Instant messaging (IM) technology is a type of synchronous computer-mediated communication involving the immediate (real-time) transmission of messages between two or more parties over the Internet or another computer network. Originally involving simple text message exchanges, modern instant messaging applications and services (also variously known as instant messenger, messaging app, chat app, chat client, or simply a messenger) tend to also feature the exchange of multimedia, emojis, file transfer, VoIP (voice calling), and video chat capabilities. Instant messaging systems facilitate connections between specified known users (often using a contact list also known as a "buddy list" or "friend list") or in chat rooms, and can be standalone apps or integrated into a wider social media platform, or in a website where it can, for instance, be used for conversational commerce. Originally the term "instant messaging" was distinguished from "text messaging" by being run on a computer network instead of a cellular/mobile network, being able to write longer messages, real-time communication, presence ("status"), and being free (only cost of access instead of per SMS message sent). Instant messaging was pioneered in the early Internet era; the IRC protocol was the earliest to achieve wide adoption. Later in the 1990s, ICQ was among the first closed and commercialized instant messengers, and several rival services appeared afterwards as it became a popular use of the Internet. Beginning with its first introduction in 2005, BlackBerry Messenger became the first popular example of mobile-based IM, combining features of traditional IM and mobile SMS. Instant messaging remains very popular today; IM apps are the most widely used smartphone apps: in 2018 for instance there were 980 million monthly active users of WeChat and 1.3 billion monthly users of WhatsApp, the largest IM network. == Overview == Instant messaging (IM), sometimes also called "messaging" or "texting", consists of computer-based human communication between two users (private messaging) or more (chat room or "group") in real-time, allowing immediate receipt of acknowledgment or reply. This is in direct contrast to email, where conversations are not in real-time, and the perceived quasi-synchrony of the communications by the users (although many systems allow users to send offline messages that the other user receives when logging in). Earlier IM networks were limited to text-based communication, not dissimilar to mobile text messaging. As technology has moved forward, IM has expanded to include voice calling using a microphone, videotelephony using webcams, file transfer, location sharing, image and video transfer, voice notes, and other features. IM is conducted over the Internet or other types of networks (see also LAN messenger). Depending on the IM protocol, the technical architecture can be peer-to-peer (direct point-to-point transmission) or client–server (when all clients have to first connect to the central server). Primary IM services are controlled by their corresponding companies and usually follow the client-server model. At one point, the term "Instant Messenger" was a service mark of AOL Time Warner and could not be used in software not affiliated with AOL in the United States. For this reason, in April 2007, the instant messaging client formerly named Gaim (or gaim) announced that they would be renamed "Pidgin". === Clients === Modern IM services generally provide their own client, either a separately installed application or a browser-based client. They are normally centralised networks run by the servers of the platform's operators, unlike peer-to-peer protocols like XMPP. These usually only work within the same IM network, although some allow limited function with other services (see #Interoperability). Third-party client software applications exist that will connect with most of the major IM services. There is the class of instant messengers that uses the serverless model, which doesn't require servers, and the IM network consists only of clients. There are several serverless messengers: RetroShare, Tox, Bitmessage, Ricochet. See also: LAN messenger. Some examples of popular IM services today include Signal, Telegram, WhatsApp Messenger, WeChat, QQ Messenger, Viber, Line, and Snapchat. The popularity of certain apps greatly differ between different countries. Certain apps have an emphasis on certain uses - for example, Skype focuses on video calling, Slack focuses on messaging and file sharing for work teams, and Snapchat focuses on image messages. Some social networking services offer messaging services as a component of their overall platform, such as Facebook's Facebook Messenger, who also own WhatsApp. Others have a direct IM function as an additional adjunct component of their social networking platforms, like