Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically. NMF finds applications in such fields as astronomy, computer vision, document clustering, missing data imputation, chemometrics, audio signal processing, recommender systems, and bioinformatics. == History == In chemometrics non-negative matrix factorization has a long history under the name "self modeling curve resolution". In this framework the vectors in the right matrix are continuous curves rather than discrete vectors. Also early work on non-negative matrix factorizations was performed by a Finnish group of researchers in the 1990s under the name positive matrix factorization. It became more widely known as non-negative matrix factorization after Lee and Seung investigated the properties of the algorithm and published some simple and useful algorithms for two types of factorizations. == Background == Let matrix V be the product of the matrices W and H, V = W H . {\displaystyle \mathbf {V} =\mathbf {W} \mathbf {H} \,.} Matrix multiplication can be implemented as computing the column vectors of V as linear combinations of the column vectors in W using coefficients supplied by columns of H. That is, each column of V can be computed as follows: v i = W h i , {\displaystyle \mathbf {v} _{i}=\mathbf {W} \mathbf {h} _{i}\,,} where vi is the i-th column vector of the product matrix V and hi is the i-th column vector of the matrix H. When multiplying matrices, the dimensions of the factor matrices may be significantly lower than those of the product matrix and it is this property that forms the basis of NMF. NMF generates factors with significantly reduced dimensions compared to the original matrix. For example, if V is an m × n matrix, W is an m × p matrix, and H is a p × n matrix then p can be significantly less than both m and n. Here is an example based on a text-mining application: Let the input matrix (the matrix to be factored) be V with 10000 rows and 500 columns where words are in rows and documents are in columns. That is, we have 500 documents indexed by 10000 words. It follows that a column vector v in V represents a document. Assume we ask the algorithm to find 10 features in order to generate a features matrix W with 10000 rows and 10 columns and a coefficients matrix H with 10 rows and 500 columns. The product of W and H is a matrix with 10000 rows and 500 columns, the same shape as the input matrix V and, if the factorization worked, it is a reasonable approximation to the input matrix V. From the treatment of matrix multiplication above it follows that each column in the product matrix WH is a linear combination of the 10 column vectors in the features matrix W with coefficients supplied by the coefficients matrix H. This last point is the basis of NMF because we can consider each original document in our example as being built from a small set of hidden features. NMF generates these features. It is useful to think of each feature (column vector) in the features matrix W as a document archetype comprising a set of words where each word's cell value defines the word's rank in the feature: The higher a word's cell value the higher the word's rank in the feature. A column in the coefficients matrix H represents an original document with a cell value defining the document's rank for a feature. We can now reconstruct a document (column vector) from our input matrix by a linear combination of our features (column vectors in W) where each feature is weighted by the feature's cell value from the document's column in H. == Clustering property == NMF has an inherent clustering property, i.e., it automatically clusters the columns of input data V = ( v 1 , … , v n ) {\displaystyle \mathbf {V} =(v_{1},\dots ,v_{n})} . More specifically, the approximation of V {\displaystyle \mathbf {V} } by V ≃ W H {\displaystyle \mathbf {V} \simeq \mathbf {W} \mathbf {H} } is achieved by finding W {\displaystyle W} and H {\displaystyle H} that minimize the error function (using the Frobenius norm) ‖ V − W H ‖ F , {\displaystyle \left\|V-WH\right\|_{F},} subject to W ≥ 0 , H ≥ 0. {\displaystyle W\geq 0,H\geq 0.} , If we furthermore impose an orthogonality constraint on H {\displaystyle \mathbf {H} } , i.e. H H T = I {\displaystyle \mathbf {H} \mathbf {H} ^{T}=I} , then the above minimization is mathematically equivalent to the minimization of K-means clustering. Furthermore, the computed H {\displaystyle H} gives the cluster membership, i.e., if H k j > H i j {\displaystyle \mathbf {H} _{kj}>\mathbf {H} _{ij}} for all i ≠ k, this suggests that the input data v j {\displaystyle v_{j}} belongs to k {\displaystyle k} -th cluster. The computed W {\displaystyle W} gives the cluster centroids, i.e., the k {\displaystyle k} -th column gives the cluster centroid of k {\displaystyle k} -th cluster. This centroid's representation can be significantly enhanced by convex NMF. When the orthogonality constraint H H T = I {\displaystyle \mathbf {H} \mathbf {H} ^{T}=I} is not explicitly imposed, the orthogonality holds to a large extent, and the clustering property holds too. When the error