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Curve-fitting compaction is data compaction accomplished by replacing data to be stored or transmitted with an analytical expression.
In telecommunication, data compaction is the reduction of the number of data elements, bandwidth, cost, and time for the generation, transmission, and storage of data without loss of information by eliminating unnecessary redundancy, removing irrelevancy, or using special coding.
Examples of curve-fitting compaction consisting of discretization and then interpolation are:
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable.
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but it might be from the "m for multiple" in the equation of a straight line "y = mx + b" or "y = mx + c".
In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations, and other aspects of logical syntax.
Compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony and released in 1982. The format was originally developed to store and play only sound recordings (CD-DA) but was later adapted for storage of data (CD-ROM). Several other formats were further derived from these, including write-once audio and data storage (CD-R), rewritable media (CD-RW), Video Compact Disc (VCD), Super Video Compact Disc (SVCD), Photo CD, PictureCD, CD-i, and Enhanced Music CD. The first commercially available audio CD player, the Sony CDP-101, was released October 1982 in Japan.
In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation. Compression can be either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.
Compact Disc Digital Audio, also known as Audio CD, is the standard format for audio compact discs. The standard is defined in the Red Book, one of a series of "Rainbow Books" that contain the technical specifications for all CD formats.
A time series is a series of data points indexed in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.
A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D computer graphics and solid modeling. The faces usually consist of triangles, quadrilaterals, or other simple convex polygons, since this simplifies rendering, but may also be composed of more general concave polygons, or polygons with holes.
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.
Linear predictive analysis is a simple form of first-order extrapolation: if it has been changing at this rate then it will probably continue to change at approximately the same rate, at least in the short term. This is equivalent to fitting a tangent to the graph and extending the line.
Compaction may refer to:
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing.
Compact multi-purpose vehicle is a car classification used in Europe to describe versions of small family compact cars, fitting between the mini MPV and large MPV sub-segments. In Japan, the term space wagon is sometimes used to refer to this type of vehicle.
A line chart or line graph is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered and joined with straight line segments. A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically. In these cases they are known as run charts.
Advanced Civil Speed Enforcement System (ACSES) is a positive train control cab signaling system developed by Alstom. The system is designed to prevent train-to-train collisions, protect against overspeed, and protect work crews with temporary speed restrictions. The information about permanent and temporary speed restrictions is transmitted to the train by transponders (Balises) lying in the track, coded track circuits and digital radio. It is installed on all of Amtrak's Northeast Corridor between Washington and Boston, and has been fully active since December 2015, a few months after the 2015 Philadelphia train derailment which it would have prevented.
XLfit is a Microsoft Excel-based plug-in which performs Regression, curve fitting and statistical analysis. XLfit generates 2D and 3D graphs and analyses data sets produced by any type of research. XLfit’s curve fitting engine allows linear and non-linear curve fits, smoothing, statistics, weighting and error bars.
The FX-601P and FX-602P were programmable calculators, manufactured by CASIO from 1981. It was the successor model to the Casio FX-502P series and was itself succeeded in 1990 by the Casio FX-603P.
In computer architecture, 16-bit integers, memory addresses, or other data units are those that are 16 bits wide. Also, 16-bit CPU and ALU architectures are those that are based on registers, address buses, or data buses of that size. 16-bit microcomputers are computers in which 16-bit microprocessors were the norm.
In statistics and data analysis the application software CumFreq is a tool for cumulative frequency analysis of a single variable and for probability distribution fitting.
The NASA Exoplanet Archive is an online astronomical exoplanet catalog and data service that collects and serves public data that support the search for and characterization of extra-solar planets (exoplanets) and their host stars. It is part of the Infrared Processing and Analysis Center and is on the campus of the California Institute of Technology (Caltech) in Pasadena, CA. The archive is funded by NASA and was launched in early December 2011 by the NASA Exoplanet Science Institute as part of NASA's Exoplanet Exploration Program. In July 2017, the archive's collection of confirmed exoplanets surpassed 3,500.
The General Services Administration (GSA), an independent agency of the United States government, was established in 1949 to help manage and support the basic functioning of federal agencies. GSA supplies products and communications for U.S. government offices, provides transportation and office space to federal employees, and develops government-wide cost-minimizing policies and other management tasks.
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