For
data analysis
Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, enco ...
, Random mapping (RM) is a fast
dimensionality reduction
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 ...
method categorized as
feature extraction
In machine learning, pattern recognition, and image processing, feature extraction starts from an initial set of measured data and builds derived values (features) intended to be informative and non-redundant, facilitating the subsequent learning a ...
method. The RM consists in generation of a random matrix that is multiplied by each original vector and result in a reduced vector. When the data vectors are high-dimensional it is computationally infeasible to use data analysis or pattern recognition algorithms which repeatedly compute similarities or distances in the original data space. It is therefore necessary to reduce the dimensionality before, for example, clustering the data. In a
text mining
Text mining, also referred to as ''text data mining'', similar to text analytics, is the process of deriving high-quality information from text. It involves "the discovery by computer of new, previously unknown information, by automatically extract ...
context, it is demonstrated that the
document classification
Document classification or document categorization is a problem in library science, information science and computer science. The task is to assign a document to one or more classes or categories. This may be done "manually" (or "intellectually") ...
accuracy obtained after the dimensionality has been reduced using a random mapping method will be almost as good as the original accuracy if the final dimensionality is sufficiently large (about 100 out of 6000). In fact, it can be shown that the inner product (similarity) between the mapped vectors follows closely the
inner product
In mathematics, an inner product space (or, rarely, a Hausdorff space, Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation (mathematics), operation called an inner product. The inner product of two ve ...
of the original
vectors.
See also
*
Random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
*
Semantic mapping
*
Random projection
In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. Random projection methods are known for their power, simplicity, and low error rates when compared ...
References
* Kaski, S. Dimensionality reduction by random mapping: fast similarity computation for clustering. Proceedings of The 1998 IEEE International Joint Conference on Neural Networks, 1998. pp. 413–418
doi: 10.1109/IJCNN.1998.682302
Data analysis
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