Semantic mapping (SM) in
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
is a method for
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 ...
(the transformation of data from a high-dimensional space into a low-dimensional space). SM can be used in a set of multidimensional vectors of features to extract a few new features that preserves the main data characteristics.
SM performs dimensionality reduction by
clustering the original features in semantic clusters and combining features mapped in the same cluster to generate an extracted feature. Given a
data set A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the ...
, this method constructs a
projection matrix
In statistics, the projection matrix (\mathbf), sometimes also called the influence matrix or hat matrix (\mathbf), maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes t ...
that can be used to map a
data element
In metadata, the term data element is an atomic unit of data that has precise meaning or precise semantics. A data element has:
# An identification such as a data element name
# A clear data element definition
# One or more representation terms
# ...
from a
high-dimensional space
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordina ...
into a reduced dimensional space.
SM can be applied in construction of
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 ...
and
information retrieval
Information retrieval (IR) in computing and information science is the process of obtaining information system resources that are relevant to an information need from a collection of those resources. Searches can be based on full-text or other co ...
systems, as well as systems managing
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
s of high dimensionality. SM is an alternative to
random mapping For data analysis, Random mapping (RM) is a fast dimensionality reduction method categorized as feature extraction method. The RM consists in generation of a random matrix that is multiplied by each original vector and result in a reduced vector. W ...
,
principal components analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...
and
latent semantic indexing
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the do ...
methods.
See also
*
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 ...
*
Principal components analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...
*
Latent semantic indexing
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the do ...
*
Unification (logic reduction)
References
* CORRÊA, R. F.; LUDERMIR, T. B. Improving Self Organization of Document Collections by Semantic Mapping. Neurocomputing(Amsterdam), v. 70, p. 62-69, 2006
doi:10.1016/j.neucom.2006.07.007* CORRÊA, R. F. and LUDERMIR, T. B. (2007
"Dimensionality Reduction of very large document collections by Semantic Mapping" Proceedings of 6th Int. Workshop on Self-Organizing Maps (WSOM). {{ISBN, 978-3-00-022473-7.
External links
Full list of publications about Semantic Mapping method
Dimension reduction