function to be used is Kullback–Leibler divergence, NMF is identical to the probabilistic latent semantic analysis (PLSA), a popular document clustering method. == Types == === Approximate non-negative matrix factorization === Usually the number of columns of W and the number of rows of H in NMF are selected so the product WH will become an approximation to V. The full decomposition of V then amounts to the two non-negative matrices W and H as well as a residual U, such that: V = WH + U. The elements of the residual matrix can either be negative or positive. When W and H are smaller than V they become easier to store and manipulate. Another reason for factorizing V into smaller matrices W and H, is that if one's goal is to approximately represent the elements of V by significantly less data, then one has to infer some latent structure in the data. === Convex non-negative matrix factorization === In standard NMF, matrix factor W ∈ R+m × k， i.e., W can be anything in that space. Convex NMF restricts the columns of W to convex combinations of the input data vectors ( v 1 , … , v n ) {\displaystyle (v_{1},\dots ,v_{n})} . This greatly improves the quality of data representation of W. Furthermore, the resulting matrix factor H becomes more sparse and orthogonal. === Nonnegative rank factorization === In case the nonnegative rank of V is equal to its actual rank, V = WH is called a nonnegative rank factorization (NRF). The problem of finding the NRF of V, if it exists, is known to be NP-hard. === Different cost functions and regularizations === There are different types of non-negative matrix factorizations. The different types arise from using different cost functions for measuring the divergence between V and WH and possibly by regularization of the W and/or H matrices. Two simple divergence functions studied by Lee and Seung are the squared error (or Frobenius norm) and an extension of the Kullback–Leibler divergence to positive matrices (the original Kullback–Leibler divergence is defined on probability distributions). Each divergence leads to a different NMF algorithm, usually minimizing the divergence using iterative update rules. The factorization problem in the squared error version of NMF may be stated as: Given a matrix V {\displaystyle \mathbf {V} } find nonnegative matrices W and H that minimize the function F ( W , H ) = ‖ V − W H ‖ F 2 {\displaystyle F(\mathbf {W} ,\mathbf {H} )=\left\|\mathbf {V} -\mathbf {WH} \right\|_{F}^{2}} Another type of NMF for images is based on the total variation norm. When L1 regularization (akin to Lasso) is added to NMF with the mean squared error cost function, the resulting problem may be called non-negative sparse coding due to the similarity to the sparse coding problem, although it may also still be referred to as NMF. === Online NMF === Many standard NMF algorithms analyze all the data together; i.e., the whole matrix is available from the start. This may be unsatisfactory in applications where there are too many data to fit into memory or where the data are provided in streaming fashion. One such use is for collaborative filtering in recommendation systems, where there may be many users and many items to recommend, and it would be inefficient to recalculate everything when one user or one item is added to the system. The cost function for o
Distribution management system
A distribution management system (DMS) is a collection of applications designed to monitor and control the electric power distribution networks efficiently and reliably. It acts as a decision support system to assist the control room and field operating personnel with the monitoring and control of the electric distribution system. Improving the reliability and quality of service in terms of reducing power outages, minimizing outage time, maintaining acceptable frequency and voltage levels are the key deliverables of a DMS. Given the complexity of distribution grids, such systems may involve communication and coordination across multiple components. For example, the control of active loads may require a complex chain of communication through different components as described in US patent 11747849B2 In recent years, utilization of electrical energy increased exponentially and customer requirement and quality definitions of power were changed enormously. As electric energy became an essential part of daily life, its optimal usage and reliability became important. Real-time network view and dynamic decisions have become instrumental for optimizing resources and managing demands, leading to the need for distribution management systems in large-scale electrical networks. == Overview == Most distribution utilities have been comprehensively using IT solutions through their Outage Management System (OMS) that makes use of other systems like Customer Information System (CIS), Geographical Information System (GIS) and Interactive Voice Response System (IVRS). An outage management system has a network component/connectivity model of the distribution system. By combining the locations of outage calls from customers with knowledge