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Data Reduction
Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimental data, experimentally into a corrected, ordered, and simplified form. The purpose of data reduction can be two-fold: reduce the number of data records by eliminating invalid data or produce summary data and statistics at different aggregation levels for various applications. When information is derived from instrument readings there may also be a transformation from digitization, analog to digital form. When the data are already in digital form the 'reduction' of the data typically involves some editing, Scaling (geometry), scaling, encoding, sorting, collating, and producing tabular summaries. When the observations are discrete but the underlying phenomenon is continuous then smoothing and interpolation are often needed. The data reduction is often undertaken in the presence of reading or measurement errors. Some idea of the nature of these errors is needed before ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Information
Digital data, in information theory and information systems, is information represented as a string of discrete symbols each of which can take on one of only a finite number of values from some alphabet, such as letters or digit (unit), digits. An example is a text document, which consists of a string of alphanumeric characters . The most common form of digital data in modern information systems is ''binary data'', which is represented by a string of binary digits (bits) each of which can have one of two values, either 0 or 1. Digital data can be contrasted with ''analog data'', which is represented by a value from a continuity (mathematics), continuous range of real numbers. Analog data is transmitted by an analog signal, which not only takes on continuous values, but can vary continuously with time, a continuous real-valued function of time. An example is the air pressure variation in a sound wave. The word ''digital'' comes from the same source as the words digit (anatomy), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet Transform
In mathematics, a wavelet series is a representation of a square-integrable (real number, real- or complex number, complex-valued) function (mathematics), function by a certain orthonormal series (mathematics), series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. Definition A function \psi \,\in\, L^2(\mathbb) is called an orthonormal wavelet if it can be used to define a Hilbert space#Orthonormal bases, Hilbert basis, that is a orthonormal basis, complete orthonormal system, for the Hilbert space L^2\left(\mathbb\right) of Square-integrable function, square integrable functions. The Hilbert basis is constructed as the family of functions \ by means of Dyadic transformation, dyadic translation (geometry), translations and dilation (operator theory), dilations of \psi\,, :\psi_(x) = 2^\frac \psi\left(2^jx - k\right)\, for integers j,\, k \,\in\, \mathbb. If under the standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Pre-processing
Data preprocessing can refer to manipulation or dropping of data before it is used in order to ensure or enhance performance, and is an important step in the data mining process. The phrase "garbage in, garbage out" is particularly applicable to data mining and machine learning projects. Data-gathering methods are often loosely controlled, resulting in out-of-range values (e.g., Income: −100), impossible data combinations (e.g., Sex: Male, Pregnant: Yes), and missing values, etc. Analyzing data that has not been carefully screened for such problems can produce misleading results. Thus, the representation and quality of data is first and foremost before running any analysis. Often, data preprocessing is the most important phase of a machine learning project, especially in computational biology. If there is much irrelevant and redundant information present or noisy and unreliable data, then knowledge discovery during the training phase is more difficult. Data preparation and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Editing
Data editing is defined as the process involving the review and adjustment of collected survey data. Data editing helps define guidelines that will reduce potential bias and ensure consistent estimates leading to a clear analysis of the data set by correct inconsistent data using the methods later in this article. The purpose is to control the quality of the collected data. Data editing can be performed manually, with the assistance of a computer or a combination of both. Editing methods Editing methods refer to a range of procedures and processes used for detecting and handling errors in data. Data editing is used with the goal to improve the quality of statistical data produced. These modifications can greatly improve the quality of analytics created by aiming to detect and correct errors. Examples of different techniques to data editing such as micro-editing, macro-editing, selective editing, or the different tools used to achieve data editings such as graphical editing and inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Cleansing
Data cleansing or data cleaning is the process of detecting and correcting (or removing) corrupt or inaccurate records from a record set, table, or database and refers to identifying incomplete, incorrect, inaccurate or irrelevant parts of the data and then replacing, modifying, or deleting the dirty or coarse data. Data cleansing may be performed interactively with data wrangling tools, or as batch processing through scripting or a data quality firewall. After cleansing, a data set should be consistent with other similar data sets in the system. The inconsistencies detected or removed may have been originally caused by user entry errors, by corruption in transmission or storage, or by different data dictionary definitions of similar entities in different stores. Data cleaning differs from data validation in that validation almost invariably means data is rejected from the system at entry and is performed at the time of entry, rather than on batches of data. The actual process of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivariant Map
In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation. Equivariant maps generalize the concept of invariants, functions whose value is unchanged by a symmetry transformation of their argument. The value of an equivariant map is often (imprecisely) called an invariant. In statistical inference, equivariance under statistical transformations of data is an important property of various estimation methods; see invariant estimator for details. In pure mathematics, equivariance is a central object of study in equivariant topology and its subtopics equivariant cohomology and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditionality Principle
The conditionality principle is a Fisherian principle of statistical inference that Allan Birnbaum formally defined and studied in his 1962 JASA article. Informally, the conditionality principle can be taken as the claim that experiments which were not actually performed are statistically irrelevant. Together with the sufficiency principle, Birnbaum's version of the principle implies the famous likelihood principle. Although the relevance of the proof to data analysis remains controversial among statisticians, many Bayesians and likelihoodists consider the likelihood principle foundational for statistical inference. Formulation The conditionality principle makes an assertion about an experiment ''E'' that can be described as a mixture of several component experiments ''E''h where ''h'' is an ancillary statistic An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Principle
In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument. For example, consider a model which gives the probability density function \; f_X(x \,\vert\, \theta)\; of observable random variable \, X \, as a function of a parameter \,\theta~. Then for a specific value \,x\, of \,X~, the function \,\mathcal(\theta \,\vert\, x) = f_X(x \,\vert\, \theta)\; is a likelihood function of \,\theta\;:~ it gives a measure of how "likely" any particular value of \,\theta\, is, if we know that \,X\, has the value \,x~. The density function may be a density with respect to counting measure, i.e. a probability mass function. Two likelihood functions are ''equivalent'' if one is a scalar multiple of the other. The like ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficient Statistic
In statistics, a statistic is ''sufficient'' with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than the statistic, as to which of those probability distributions is the sampling distribution. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log-linear Model
A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form :\exp \left(c + \sum_ w_i f_i(X) \right), in which the are quantities that are functions of the variable , in general a vector of values, while and the stand for the model parameters. The term may specifically be used for: *A log-linear plot or graph, which is a type of semi-log plot. *Poisson regression for contingency tables, a type of generalized linear model. The specific applications of log-linear models are where the output quantity lies in the range 0 to ∞, for values of the independent variables , or more immediately, the transformed quantities in the range −∞ to +∞. This may be contrasted to logistic models, similar to the logistic function, for which the output quantity lies in the range 0 to 1. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