Instagram, Reddit, Tumblr, TikTok, Clubhouse and Twitter; this also includes for example dating websites, such as OkCupid or Plenty of Fish, and online gaming chat platforms. === Features === ==== Private and group messaging ==== Private chat allows users to converse privately with another person or a group. Privacy can also be enhanced in several ways, such as end-to-end encryption by default. Public and group chat features allow users to communicate with multiple people simultaneously. ==== Calling ==== Many major IM services and applications offer a call feature for user-to-user voice calls, conference calls, and voice messages. The call functionality is useful for professionals who utilize the application for work purposes and as a hands-free method. Videotelephony using a webcam is also possible by some. ==== Games and entertainment ==== Some IM applications include in-app games for entertainment. Yahoo! Messenger, for example, introduced these where users could play a game and viewed by friends in real-time. MSN Messenger featured a number of playable games within the interface. Facebook's Messenger has had a built-in option to play games with people in a chat, including games like Tetris and Blackjack. Discord features multiple games built inside the "activities" tab in voice channels. ==== Payments ==== A relatively new feature to instant messaging, peer-to-peer payments are available for financial tasks on top of communication. The lack of a service fee also makes these advantageous to financial applications. IM services such as Facebook Messenger and the WeChat 'super-app' for example offer a payment feature. == History == === Early systems === Though the term dates from the 1990s, instant messaging predates the Internet, first appearing on multi-user operating systems like Compatible Time-Sharing System (CTSS) and Multiplexed Information and Computing Service (Multics) in the mid-1960s. Initially, some of these systems were used as notification systems for services like printing, but quickly were used to facilitate communication with other users logged into the same machine. CTSS facilitated communication via text message for up to 30 people. Parallel to instant messaging were early online chat facilities, the earliest of which was Talkomatic (1973) on the PLATO system, which allowed 5 people to chat simultaneously on a 512 x 512 plasma display (5 lines of text + 1 status line per person). During the bulletin board system (BBS) phenomenon that peaked during the 1980s, some systems incorporated chat features which were similar to instant messaging; Freelancin' Roundtable was one prime example. The first such general-availability commercial online chat service (as opposed to PLATO, which was educational) was the CompuServe CB Simulator in 1980, created by CompuServe executive Alexander "Sandy" Trevor in Columbus, Ohio. As networks developed, the protocols spread with the networks. Some of these used a peer-to-peer protocol (e.g. talk, ntalk and ytalk), while others required peers to connect to a server (see talker and IRC). The Zephyr Notification Service (still in use at some institutions) was invented at MIT's Project Athena in the 1980s to allow service providers to locate and send messages to users. Early instant messaging programs were primarily real-time text, where characters appeared as they were typed. This includes the Unix "talk" command line program, which was popular in the 1980s and early 1990s. Some BBS chat programs (i.e. Celerity BBS) also used a similar interface. Modern implementations of real-time text also exist in instant messengers, such as AOL's Real-Time IM as an optional feature. In the latter half of the 1980s and into the early 1990s, the Quantum Link online service for Commodore 64 computers offered user-to-user messages between concurrently connected customers, which they called "On-Line Messages" (or OLM for short), and later "FlashMail." Quantum Link later became America Online and made AOL Instant Messenger (AIM, discussed later). While the Quantum Link client software ran on a Commodore 64, using only
Sample complexity
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g., only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. == Definition == Let X {\displaystyle X} be a space which we call the input space, and Y {\displaystyle Y} be a space which we call the output space, and let Z {\displaystyle Z} denote the product X × Y {\displaystyle X\times Y} . For example, in the setting of binary classification, X {\displaystyle X} is typically a finite-dimensional vector space and Y {\displaystyle Y} is the set { − 1 , 1 } {\displaystyle \{-1,1\}} . Fix a hypothesis space H {\displaystyle {\mathcal {H}}} of functions h : X → Y {\displaystyle h\colon X\to Y} . A learning algorithm over H {\displaystyle {\mathcal {H}}} is a computable map from Z {\displaystyle Z} to H {\displaystyle {\mathcal {H}}} . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} . Typical learning algorithms include empirical risk minimization, without or with Tikhonov regularization. Fix a loss function L : Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X × Y {\displaystyle X\times Y} , the expected risk of a hypothesis (a function) h ∈ H {\displaystyle h\in {\mathcal {H}}} is E ( h ) := E ρ [ L ( h ( x ) , y ) ] = ∫ X × Y L ( h ( x ) , y ) d ρ ( x , y ) {\displaystyle {\mathcal {E}}(h):=\mathbb {E} _{\rho }[{\mathcal {L}}(h(x),y)]=\int _{X\times Y}{\mathcal {L}}(h(x),y)\,d\rho (x,y)} In our setting, we have h = A ( S n ) {\displaystyle h={\mathcal {A}}(S_{n})} , where A {\displaystyle {\mathcal {A}}} is a learning algorithm and S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} is a sequence of vectors which are all drawn independently from ρ {\displaystyle \rho } . Define the optimal risk E H ∗ = inf h ∈ H E ( h ) . {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}={\underset {h\in {\mathcal {H}}}{\inf }}{\mathcal {E}}(h).} Set h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , for each sample size n {\displaystyle n} . h n {\displaystyle h_{n}} is a random variable and depends on the random variable S n {\displaystyle S_{n}} , which is drawn from the distribution ρ n {\displaystyle \rho ^{n}} . The algorithm A {\displaystyle {\mathcal {A}}} is called consistent if E ( h n ) {\displaystyle {\mathcal {E}}(h_{n})} probabilistically converges to E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} . In other words, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} , such that, for all sample sizes n ≥ N {\displaystyle n\geq N} , we have Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] < δ . {\displaystyle \Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]<\delta .} The sample complexity of A {\displaystyle {\mathcal {A}}} is then the minimum N {\displaystyle N} for which this holds, as a function of ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . We write the sample complexity as N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} to emphasize that this value of N {\displaystyle N} depends on ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . If A {\displaystyle {\mathcal {A}}} is not consistent, then we set N ( ρ , ϵ , δ ) = ∞ {\displaystyle N(\rho ,\epsilon ,\delta )=\infty } . If there exists an algorithm for which N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is finite, then we say that the hypothesis space H {\displaystyle {\mathcal {H}}} is learnable. In others words, the sample complexity N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} defines the rate of consistency of the algorithm: given a desired accuracy ϵ {\displaystyle \epsilon } and confidence δ {\displaystyle \delta } , one needs to sample N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} data points to guarantee that the risk of the output function is within ϵ {\displaystyle \epsilon } of the best possible, with probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity is polynomial, that is, whether N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is bounded by a polynomial in 1 / ϵ {\displaystyle 1/\epsilon } and 1 / δ {\displaystyle 1/\delta } . If N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is polynomial for some learning algorithm, then one says that the hypothesis space H {\displaystyle {\mathcal {H}}} is PAC-learnable. This is a stronger notion than being learnable. == Unrestricted hypothesis space: infinite sample complexity == One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) < δ , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right)<\delta ,} where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large. Thus, in order to make statements about the rate of convergence of the quantity sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right),} one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. == Restricted hypothesis space: finite sample-complexity == The latter approach leads to concepts such as VC dimension and Rademacher complexity which control the complexity of the space H {\displaystyle {\mathcal {H}}} . A smaller hypothesis space introduces more bias into the inference process, meaning that E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} may be greater than the best possible risk in a larger space. However, by restricting the complexity of the hypothesis space it becomes possible for an algorithm to produce more uniformly consistent functions. This trade-off leads to the concept of regularization. It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}} : H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class. This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. === An example of a PAC-learnable hypothesis space === X = R d , Y = { − 1 , 1 } {\displaystyle X=\mathbb {R} ^{d},Y=\{-1,1\}} , and let H {\displaystyle {\mathcal {H}}} be the space of affine functions on X {\displaystyle X} , that is, functions of the form x ↦ ⟨ w , x ⟩ + b {\displaystyle x\mapsto \langl