of the locations of the protection devices (such as circuit breakers) on the network, a rule engine is used to predict the locations of outages. Based on this, restoration activities are charted out and the crew is dispatched for the same. In parallel with this, distribution utilities began to roll out Supervisory Control and Data Acquisition (SCADA) systems, initially only at their higher voltage substations. Over time, use of SCADA has progressively extended downwards to sites at lower voltage levels. DMSs access real-time data and provide all information on a single console at the control centre in an integrated manner. Their development varied across different geographic territories. In the US, for example, DMSs typically grew by taking Outage Management Systems to the next level, automating the complete sequences and providing an end to end, integrated view of the entire distribution spectrum. In the UK, by contrast, the much denser and more meshed network topologies, combined with stronger Health & Safety regulation, had led to early centralisation of high-voltage switching operations, initially using paper records and schematic diagrams printed onto large wallboards which were 'dressed' with magnetic symbols to show the current running states. There, DMSs grew initially from SCADA systems as these were expanded to allow these centralised control and safety management procedures to be managed electronically. These DMSs required even more detailed component/connectivity models and schematics than those needed by early OMSs as every possible isolation and earthing point on the networks had to be included. In territories such as the UK, therefore, the network component/connectivity models were usually developed in the DMS first, whereas in the USA these were generally built in the GIS. The typical data flow in a DMS has the SCADA system, the Information Storage & Retrieval (ISR) system, Communication (COM) Servers, Front-End Processors (FEPs) & Field Remote Terminal Units (FRTUs). == Why DMS? == Reduce the duration of outages Improve the speed and accuracy of outage predictions. Reduce crew patrol and drive times through improved outage locating. Improve the operational efficiency Determine the crew resources necessary to achieve restoration objectives. Effectively utilize resources between operating regions. Determine when best to schedule mutual aid crews. Increased customer satisfaction A DMS incorporates IVR and other mobile technologies, through which there is an improved outage communications for customer calls. Provide customers with more accurate estimated restoration times. Improve service reliability by tracking all customers affected by an outage, determining electrical configurations of every device on every feeder, and compiling details about each restoration process. == DMS Functions == In order to support proper decision making and O&M activities, DMS solutions should support the following functions: Network visualization & support tools Applications for Analytical & Remedial Action Utility Planning Tools System Protection Schemes The various sub functions of the same, carried out by the DMS are listed below:- === Network Connectivity Analysis (NCA) === Distribution network usually covers over a large area and catering power to different customers at different voltage levels. So locating required sources and loads on a larger GIS/Operator interface is often very difficult. Panning & zooming provided with normal SCADA system GUI does not cover the exact operational requirement. Network connectivity analysis is an operator specific functionality which helps the operator to identify or locate the preferred network or component very easily. NCA does the required analyses and provides display of the feed point of various network loads. Based on the status of all the switching devices such as circuit breaker (CB), Ring Main Unit (RMU) and/or isolators that affect the topology of the network modeled, the prevailing network topology is determined. The NCA further assists the operator to know operating state of the distribution network indicating radial mode, loops and parallels in the network. === Switching Schedule & Safety Management === In territories such as the UK a core function of a DMS has always been to support safe switching and work on the networks. Control engineers prepare switching schedules to isolate and make safe a section of network before work is carried out, and the DMS validates these schedules using its network model. Switching schedules can combine telecontrolled and manual (on-site) switching operations. When the required section has been made safe, the DMS allows a Permit To Work (PTW) document to be issued. After its cancellation when the work has been finished, the switching schedule then facilitates restoration of the normal running arrangements. Switching components can also be tagged to reflect any Operational Restrictions that are in force. The network component/connectivity model, and associated diagrams, must always be kept absolutely up to date. The switching schedule facility