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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 content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images or sounds.
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
The principal components of a collection of points in a real coordinate space are a sequence of unit vectors, where the -th vector is the direction of a line that best fits the data while being orthogonal to the first vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. Principal component analysis (PCA) is the process of computing the principal components and using them to perform a change of basis on the data, sometimes using only the first few principal components and ignoring the rest.
A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional representation of a higher dimensional data set while preserving the topological structure of the data. For example, a data set with p variables measured in n observations could be represented as clusters of observations with similar values for the variables. These clusters then could be visualized as a two-dimensional "map" such that observations in proximal clusters have more similar values than observations in distal clusters. This can make high-dimensional data easier to visualize and analyze.
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 and generalization steps, and in some cases leading to better human interpretations. Feature extraction is related to dimensionality reduction.
High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies within lower-dimensional space. If the data of interest is of low enough dimension, the data can be visualised in the low-dimensional space.
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. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable. Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as signal processing, speech recognition, neuroinformatics, and bioinformatics.
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 documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text. A matrix containing word counts per document is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by taking the cosine of the angle between the two vectors formed by any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents.
Generative topographic map (GTM) is a machine learning method that is a probabilistic counterpart of the self-organizing map (SOM), is probably convergent and does not require a shrinking neighborhood or a decreasing step size. It is a generative model: the data is assumed to arise by first probabilistically picking a point in a low-dimensional space, mapping the point to the observed high-dimensional input space, then adding noise in that space. The parameters of the low-dimensional probability distribution, the smooth map and the noise are all learned from the training data using the expectation-maximization (EM) algorithm. GTM was introduced in 1996 in a paper by Christopher Bishop, Markus Svensen, and Christopher K. I. Williams.
A document-term matrix is a mathematical matrix that describes the frequency of terms that occur in a collection of documents. In a document-term matrix, rows correspond to documents in the collection and columns correspond to terms. This matrix is a specific instance of a document-feature matrix where "features" may refer to other properties of a document besides terms. It is also common to encounter the transpose, or term-document matrix where documents are the columns and terms are the rows. They are useful in the field of natural language processing and computational text analysis.
Probabilistic latent semantic analysis (PLSA), also known as probabilistic latent semantic indexing is a statistical technique for the analysis of two-mode and co-occurrence data. In effect, one can derive a low-dimensional representation of the observed variables in terms of their affinity to certain hidden variables, just as in latent semantic analysis, from which PLSA evolved.
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. 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. In Text mining context, it is demonstrated that the document classification 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. In fact, it can be shown that the inner product (similarity) between the mapped vectors follows closely the inner product of the original vectors.
Distributional semantics is a research area that develops and studies theories and methods for quantifying and categorizing semantic similarities between linguistic items based on their distributional properties in large samples of language data. The basic idea of distributional semantics can be summed up in the so-called Distributional hypothesis: linguistic items with similar distributions have similar meanings.
Latent semantic mapping (LSM) is a data-driven framework to model globally meaningful relationships implicit in large volumes of data. It is a generalization of latent semantic analysis. In information retrieval, LSA enables retrieval on the basis of conceptual content, instead of merely matching words between queries and documents.
Multilinear subspace learning is an approach to dimensionality reduction. Dimensionality reduction can be performed on a data tensor whose observations have been vectorized and organized into a data tensor, or whose observations are matrices that are concatenated into a data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D).
Multimedia information retrieval is a research discipline of computer science that aims at extracting semantic information from multimedia data sources. Data sources include directly perceivable media such as audio, image and video, indirectly perceivable sources such as text, semantic descriptions, biosignals as well as not perceivable sources such as bioinformation, stock prices, etc. The methodology of MMIR can be organized in three groups:
- Methods for the summarization of media content. The result of feature extraction is a description.
- Methods for the filtering of media descriptions
- Methods for the categorization of media descriptions into classes.
Random indexing is a dimensionality reduction method and computational framework for distributional semantics, based on the insight that very-high-dimensional vector space model implementations are impractical, that models need not grow in dimensionality when new items are encountered, and that a high-dimensional model can be projected into a space of lower dimensionality without compromising L2 distance metrics if the resulting dimensions are chosen appropriately.
In natural language processing (NLP), word embedding is a term used for the representation of words for text analysis, typically in the form of a real-valued vector that encodes the meaning of the word such that the words that are closer in the vector space are expected to be similar in meaning. Word embeddings can be obtained using a set of language modeling and feature learning techniques where words or phrases from the vocabulary are mapped to vectors of real numbers. Conceptually it involves the mathematical embedding from space with many dimensions per word to a continuous vector space with a much lower dimension.
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 to other methods. According to experimental results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural language tasks under the name random indexing.
The following outline is provided as an overview of and topical guide to machine learning. Machine learning is a subfield of soft computing within computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. In 1959, Arthur Samuel defined machine learning as a "field of study that gives computers the ability to learn without being explicitly programmed". Machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from an example training set of input observations in order to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions.
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.