Elastic net regularizationIn statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods. The elastic net method overcomes the limitations of the LASSO (least absolute shrinkage and selection operator) method which uses a penalty function based on Use of this penalty function has several limitations. For example, in the "large p, small n" case (high-dimensional data with few examples), the LASSO selects at most n variables before it saturates.
G-structure on a manifoldIn differential geometry, a G-structure on an n-manifold M, for a given structure group G, is a principal G-subbundle of the tangent frame bundle FM (or GL(M)) of M. The notion of G-structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields. For example, for the orthogonal group, an O(n)-structure defines a Riemannian metric, and for the special linear group an SL(n,R)-structure is the same as a volume form.
K-nearest neighbors algorithmIn statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the k closest training examples in a data set. The output depends on whether k-NN is used for classification or regression: In k-NN classification, the output is a class membership.
Digital image processingDigital image processing is the use of a digital computer to process s through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over . It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems.
Document classificationDocument 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") or algorithmically. The intellectual classification of documents has mostly been the province of library science, while the algorithmic classification of documents is mainly in information science and computer science.
Automatic image annotationAutomatic image annotation (also known as automatic image tagging or linguistic indexing) is the process by which a computer system automatically assigns metadata in the form of captioning or keywords to a . This application of computer vision techniques is used in systems to organize and locate images of interest from a database. This method can be regarded as a type of multi-class with a very large number of classes - as large as the vocabulary size.
Reasonable personIn law, a reasonable person, reasonable man, or the man on the Clapham omnibus, is a hypothetical person of legal fiction crafted by the courts and communicated through case law and jury instructions. Strictly according to the fiction, it is misconceived for a party to seek evidence from actual people to establish how the reasonable man would have acted or what he would have foreseen. This person's character and care conduct under any common set of facts, is decided through reasoning of good practice or policy—or "learned" permitting there is a compelling consensus of public opinion—by high courts.
GrassmannianIn mathematics, the Grassmannian Gr(k, V) is a space that parameterizes all k-dimensional linear subspaces of the n-dimensional vector space V. For example, the Grassmannian Gr(1, V) is the space of lines through the origin in V, so it is the same as the projective space of one dimension lower than V. When V is a real or complex vector space, Grassmannians are compact smooth manifolds.
Scale spaceScale-space theory is a framework for multi-scale signal representation developed by the computer vision, and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures.
Curse of dimensionalityThe curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases.