therefore also allows 'patches' to the network model to be applied to the live version at the appropriate stage(s) of the jobs. The term 'patch' is derived from the method previously used to maintain the wallboard diagrams. === State Estimation (SE) === The state estimator is an integral part of the overall monitoring and control systems for transmission networks. It is mainly aimed at providing a reliable estimate of the system voltages. This information from the state estimator flows to control centers and database servers across the network. The variables of interest are indicative of parameters like margins to operating limits, health of equipment and required operator action. State estimators allow the calculation of these variables of interest with high confidence despite the facts that the measurements may be corrupted by noise, or could be missing or inaccurate. Even though we may not be able to directly observe the state, it can be inferred from a scan of measurements which are assumed to be synchronized. The algorithms need to allow for the fact that presence of noise might skew the measurements. In a typical power system, the State is quasi-static. The time constants are sufficiently fast so that system dynamics decay away quickly (with respect to measurement frequency). The system appears to be progressing through a sequence of static states that are driven by various parameters like changes in load profile. The inputs of the state estimator can be given to various applications like Load Flow Analysis, Contingency Analysis, and other applications. === Load Flow Applications (LFA) === Load flow study is an important tool involving numerical analysis applied to a power system. The load flow study usually uses simplified notations like a single-line diagram and focuses on various forms of AC power rather than voltage and current. It analyzes the power systems in normal steady-state operation. The goal of a power flow study is to obtain complete voltage angle and magnitude information for each bus in a power system for specified load and generator real power and voltage conditions. Once this
OpenVINO
OpenVINO is an open-source software toolkit developed by Intel for optimizing and deploying deep learning models. It supports several popular model formats and categories, such as large language models, computer vision, and generative AI. OpenVINO is optimized for Intel hardware, but offers support for ARM/ARM64 processors. It sees great use in AI Sound Processing drivers when tied with Intel's Gaussian & Neural Accelerator (GNA). Based in C++, it extends API support for C and Python, as well as Node.js (in early preview). OpenVINO is cross-platform and free for use under Apache License 2.0. == Workflow == The simplest OpenVINO usage involves obtaining a model and running it as is. Yet for the best results, a more complete workflow is suggested: obtain a model in one of supported frameworks, convert the model to OpenVINO IR using the OpenVINO Converter tool, optimize the model, using training-time or post-training options provided by OpenVINO's NNCF. execute inference, using OpenVINO Runtime by specifying one of several inference modes. == OpenVINO model format == OpenVINO IR is the default format used to run inference. It is saved as a set of two files, .bin and .xml, containing weights and topology, respectively. It is obtained by converting a model from one of the supported frameworks, using the application's API or a dedicated converter. Models of the supported formats may also be used for inference directly, without prior conversion to OpenVINO IR. Such an approach is more convenient but offers fewer optimization options and lower performance, since the conversion is performed automatically before inference. Some pre-converted models can be found in the Hugging Face repository. The supported model formats are: PyTorch TensorFlow TensorFlow Lite ONNX (including formats that may be serialized to ONNX) PaddlePaddle JAX/Flax == OS support == OpenVINO runs on Windows, Linux and MacOS.
Brain.js
Brain.js is a JavaScript library used for neural networking, which is released as free and open-source software under the MIT License. It can be used in both the browser and Node.js backends. Brain.js is most commonly used as a simple introduction to neural networking, as it hides complex mathematics and has a familiar modern JavaScript syntax. It is maintained by members of the Brain.js organization and open-source contributors. == Examples == Creating a feedforward neural network with backpropagation: Creating a recurrent neural network: Train the neural network on RGB color contrast:
LipNet
LipNet is a deep neural network for audio-visual speech recognition (ASVR). It was created by University of Oxford researchers Yannis Assael, Brendan Shillingford, Shimon Whiteson, and Nando de Freitas. The researchers stated that could match mouth movements to text with 93 percent accuracy, though it was criticized for its test using a limited dataset of words and grammar. It was used in Nvidia's autonomous "backseat driver" prototype Co-Pilot.