PhyCV
PhyCV is the first computer vision library which utilizes algorithms directly derived from the equations of physics governing physical phenomena. The algorithms appearing in the first release emulate the propagation of light through a physical medium with natural and engineered diffractive properties followed by coherent detection. Unlike traditional algorithms that are a sequence of hand-crafted empirical rules, physics-inspired algorithms leverage physical laws of nature as blueprints. In addition, these algorithms can, in principle, be implemented in real physical devices for fast and efficient computation in the form of analog computing. Currently PhyCV has three algorithms, Phase-Stretch Transform (PST) and Phase-Stretch Adaptive Gradient-Field Extractor (PAGE), and Vision Enhancement via Virtual diffraction and coherent Detection (VEViD). All algorithms have CPU and GPU versions. PhyCV is now available on GitHub and can be installed from pip. == History == Algorithms in PhyCV are inspired by the physics of the photonic time stretch (a hardware technique for ultrafast and single-shot data acquisition). PST is an edge detection algorithm that was open-sourced in 2016 and has 800+ stars and 200+ forks on GitHub. PAGE is a directional edge detection algorithm that was open-sourced in February, 2022. PhyCV was originally developed and open-sourced by Jalali-Lab @ UCLA in May 2022. In the initial release of PhyCV, the original open-sourced code of PST and PAGE is significantly refactored and improved to be modular, more efficient, GPU-accelerated and object-oriented. VEViD is a low-light and color enhancement algorithm that was added to PhyCV in November 2022. == Background == === Phase-Stretch Transform (PST) === Phase-Stretch Transform (PST) is a computationally efficient edge and texture detection algorithm with exceptional performance in visually impaired images. The algorithm transforms the image by emulating propagation of light through a device with engineered diffractive property followed by coherent detection. It has been applied in improving the resolution of MRI image, extracting blood vessels in retina images, dolphin identification, and waste water treatment, single molecule biological imaging, and classification of UAV using micro Doppler imaging. === Phase-Stretch Adaptive Gradient-Field Extractor (PAGE) === Phase-Stretch Adaptive Gradient-Field Extractor (PAGE) is a physics-inspired algorithm for detecting edges and their orientations in digital images at various scales. The algorithm is based on the diffraction equations of optics. Metaphorically speaking, PAGE emulates the physics of birefringent (orientation-dependent) diffractive propagation through a physical device with a specific diffractive structure. The propagation converts a real-valued image into a complex function. Related information is contained in the real and imaginary components of the output. The output represents the phase of the complex function. === Vision Enhancement via Virtual diffraction and coherent Detection (VEViD) === Vision Enhancement via Virtual diffraction and coherent Detection (VEViD) an efficient and interpretable low-light and color enhancement algorithm that reimagines a digital image as a spatially varying metaphoric light field and then subjects the field to the physical processes akin to diffraction and coherent detection. The term “Virtual” captures the deviation from the physical world. The light field is pixelated and the propagation imparts a phase with an arbitrary dependence on frequency which can be different from the quadratic behavior of physical diffraction. VEViD can be further accelerated through mathematical approximations that reduce the computation time without appreciable sacrifice in image quality. A closed-form approximation for VEViD which we call VEViD-lite can achieve up to 200 FPS for 4K video enhancement. == PhyCV on the Edge == Featuring low-dimensionality and high-efficiency, PhyCV is ideal for edge computing applications. In this section, we demonstrate running PhyCV on NVIDIA Jetson Nano in real-time. === NVIDIA Jetson Nano Developer Kit === NVIDIA Jetson Nano Developer Kit is a small- sized and power-efficient platform for edge computing applications. It is equipped with an NVIDIA Maxwell architecture GPU with 128 CUDA cores, a quad-core ARM Cortex-A57 CPU, 4GB 64-bit LPDDR4 RAM, and supports video encoding and decoding up to 4K resolution. Jetson Nano also offers a variety of interfaces for connectivity and expansion, making it ideal for a wide range of AI and IoT applications. In our setup, we connect a USB camera to the Jetson Nano to acquire videos and demonstrate using