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In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.
In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.
There is an exponential increase in volume associated with adding extra dimensions to a mathematical space.For example, 10 2 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube) with no more than 10 −2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10 −2 ...
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.
A reference dimension is a dimension on an engineering drawing provided for information only. [1] Reference dimensions are provided for a variety of reasons and are often an accumulation of other dimensions that are defined elsewhere [2] (e.g. on the drawing or other related documentation).
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Data augmentation is a statistical technique which allows maximum likelihood estimation from incomplete data. [1] [2] Data augmentation has important applications in Bayesian analysis, [3] and the technique is widely used in machine learning to reduce overfitting when training machine learning models, [4] achieved by training models on several slightly-modified copies of existing data.
The concept of data type is similar to the concept of level of measurement, but more specific. For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale).