it is held those years which ICCV is not. It is considered to be one of the top conferences in computer vision, alongside CVPR and ICCV, with an 'A' rating from the Australian Ranking of ICT Conferences and an 'A1' rating from the Brazilian ministry of education. The acceptance rate for ECCV 2010 was 24.4% for posters and 3.3% for oral presentations. Like other top computer vision conferences, ECCV has tutorial talks, technical sessions, and poster sessions. The conference is usually spread over five to six days with the main technical program occupying three days in the middle, and tutorial and workshops, focused on specific topics, being held in the beginning and at the end. The ECCV presents the Koenderink Prize annually to recognize fundamental contributions in computer vision. == Location == The conference is usually held in autumn in Europe.
Self-organizing map
A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher-dimensional data set while preserving the topological structure of the data. For example, a data set with p {\displaystyle p} variables measured in n {\displaystyle n} observations could be represented as clusters of observations with similar values for the variables. These clusters then could be visualized as a two-dimensional "map" such that observations in proximal clusters have more similar values than observations in distal clusters. This can make high-dimensional data easier to visualize and analyze. A SOM is a type of artificial neural network but is trained using competitive learning rather than the error-correction learning (e.g., backpropagation with gradient descent) used by other artificial neural networks. The SOM was introduced by the Finnish professor Teuvo Kohonen in the 1980s and therefore is sometimes called a Kohonen map or Kohonen network. The Kohonen map or network is a computationally convenient abstraction building on biological models of neural systems from the 1970s and morphogenesis models dating back to Alan Turing in the 1950s. SOMs create internal representations reminiscent of the cortical homunculus, a distorted representation of the human body, based on a neurological "map" of the areas and proportions of the human brain dedicated to processing sensory functions, for different parts of the body. == Overview == Self-organizing maps, like most artificial neural networks, operate in two modes: training and mapping. First, training uses an input data set (the "input space") to generate a lower-dimensional representation of the input data (the "map space"). Second, mapping classifies additional input data using the generated map. The goal of training is to represent an input space with p dimensions as a map space with n dimensions, where p > n. Specifically, an input space with p variables is said to have p dimensions. A map space consists of components called "nodes" or "neurons", which are arranged as a hexagonal or rectangular grid with two dimensions. The number of nodes and their arrangement are specified beforehand based on the larger goals of the analysis and exploration of the data. Each node in the map space is associated with a "weight" vector, which is the position of the node in the input space. While nodes in the map space stay fixed, training consists in moving weight vectors toward the input data (reducing a distance metric such as Euclidean distance) without spoiling the topology induced from the map space. After training, the map can be used to classify additional observations for the input space by finding the node with the closest weight vector (smallest distance metric) to the input space vector. == Learning algorithm == The goal of learning in the self-organizing map is to cause different parts of the network to respond similarly to certain input patterns. This is partly motivated by how visual, auditory or other sensory information is handled in separate parts of the cerebral cortex in the human brain. The weights of the neurons are initialized either to small random values or sampled evenly from the subspace spanned by the two largest principal component eigenvectors. With the latter alternative, learning is much faster because the initial weights already give a good approximation of SOM weights. The network must be fed a large number of example vectors that represent, as close as possible, the kinds of vectors expected during mapping. The examples are usually administered several times as iterations. The training utilizes competitive learning. When a training example is fed to the network, its Euclidean distance to all weight vectors is computed. The neuron whose weight vector is most similar