PhyCV to process the videos in real-time. === Real-time PhyCV on Jetson Nano === We use the Jetson Nano (4GB) with NVIDIA JetPack SDK version 4.6.1, which comes with pre- installed Python 3.6, CUDA 10.2, and OpenCV 4.1.1. We further install PyTorch 1.10 to enable the GPU accelerated PhyCV. We demonstrate the results and metrics of running PhyCV on Jetson Nano in real-time for edge detection and low-light enhancement tasks. For 480p videos, both operations achieve beyond 38 FPS, which is sufficient for most cameras that capture videos at 30 FPS. For 720p videos, PhyCV low-light enhancement can operate at 24 FPS and PhyCV edge detection can operate at 17 FPS. == Highlights == === Modular Code Architecture === The code in PhyCV has a modular design which faithfully follows the physical process from which the algorithm was originated. Both PST and PAGE modules in the PhyCV library emulate the propagation of the input signal (original digital image) through a device with engineered diffractive property followed by coherent (phase) detection. The dispersive propagation applies a phase kernel to the frequency domain of the original image. This process has three steps in general, loading the image, initializing the kernel and applying the kernel. In the implementation of PhyCV, each algorithm is represented as a class in Python and each class has methods that simulate the steps described above. The modular code architecture follows the physics behind the algorithm. Please refer to the source code on GitHub for more details. === GPU Acceleration === PhyCV supports GPU acceleration. The GPU versions of PST and PAGE are built on PyTorch accelerated by the CUDA toolkit. The acceleration is beneficial for applying the algorithms in real-time image video processing and other deep learning tasks. The running time per frame of PhyCV algorithms on CPU (Intel i9-9900K) and GPU (NVIDIA TITAN RTX) for videos at different resolutions are shown below. Note that the PhyCV low-light enhancement operates in the HSV color space, so the running time also includes RGB to HSV conversion. However, for all running times using GPUs, we ignore the time of moving data from CPUs to GPUs and count the algorithm operation time only. == Installation and Examples == Please refer to the GitHub README file for a detailed technical documentation. == Current Limitations == === I/O (Input/Output) Bottleneck for Real-time Video Processing === When dealing with real-time video streams from cameras, the frames are captured and buffered in CPU and have to be moved to GPU to run the GPU-accelerated PhyCV algorithms. This process is time-consuming and it is a common bottleneck for real-time video-processing algorithms. === Lack of Parameter Adaptivity for Different Images === Currently, the parameters of PhyCV algorithms have to be manually tuned for different images. Although a set of pre-selected parameters work relatively well for a wide range of images, the lack of parameter adaptivity for different images remains a limitation for now.
Quantexa
Quantexa is a UK-based software company that develops artificial intelligence-based applications for data analytics and decision-making. The company was founded in 2016 and is headquartered in London, with operations in North America, Europe, and the Asia-Pacific region. As of 2025, Quantexa reported a valuation of $2.6 billion and provides services to organizations in over 70 countries. Investors include Warburg Pincus, HSBC, and the Ontario Teachers’ Pension Plan. == History == Quantexa was founded in London in 2016 by several co-founders, including Jamie Hutton, Richard Seewald, Imam Hoque, Felix Hoddinott, and Vishal Marria, who also serves as the company's chief executive officer. The company was established to develop tools intended to address limitations in traditional data analysis methods, particularly those related to identifying hidden connections across large datasets. The name "Quantexa" is derived from the company's focus on quantitative methods and data analysis. In 2023, Quantexa acquired Dublin-based AI firm Aylien. In April 2023, the company completed a Series E funding round, raising $129 million at a valuation of approximately $1.8 billion, marking its entry into "unicorn" status. In October 2024, the company reported annual recurring revenue (ARR) exceeding $100 million. In early 2025, Quantexa participated in the World Economic Forum's Unicorn Program, which supports high-growth technology companies. In March 2025, Quantexa completed a Series F funding round of $175 million, led by Teachers' Venture Growth, the venture arm of the Ontario Teachers' Pension Plan. That August, the company was reported to be considering a 2026 IPO. The company formed a partnership with Zurich in October 2025, the first insurer to add its AI-based Decision Intelligence platform to enhance fraud detection.
