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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
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.
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.
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 ...
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
For example, when dealing with mixed-type data that contain numerical as well as categorical descriptors, Gower's distance is a common alternative. [ citation needed ] In other words, MDS attempts to find a mapping from the M {\displaystyle M} objects into R N {\displaystyle \mathbb {R} ^{N}} such that distances are preserved.
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 ...
Real high-dimensional data is typically sparse, and tends to have relevant low dimensional features. One task of TDA is to provide a precise characterization of this fact. For example, the trajectory of a simple predator-prey system governed by the Lotka–Volterra equations [1] forms a closed circle in state space. TDA provides tools to detect ...