to the input is called the best matching unit (BMU). The weights of the BMU and neurons close to it in the SOM grid are adjusted towards the input vector. The magnitude of the change decreases with time and with the grid-distance from the BMU. The update formula for a neuron v with weight vector Wv(s) is W v ( s + 1 ) = W v ( s ) + θ ( u , v , s ) ⋅ α ( s ) ⋅ ( D ( t ) − W v ( s ) ) {\displaystyle W_{v}(s+1)=W_{v}(s)+\theta (u,v,s)\cdot \alpha (s)\cdot (D(t)-W_{v}(s))} , where s is the step index, t is an index into the training sample, u is the index of the BMU for the input vector D(t), α(s) is a monotonically decreasing learning coefficient; θ(u, v, s) is the neighborhood function which gives the distance between the neuron u and the neuron v in step s. Depending on the implementations, t can scan the training data set systematically (t is 0, 1, 2...T-1, then repeat, T being the training sample's size), be randomly drawn from the data set (bootstrap sampling), or implement some other sampling method (such as jackknifing). The neighborhood function θ(u, v, s) (also called function of lateral interaction) depends on the grid-distance between the BMU (neuron u) and neuron v. In the simplest form, it is 1 for all neurons close enough to BMU and 0 for others, but the Gaussian and Mexican-hat functions are common choices, too. Regardless of the functional form, the neighborhood function shrinks with time. At the beginning when the neighborhood is broad, the self-organizing takes place on the global scale. When the neighborhood has shrunk to just a couple of neurons, the weights are converging to local estimates. In some implementations, the learning coefficient α and the neighborhood function θ decrease steadily with increasing s, in others (in particular those where t scans the training data set) they decrease in step-wise fashion, once every T steps. This process is repeated for each input vector for a (usually large) number of cycles λ. The network winds up associating output nodes with groups or patterns in the input data set. If these patterns can be named, the names can be attached to the associated nodes in the trained net. During mapping, there will be one single winning neuron: the neuron whose weight vector lies closest to the input vector. This can be simply determined by calculating the Euclidean distance between input vector and weight vector. While representing input data as vectors has been emphasized in this article, any kind of object which can be represented digitally, which has an appropriate distance measure associated with it, and in which the necessary operations for training are possible can be used to construct a self-organizing map. This includes matrices, continuous functions or even other self-organizing maps. === Algorithm === Randomize the node weight vectors in a map For s = 0 , 1 , 2 , . . . , λ {\displaystyle s=0,1,2,...,\lambda } Randomly pick an input vector D ( t ) {\displaystyle {D}(t)} Find the node in the map closest to the input vector. This node is the best matching unit (BMU). Denote it by u {\displaystyle u} For each node v {\displaystyle v} , update its vector by pulling it closer to the input vector: W v ( s + 1 ) = W v ( s ) + θ ( u , v , s ) ⋅ α ( s ) ⋅ ( D ( t ) − W v ( s ) ) {\displaystyle W_{v}(s+1)=W_{v}(s)+\theta (u,v,s)\cdot \alpha (s)\cdot (D(t)-W_{v}(s))} The variable names mean the following, with vectors in bold, s {\displaystyle s} is the current iteration λ {\displaystyle \lambda } is the iteration limit t {\displaystyle t} is the index of the target input data vector in the input data set D {\displaystyle \mathbf {D} } D ( t ) {\displaystyle {D}(t)} is a target input data vector v {\displaystyle v} is the index of the node in the map W v {\displaystyle \mathbf {W} _{v}} is the current weight vector of node v {\displaystyle v} u {\displaystyle u} is the index of the best matching unit (BMU) in the map θ ( u , v , s ) {\displaystyle \theta (u,v,s)} is the neighbourhood function, α ( s ) {\displaystyle \alpha (s)} is the learning rate schedule. The key design choices are the shape of the SOM, the neighbourhood function, and the learning rate schedule. The idea of the neighborhood function is to make it such that the BMU is updated the most, its immediate neighbors are updated a little less, and so on. The idea of the learning rate schedule is to make it so that the map updates are large at the start, and gradually stop updating. For example, if we want to learn a SOM using a square grid, we can index it using ( i , j ) {\displaystyle (i,j)} where both i , j ∈ 1 : N {\displaystyle i,j\in 1:N} . The neighborhood function can make it so that the BMU updates in full, the nearest neighbors update in half, and their neighbors update in half again, etc. θ ( ( i , j ) , ( i ′ , j ′ ) , s ) = 1 2 | i − i ′ | + | j − j ′ | = { 1 if i = i ′ , j = j ′ 1 / 2 if | i − i ′ | + | j − j ′ | = 1 1 / 4 if | i − i ′ | + | j − j ′ | = 2 ⋯ ⋯ {\displaystyle \theta ((i,j),(i',j'),s)={\frac {1}{2^{|i-i'|+|j-j'|}}}={\begin{cases}1&{\text{if }}i=i',j=j'\\1/2&{\text{if
Error tolerance (PAC learning)
In PAC learning, error tolerance refers to the ability of an algorithm to learn when the examples received have been corrupted in some way. In fact, this is a very common and important issue since in many applications it is not possible to access noise-free data. Noise can interfere with the learning process at different levels: the algorithm may receive data that have been occasionally mislabeled, or the inputs may have some false information, or the classification of the examples may have been maliciously adulterated. == Notation and the Valiant learning model == In the following, let X {\displaystyle X} be our n {\displaystyle n} -dimensional input space. Let H {\displaystyle {\mathcal {H}}} be a class of functions that we wish to use in order to learn a { 0 , 1 } {\displaystyle \{0,1\}} -valued target function f {\displaystyle f} defined over X {\displaystyle X} . Let D {\displaystyle {\mathcal {D}}} be the distribution of the inputs over X {\displaystyle X} . The goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} . Let us suppose we have a function s i z e ( f ) {\displaystyle size(f)} that can measure the complexity of f {\displaystyle f} . Let Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} be an oracle that, whenever called, returns an example x {\displaystyle x} and its correct label f ( x ) {\displaystyle f(x)} . When no noise corrupts the data, we can define learning in the Valiant setting: Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the Valiant setting if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} and a polynomial p ( ⋅ , ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot ,\cdot )} such that for any 0 < ε ≤ 1 {\displaystyle 0<\varepsilon \leq 1} and 0 < δ ≤ 1 {\displaystyle 0<\delta \leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 ε , 1 δ , n , size ( f ) ) {\displaystyle p\left({\frac {1}{\varepsilon }},{\frac {1}{\delta }},n,{\text{size}}(f)\right)} , a function h ∈ H {\displaystyle h\in {\mathcal {H}}} that satisfies with probability at least 1 − δ {\displaystyle 1-\delta } the condition error ( h ) ≤ ε {\displaystyle {\text{error}}(h)\leq \varepsilon } . In the following we will define learnability of f {\displaystyle f} when data have suffered some modification. == Classification noise == In the classification noise model a noise rate 0 ≤ η < 1 2 {\displaystyle 0\leq \eta <{\frac {1}{2}}} is introduced. Then, instead of Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} that returns always the correct label of example x {\displaystyle x} , algorithm A {\displaystyle {\mathcal {A}}} can only call a faulty oracle Oracle ( x , η ) {\displaystyle {\text{Oracle}}(x,\eta )} that will flip the label of x {\displaystyle x} with probability η {\displaystyle \eta } . As in the Valiant case, the goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} . In applications it is difficult to have access to the real value of η {\displaystyle \eta } , but we assume we have access to its upperbound η B {\displaystyle \eta _{B}} . Note that if we allow the noise rate to be 1 / 2 {\displaystyle 1/2} , then learning becomes impossible in any amount of computation time, because every label conveys no information about the target function. Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the classification noise model if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , η ) {\displaystyle {\text{Oracle}}(x,\eta )} and a polynomial p ( ⋅ , ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot ,\cdot )} such that for any 0 ≤ η ≤ 1 2 {\displaystyle 0\leq \eta \leq {\frac {1}{2}}} , 0 ≤ ε ≤ 1 {\displaystyle 0\leq \varepsilon \leq 1} and 0 ≤ δ ≤ 1 {\displaystyle 0\leq \delta \leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 1 − 2 η B , 1 ε , 1 δ , n , s i z e ( f ) ) {\displaystyle p\left({\frac {1}{1-2\eta _{B}}},{\frac {1}{\varepsilon }},{\frac {1}{\delta }},n,size(f)\right)} , a function h ∈ H {\displaystyle h\in {\mathcal {H}}} that satisfies with probability at least 1 − δ {\displaystyle 1-\delta } the condition e r r o r ( h ) ≤ ε {\displaystyle error(h)\leq \varepsilon } . == Statistical query learning == Statistical Query Learning is a kind of active learning problem in which the learning algorithm A {\displaystyle {\mathcal {A}}} can decide if to request information about the likelihood P f ( x ) {\displaystyle P_{f(x)}} that a function f {\displaystyle f} correctly labels example x {\displaystyle x} , and receives an answer accurate within a tolerance α {\displaystyle \alpha } . Formally, whenever the learning algorithm A {\displaystyle {\mathcal {A}}} calls the oracle Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} , it receives as feedback probability Q f ( x ) {\displaystyle Q_{f(x)}} , such that Q f ( x ) − α ≤ P f ( x ) ≤ Q f ( x ) + α {\displaystyle Q_{f(x)}-\alpha \leq P_{f(x)}\leq Q_{f(x)}+\alpha } . Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the statistical query learning model if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} and polynomials p ( ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot )} , q ( ⋅ , ⋅ , ⋅ ) {\displaystyle q(\cdot ,\cdot ,\cdot )} , and r ( ⋅ , ⋅ , ⋅ ) {\displaystyle r(\cdot ,\cdot ,\cdot )} such that for any 0 < ε ≤ 1 {\displaystyle 0<\varepsilon \leq 1} the following hold: Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} can evaluate P f ( x ) {\displaystyle P_{f(x)}} in time q ( 1 ε , n , s i z e ( f ) ) {\displaystyle q\left({\frac {1}{\varepsilon }},n,size(f)\right)} ; 1 α {\displaystyle {\frac {1}{\alpha }}} is bounded by r ( 1 ε , n , s i z e ( f ) ) {\displaystyle r\left({\frac {1}{\varepsilon }},n,size(f)\right)} A {\displaystyle {\mathcal {A}}} outputs a model h {\displaystyle h} such that e r r ( h ) < ε {\displaystyle err(h)<\varepsilon } , in a number of calls to the oracle bounded by p ( 1 ε , n , s i z e ( f ) ) {\displaystyle p\left({\frac {1}{\varepsilon }},n,size(f)\right)} . Note that the confidence parameter δ {\displaystyle \delta } does not appear in the definition of learning. This is because the main purpose of δ {\displaystyle \delta } is to allow the learning algorithm a small probability of failure due to an unrepresentative sample. Since now Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} always guarantees to meet the approximation criterion Q f ( x ) − α ≤ P f ( x ) ≤ Q f ( x ) + α {\displaystyle Q_{f(x)}-\alpha \leq P_{f(x)}\leq Q_{f(x)}+\alpha } , the failure probability is no longer needed. The statistical query model is strictly weaker than the PAC model: any efficiently SQ-learnable class is efficiently PAC learnable in the presence of classification noise, but there exist efficient PAC-learnable problems such as parity that are not efficiently SQ-learnable. == Malicious classification == In the malicious classification model an adversary generates errors to foil the learning algorithm. This setting describes situations of error burst, which may occur when for a limited time transmission equipment malfunctions repeatedly. Formally, algorithm A {\displaystyle {\mathcal {A}}} calls an oracle Oracle ( x , β ) {\displaystyle {\text{Oracle}}(x,\beta )} that returns a correctly labeled example x {\displaystyle x} drawn, as usual, from distribution D {\displaystyle {\mathcal {D}}} over the input space with probability 1 − β {\displaystyle 1-\beta } , but it returns with probability β {\displaystyle \beta } an example drawn from a distribution that is not related to D {\displaystyle {\mathcal {D}}} . Moreover, this maliciously chosen example may strategically selected by an adversary who has knowledge of f {\displaystyle f} , β {\displaystyle \beta } , D {\displaystyle {\mathcal {D}}} , or the current progress of the learning algorithm. Definition: Given a bound β B < 1 2 {\displaystyle \beta _{B}<{\frac {1}{2}}} for 0 ≤ β < 1 2 {\displaystyle 0\leq \beta <{\frac {1}{2}}} , we say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the malicious classification model, if there exist a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , β ) {\displaystyle {\text{Oracle}}(x,\beta )}
Collabora Online
Collabora Online (often abbreviated as COOL) is an open-source online office suite developed by Collabora, based on LibreOffice Online, the web-based edition of the LibreOffice office suite. It enables real-time collaborative editing of documents, spreadsheets, presentations, and vector graphics in a web browser. Optional applications are available for offline use on Android, ChromeOS, iOS, iPadOS, Linux distributions, macOS, and Windows. It supports the OpenDocument format and is compatible with other major formats, including those used by Microsoft Office. The Document Foundation (TDF), the nonprofit organization behind LibreOffice, states that a majority of the LibreOffice software development is done by its partners like Collabora. Collabora Online is an open-source alternative to proprietary cloud office platforms such as Google Workspace and Microsoft 365. Unlike these services, it can be self-hosted or hosted by third-party providers. The platform is marketed particularly toward enterprises and public institutions seeking greater digital sovereignty and independence from U.S.-based "big tech" companies. Collabora also develops Collabora Office, a standalone desktop and mobile app suite based on LibreOffice. Although Collabora Online has increasingly taken on a central role, both products may be used in parallel, similar to Microsoft Office and Microsoft 365. In November 2025, Collabora released Collabora Office Desktop and renamed the previous product Collabora Office Classic. The new product shares code with Collabora Online and brings the same user interface to the desktop on Linux, Windows and MacOS. A separate version, the Collabora Online Development Edition (CODE), is offered free of charge and is recommended for individuals, small teams, and developers. CODE provides early access to new features and serves as a testing and development platform for open-source community contributors. As TDF does not offer a free version of LibreOffice Online, CODE represents the primary freely available option for organizations and individuals interested in deploying LibreOffice in a web-based, collaborative setting. == Applications == Collabora Online includes several applications for document editing, available through the web-based interface and optional desktop and mobile apps: Collabora Writer – A word processor based on LibreOffice Writer, comparable to Microsoft Word and Google Docs. It supports WYSIWYG editing, styles, formatting tools, comment threads, and change tracking. Collabora Calc – A spreadsheet editor based on LibreOffice Calc, similar to Microsoft Excel and Google Sheets. Features include pivot tables, formulas, data validation, conditional formatting, advanced sorting and filtering, charts, and support for up to 16,000 columns. Compatible with some macros written in VBA. Collabora Impress – A presentation program based on LibreOffice Impress, comparable to Microsoft PowerPoint and Google Slides. It supports master slides, transitions, speaker notes, and multimedia elements. Collabora Draw is not a separate application, most of the functionality of the Draw application is now integrated in Writer and Impress – vector graphics editor based on LibreOffice Draw, comparable to Microsoft Visio and Google Drawings. == Features == Collabora Online can be accessed from modern web browsers without the need for plug-ins or add-ons. It supports real-time collaborative editing of word processing documents, spreadsheets, presentations, and vector graphics. Collaboration features include commenting, version tracking with document comparison and restoration, and integration with communication tools such as chat or video calls. These functions are often enabled through integration with enterprise open-source cloud platforms like Nextcloud, ownCloud, Seafile, EGroupware, GroupOffice and others. Collabora Online can also be embedded or integrated into a variety of third-party applications. Although client apps are not required to use the web-based suite, optional applications are available for offline use on Android, ChromeOS, iOS, iPadOS, Linux distributions, macOS, and Windows. These apps share the same LibreOffice-based core as the server version, ensuring document compatibility across platforms. Development of the LibreOffice core benefits both the online server and the client applications simultaneously. The mobile apps offer touch-optimized interfaces that adapt to different screen sizes and can be used offline, with optional integration into cloud storage services. Collabora Online supports OpenDocument formats (ODF; .odt, .odp, .ods, .odg) in accordance with ISO/IEC 26300. It is also compatible with Microsoft Office formats, including Office Open XML (.docx, .pptx, .xlsx) and legacy binary formats (.doc, .ppt, .xls). Additional supported formats include PDF, PNG, CSV, TSV, RTF, EPUB, and others. The suite can import a range of formats supported by LibreOffice, including Microsoft Visio and Publisher files, Apple Keynote, Numbers, and Pages files, as well as legacy formats used by Lotus 1-2-3, Microsoft Works, and Quattro Pro. The core of Collabora Online is written in C++ and utilizes LibreOfficeKit, a programming interface that enables reuse of much of LibreOffice's existing code for document saving, loading, and rendering. Collabora Online operates on the principle that documents remain on the server, with users viewing tile-rendered images of the document and sending their edits back to the server. The user interface is implemented in JavaScript. For file access and authentication with file hosting services, Collabora Online uses Microsoft's WOPI protocol, allowing compatibility with any service supporting Microsoft 365 integration. == Server == The server component can be self-hosted or deployed through third-party enterprise open-source cloud platforms, allowing organizations to maintain control over data and infrastructure. It is available for various Linux distributions and as a Docker image. The server enables features such as in-browser document editing, file synchronization, and real-time communication. These third-party cloud platforms typically offer additional functionality comparable to services such as Dropbox, Google Workspace, Microsoft 365, or Zoom, including file sharing, calendars, email, contacts, chat, and video conferencing. Collabora Online can be integrated into these applications, as well as with other services such as learning management systems and enterprise content platforms, through open APIs and an SDK. == Reception == Various online and print publications have discussed Collabora Online. In December 2016 the technology website Softpedia mentioned the availability of collaborative editing in version 2.0 and the integration with ownCloud, Nextcloud, and other file synchronization and sharing solutions. In June 2020, ZDNET reported that Collabora Online would be included as the standard office suite in Nextcloud version 19, noting that direct document editing was added to the native video conferencing software Talk. The technology blog OMG! Ubuntu! covered the release of Collabora's Android and iOS apps, emphasizing their offline functionality. In September 2020, Linux Magazine compared Collabora Online with OnlyOffice, noting the flexibility and platform independence of both tools and highlighting Collabora's extensive feature set derived from LibreOffice. === Digital sovereignty === Collabora Online's open-source design and support for self-hosting have made it notable in discussions about digital sovereignty—the ability of users and organizations to control their own data. This is particularly relevant in Europe, where concerns about dependence on U.S.-based "big tech" companies and data privacy have grown in recent years. On 10th June 2025, Microsoft executives under oath in the French Senate admitted that they cannot guarantee data sovereignty and would be compelled to pass French (and by implication the wider European Union) information to the US administration if requested via a warrant or subpoena. The Cloud Act is a law that gives the US government authority to obtain digital data held by US-based tech corporations, irrespective of whether that data is stored on servers at home or on foreign soil. A 2020 briefing by the European Parliament highlighted risks associated with reliance on major technology companies that collect and exploit user data. Legal decisions such as the Schrems II ruling have further underscored these concerns. Several European government agencies have adopted private cloud solutions using Collabora Online and related platforms to enhance data security and maintain control over sensitive information. == History == The former LibreOffice development team from SUSE joined Collabora in September 2013, forming the subsidiary Collabora Productivity. In 2015 Collabora and IceWarp announced the development of an enterprise-ready version of LibreOffice Online to compete wi
Dendrogram
A dendrogram is a diagram representing a tree graph. This diagrammatic representation is frequently used in different contexts: in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses. in computational biology, it shows the clustering of genes or samples, sometimes in the margins of heatmaps. in phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree. The name dendrogram derives from the two ancient greek words δένδρον (déndron), meaning "tree", and γράμμα (grámma), meaning "drawing, mathematical figure". == Clustering example == For a clustering example, suppose that five taxa ( a {\displaystyle a} to e {\displaystyle e} ) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity). The distance between merged clusters is monotone, increasing with the level of the merger: the height of each node in the plot is proportional to the value of the intergroup dissimilarity between its two daughters (the nodes on the right representing individual observations all plotted at zero height).