Semantic compression
In natural language processing, semantic compression is a process of compacting a lexicon used to build a textual document (or a set of documents) by reducing language heterogeneity, while maintaining text semantics. As a result, the same ideas can be represented using a smaller set of words. In most applications, semantic compression is a lossy compression. Increased prolixity does not compensate for the lexical compression and an original document cannot be reconstructed in a reverse process. == By generalization == Semantic compression is basically achieved in two steps, using frequency dictionaries and semantic network: determining cumulated term frequencies to identify target lexicon, replacing less frequent terms with their hypernyms (generalization) from target lexicon. Step 1 requires assembling word frequencies and information on semantic relationships, specifically hyponymy. Moving upwards in word hierarchy, a cumulative concept frequency is calculating by adding a sum of hyponyms' frequencies to frequency of their hypernym: c u m f ( k i ) = f ( k i ) + ∑ j c u m f ( k j ) {\displaystyle cumf(k_{i})=f(k_{i})+\sum _{j}cumf(k_{j})} where k i {\displaystyle k_{i}} is a hypernym of k j {\displaystyle k_{j}} . Then a desired number of words with top cumulated frequencies are chosen to build a target lexicon. In the second step, compression mapping rules are defined for the remaining words in order to handle every occurrence of a less frequent hyponym as its hypernym in output text. Example The below fragment of text has been processed by the semantic compression. Words in bold have been replaced by their hypernyms. They are both nest building social insects, but paper wasps and honey bees organize their colonies in very different ways. In a new study, researchers report that despite their differences, these insects rely on the same network of genes to guide their social behavior.The study appears in the Proceedings of the Royal Society B: Biological Sciences. Honey bees and paper wasps are separated by more than 100 million years of evolution, and there are striking differences in how they divvy up the work of maintaining a colony. The procedure outputs the following text: They are both facility building insect, but insects and honey insects arrange their biological groups in very different structure. In a new study, researchers report that despite their difference of opinions, these insects act the same network of genes to steer their party demeanor. The study appears in the proceeding of the institution bacteria Biological Sciences. Honey insects and insect are separated by more than hundred million years of organic processes, and there are impinging differences of opinions in how they divvy up the work of affirming a biological group. == Implicit semantic compression == A natural tendency to keep natural language expressions concise can be perceived as a form of implicit semantic compression, by omitting unmeaningful words or redundant meaningful words (especially to avoid pleonasms). == Applications and advantages == In the vector space model, compacting a lexicon leads to a reduction of dimensionality, which results in less computational complexity and a positive influence on efficiency. Semantic compression is advantageous in information retrieval tasks, improving their effectiveness (in terms of both precision and recall). This is due to more precise descriptors (reduced effect of language diversity – limited language redundancy, a step towards a controlled dictionary). As in the example above, it is possible to display the output as natural text (re-applying inflexion, adding stop words).
Himmat (app)
Himmat is a women's safety mobile application of Delhi Police. It was launched by Home Minister Rajnath Singh on 1 January 2015. The app is freely available for Android mobile phones and can be downloaded from Delhi Police website. Delhi Police plans to launch app for other platforms in future. Low registrations and other problems resulted in a parliamentary panel calling the app a failure in 2018. Himmat has gone on to be called as one of India's best safety apps for women.
Eigenmoments