Smart environment
Smart environments link computers and other smart devices to everyday settings and tasks. Smart environments include smart homes, smart cities, and smart manufacturing. == Introduction == Smart environments are an extension of pervasive computing. According to Mark Weiser, pervasive computing promotes the idea of a world that is connected to sensors and computers. These sensors and computers are integrated with everyday objects in peoples' lives and are connected through networks. == Definition == Cook and Das, define a smart environment as "a small world where different kinds of smart devices are continuously working to make inhabitants' lives more comfortable." Smart environments aim to satisfy the experience of individuals from every environment, by replacing hazardous work, physical labor, and repetitive tasks with automated agents. Poslad differentiates three different kinds of smart environments for systems, services, and devices: virtual (or distributed) computing environments, physical environments, and human environments, or a hybrid combination of these: Virtual computing environments enable smart devices to access pertinent services anywhere and anytime. Physical environments may be embedded with various smart devices of different types including tags, sensors, and controllers, and have different form factors ranging from nano- to micro- to macro-sized. Human environments: humans, either individually or collectively, inherently form a smart environment for devices. However, humans themselves may be accompanied by smart devices such as mobile phones, use surface-mounted devices (wearable computing), and contain embedded devices (e.g., pacemakers to maintain a healthy heart operation or AR contact lenses) == Features == Smart environments encompass a range of features and services across various domains, including smart homes, smart cities, smart health, and smart factories. Some of the key features of smart environments are: Sensors and Actuators: Smart environments are equipped with an assembly of sensors and actuators that collect data and initiate actions to provide services for the betterment of human life. Interconnected Systems: These environments consist of interconnected systems that enable seamless communication and coordination among various devices and components. Data-Driven Technologies: Smart environments leverage data-driven technologies, such as the Internet of Things (IoT), to obtain information from the physical world, process it, and perform actions accordingly. Efficiency and Sustainability: They are designed to improve efficiency, sustainable practices, and resource management across different settings, such as energy efficiency in smart homes and environmental quality management in smart cities. Diverse Requirements: Different types of smart environments have diverse requirements and technology choices, influencing the processing and utilization of data within a specific environment. == Technologies == Building a smart environment involves technologies of Wireless communication Algorithm design, signal prediction & classification, information theory Multilayered software architecture, Corba, middleware Speech recognition Image processing, image recognition Sensors design, calibration, motion detection, temperature, pressure sensors, accelerometers Semantic Web and knowledge graphs Adaptive control, Kalman filters Computer networking Parallel processing Operating systems == Existing projects == The Aware Home Research Initiative at Georgia Tech "is devoted to the multidisciplinary exploration of emerging technologies and services based in the home" and was launched in 1998 as one of the first "living laboratories." The Mav Home (Managing an Adaptive Versatile Home) project, at UT Arlington, is a smart environment-lab with state-of-the-art algorithms and protocols used to provide a customized, personal environment to the users of this space. The Mav Home project, in addition to providing a safe environment, wants to reduce the energy consumption of the inhabitants. Other projects include House at the MIT Media Lab and many others.
Linguistic value
In artificial intelligence, fuzzy logic operations research, and related fields, a linguistic value is a natural language term which is derived using quantitative or qualitative reasoning such as with probability and statistics or fuzzy sets and systems. Variables that take linguistic values are called linguistic variables. == Examples of linguistic variables and values == For example, "age" may be a linguistic variable if its values are not numerical, e.g. very young, quite young, not young, old, not very old etc. These values could be derived from the numeric values for age. As another example, if a shuttle heat shield is deemed of having a linguistic value of a "very low" percentage of damage in re-entry, based upon knowledge from experts in the field, that probability would be given a value of say, 5%. From there on out, if it were to be used in an equation, the variable of percentage of damage will be at 5% if it deemed very low percentage.