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Data reduction is the transformation of numerical or alphabetical digital information derived empirically or 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
The data transformation may be linear, as in principal component analysis (PCA), but many nonlinear dimensionality reduction techniques also exist. [4] [5] For multidimensional data, tensor representation can be used in dimensionality reduction through multilinear subspace learning. [6]
Data compression ratio, also known as compression power, is a measurement of the relative reduction in size of data representation produced by a data compression algorithm. It is typically expressed as the division of uncompressed size by compressed size.
While data reduction (compression, be it lossy or lossless) is a main goal of transform coding, it also allows other goals: one may represent data more accurately for the original amount of space [5] – for example, in principle, if one starts with an analog or high-resolution digital master, an MP3 file of a given size should provide a better ...
In information theory, data compression, source coding, [1] or bit-rate reduction is the process of encoding information using fewer bits than the original representation. [2] Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in ...
Nonlinear dimensionality reduction, also known as manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds which cannot be adequately captured by linear decomposition methods, onto lower-dimensional latent manifolds, with the goal of either visualizing ...
Lossless data compression is used in many applications. For example, it is used in the ZIP file format and in the GNU tool gzip. It is also often used as a component within lossy data compression technologies (e.g. lossless mid/side joint stereo preprocessing by MP3 encoders and other lossy audio encoders). [2]
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology.Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging.