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Classification of unions of subspaces with sparse representations

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Neural coding

Neural coding (or neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity of the neurons in the ensemble. Based on the theory that sensory and other information is represented in the brain by networks of neurons, it is thought that neurons can encode both digital and analog information.

Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. What kind of graph is used depends on the application.

Ensemble learning

In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.

Hierarchical temporal memory

Hierarchical temporal memory (HTM) is a biologically constrained machine intelligence technology developed by Numenta. Originally described in the 2004 book On Intelligence by Jeff Hawkins with Sandra Blakeslee, HTM is primarily used today for anomaly detection in streaming data. The technology is based on neuroscience and the physiology and interaction of pyramidal neurons in the neocortex of the mammalian (in particular, human) brain. At the core of HTM are learning algorithms that can store, learn, infer, and recall high-order sequences.

Invariant subspace

In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by T; that is, T(W) ⊆ W. Consider a linear mapping An invariant subspace of has the property that all vectors are transformed by into vectors also contained in . This can be stated as Since maps every vector in into Since a linear map has to map A basis of a 1-dimensional space is simply a non-zero vector . Consequently, any vector can be represented as where is a scalar.

Krylov subspace

In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the of b under the first r powers of A (starting from ), that is, The concept is named after Russian applied mathematician and naval engineer Alexei Krylov, who published a paper about it in 1931. Vectors are linearly independent until , and . Thus, denotes the maximal dimension of a Krylov subspace. The maximal dimension satisfies and . More exactly, , where is the minimal polynomial of .

Autoencoder

An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning). An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation. The autoencoder learns an efficient representation (encoding) for a set of data, typically for dimensionality reduction. Variants exist, aiming to force the learned representations to assume useful properties.

Multilinear subspace learning

Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality reduction can be performed on a data tensor that contains a collection of observations have been vectorized, or observations that are treated as matrices and 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 s (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D).

TensorFlow

TensorFlow is a free and open-source software library for machine learning and artificial intelligence. It can be used across a range of tasks but has a particular focus on training and inference of deep neural networks. TensorFlow was developed by the Google Brain team for internal Google use in research and production. The initial version was released under the Apache License 2.0 in 2015. Google released the updated version of TensorFlow, named TensorFlow 2.0, in September 2019.

Deductive classifier

A deductive classifier is a type of artificial intelligence inference engine. It takes as input a set of declarations in a frame language about a domain such as medical research or molecular biology. For example, the names of classes, sub-classes, properties, and restrictions on allowable values. The classifier determines if the various declarations are logically consistent and if not will highlight the specific inconsistent declarations and the inconsistencies among them.