EigenMoments is a set of orthogonal, noise robust, invariant to rotation, scaling and translation and distribution sensitive moments. Their application can be found in signal processing and computer vision as descriptors of the signal or image. The descriptors can later be used for classification purposes. It is obtained by performing orthogonalization, via eigen analysis on geometric moments. == Framework summary == EigenMoments are computed by performing eigen analysis on the moment space of an image by maximizing signal-to-noise ratio in the feature space in form of Rayleigh quotient. This approach has several benefits in Image processing applications: Dependency of moments in the moment space on the distribution of the images being transformed, ensures decorrelation of the final feature space after eigen analysis on the moment space. The ability of EigenMoments to take into account distribution of the image makes it more versatile and adaptable for different genres. Generated moment kernels are orthogonal and therefore analysis on the moment space becomes easier. Transformation with orthogonal moment kernels into moment space is analogous to projection of the image onto a number of orthogonal axes. Nosiy components can be removed. This makes EigenMoments robust for classification applications. Optimal information compaction can be obtained and therefore a few number of moments are needed to characterize the images. == Problem formulation == Assume that a signal vector s ∈ R n {\displaystyle s\in {\mathcal {R}}^{n}} is taken from a certain distribution having correlation C ∈ R n × n {\displaystyle C\in {\mathcal {R}}^{n\times n}} , i.e. C = E [ s s T ] {\displaystyle C=E[ss^{T}]} where E[.] denotes expected value. Dimension of signal space, n, is often too large to be useful for practical application such as pattern classification, we need to transform the signal space into a space with lower dimensionality. This is performed by a two-step linear transformation: q = W T X T s , {\displaystyle q=W^{T}X^{T}s,} where q = [ q 1 , . . . , q n ] T ∈ R k {\displaystyle q=[q_{1},...,q_{n}]^{T}\in {\mathcal {R}}^{k}} is the transformed signal, X = [ x 1 , . . . , x n ] T ∈ R n × m {\displaystyle X=[x_{1},...,x_{n}]^{T}\in {\mathcal {R}}^{n\times m}} a fixed transformation matrix which transforms the signal into the moment space, and W = [ w 1 , . . . , w n ] T ∈ R m × k {\displaystyle W=[w_{1},...,w_{n}]^{T}\in {\mathcal {R}}^{m\times k}} the transformation matrix which we are going to determine by maximizing the SNR of the feature space resided by q {\displaystyle q} . For the case of Geometric Moments, X would be the monomials. If m = k = n {\displaystyle m=k=n} , a full rank transformation would result, however usually we have m ≤ n {\displaystyle m\leq n} and k ≤ m {\displaystyle k\leq m} . This is specially the case when n {\displaystyle n} is of high dimensions. Finding W {\displaystyle W} that maximizes the SNR of the feature space: S N R t r a n s f o r m = w T X T C X w w T X T N X w , {\displaystyle SNR_{transform}={\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}},} where N is the correlation matrix of the noise signal. The problem can thus be formulated as w 1 , . . . , w k = a r g m a x w w T X T C X w w T X T N X w {\displaystyle {w_{1},...,w_{k}}=argmax_{w}{\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}}} subject to constraints: w i T X T N X w j = δ i j , {\displaystyle w_{i}^{T}X^{T}NXw_{j}=\delta _{ij},} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. It can be observed that this maximization is Rayleigh quotient by letting A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} and therefore can be written as: w 1 , . . . , w k = a r g m a x x w T A w w T B w {\displaystyle {w_{1},...,w_{k}}={\underset {x}{\operatorname {arg\,max} }}{\frac {w^{T}Aw}{w^{T}Bw}}} , w i T B w j = δ i j {\displaystyle w_{i}^{T}Bw_{j}=\delta _{ij}} === Rayleigh quotient === Optimization of Rayleigh quotient has the form: max w R ( w ) = max w w T A w w T B w {\displaystyle \max _{w}R(w)=\max _{w}{\frac {w^{T}Aw}{w^{T}Bw}}} and A {\displaystyle A} and B {\displaystyle B} , both are symmetric and B {\displaystyle B} is positive definite and therefore invertible. Scaling w {\displaystyle w} does not change the value of the object function and hence and additional scalar constraint w T B w = 1 {\displaystyle w^{T}Bw=1} can be imposed on w {\displaystyle w} and no solution would be lost when the objective function is optimized. This constraint optimization problem can be solved using Lagrangian multiplier: max w w T A w {\displaystyle \max _{w}{w^{T}Aw}} subject to w T B w = 1 {\displaystyle {w^{T}Bw}=1} max w L ( w ) = max w ( w T A w − λ w T B w ) {\displaystyle \max _{w}{\mathcal {L}}(w)=\max _{w}(w{T}Aw-\lambda w^{T}Bw)} equating first derivative to zero and we will have: A w = λ B w {\displaystyle Aw=\lambda Bw} which is an instance of Generalized Eigenvalue Problem (GEP). The GEP has the form: A w = λ B w {\displaystyle Aw=\lambda Bw} for any pair ( w , λ ) {\displaystyle (w,\lambda )} that is a solution to above equation, w {\displaystyle w} is called a generalized eigenvector and λ {\displaystyle \lambda } is called a generalized eigenvalue. Finding w {\displaystyle w} and λ {\displaystyle \lambda } that satisfies this equations would produce the result which optimizes Rayleigh quotient. One way of maximizing Rayleigh quotient is through solving the Generalized Eigen Problem. Dimension reduction can be performed by simply choosing the first components w i {\displaystyle w_{i}} , i = 1 , . . . , k {\displaystyle i=1,...,k} , with the highest values for R ( w ) {\displaystyle R(w)} out of the m {\displaystyle m} components, and discard the rest. Interpretation of this transformation is rotating and scaling the moment space, transforming it into a feature space with maximized SNR and therefore, the first k {\displaystyle k} components are the components with highest k {\displaystyle k} SNR values. The other method to look at this solution is to use the concept of simultaneous diagonalization instead of Generalized Eigen Problem. === Simultaneous diagonalization === Let A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} as mentioned earlier. We can write W {\displaystyle W} as two separate transformation matrices: W = W 1 W 2 . {\displaystyle W=W_{1}W_{2}.} W 1 {\displaystyle W_{1}} can be found by first diagonalize B: P T B P = D B {\displaystyle P^{T}BP=D_{B}} . Where D B {\displaystyle D_{B}} is a diagonal matrix sorted in increasing order. Since B {\displaystyle B} is positive definite, thus D B > 0 {\displaystyle D_{B}>0} . We can discard those eigenvalues that large and retain those close to 0, since this means the energy of the noise is close to 0 in this space, at this stage it is also possible to discard those eigenvectors that have large eigenvalues. Let P ^ {\displaystyle {\hat {P}}} be the first k {\displaystyle k} columns of P {\displaystyle P} , now P T ^ B P ^ = D B ^ {\displaystyle {\hat {P^{T}}}B{\hat {P}}={\hat {D_{B}}}} where D B ^ {\displaystyle {\hat {D_{B}}}} is the k × k {\displaystyle k\times k} principal submatrix of D B {\displaystyle D_{B}} . Let W 1 = P ^ D B ^ − 1 / 2 {\displaystyle W_{1}={\hat {P}}{\hat {D_{B}}}^{-1/2}} and hence: W 1 T B W 1 = ( P ^ D B ^ − 1 / 2 ) T B ( P ^ D B ^ − 1 / 2 ) = I {\displaystyle W_{1}^{T}BW_{1}=({\hat {P}}{\hat {D_{B}}}^{-1/2})^{T}B({\hat {P}}{\hat {D_{B}}}^{-1/2})=I} . W 1 {\displaystyle W_{1}} whiten B {\displaystyle B} and reduces the dimensionality from m {\displaystyle m} to k {\displaystyle k} . The transformed space resided by q ′ = W 1 T X T s {\displaystyle q'=W_{1}^{T}X^{T}s} is called the noise space. Then, we diagonalize W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} : W 2 T W 1 T A W 1 W 2 = D A {\displaystyle W_{2}^{T}W_{1}^{T}AW_{1}W_{2}=D_{A}} , where W 2 T W 2 = I {\displaystyle W_{2}^{T}W_{2}=I} . D A {\displaystyle D_{A}} is the matrix with eigenvalues of W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} on its diagonal. We may retain all the eigenvalues and their corresponding eigenvectors since most of the noise are already discarded in previous step. Finally the transformation is given by: W = W 1 W 2 {\displaystyle W=W_{1}W_{2}} where W {\displaystyle W} diagonalizes both the numerator and denominator of the SNR, W T A W = D A {\displaystyle W^{T}AW=D_{A}} , W T B W = I {\displaystyle W^{T}BW=I} and the transformation of signal s {\displaystyle s} is defined as q = W T X T s = W 2 T W 1 T X T s {\displaystyle q=W^{T}X^{T}s=W_{2}^{T}W_{1}^{T}X^{T}s} . === Information loss === To find the information loss when we discard some of the eigenvalues and eigenvectors we can perform following analysis: η = 1 − t r a c e ( W 1 T A W 1 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) = 1 − t r a c e ( D B ^ − 1 / 2 P ^ T A P ^ D B ^ − 1 / 2 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) {\displaystyle {\begin{array}{lll}\eta &=&