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In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++. GNU Scientific Library [6] GNU Project C, C++ 1996 2.7.1 / 11.2021 Free GPL: General purpose numerical analysis library. Includes some support for linear algebra. IMSL Numerical Libraries: Rogue Wave Software: C, Java, C#, Fortran, Python 1970 many ...
In natural language processing, a word embedding is a representation of a word. The embedding is used in text analysis.Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning. [1]
Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words.
Xerus [52] is a C++ tensor algebra library for tensors of arbitrary dimensions and tensor decomposition into general tensor networks (focusing on matrix product states). It offers Einstein notation like syntax and optimizes the contraction order of any network of tensors at runtime so that dimensions need not be fixed at compile-time.
The tensor product of V and its dual space is isomorphic to the space of linear maps from V to V: a dyadic tensor vf is simply the linear map sending any w in V to f(w)v. When V is Euclidean n-space, we can use the inner product to identify the dual space with V itself, making a dyadic tensor an elementary tensor product of two vectors in ...
A multi-way graph with K perspectives is a collection of K matrices ,..... with dimensions I × J (where I, J are the number of nodes). This collection of matrices is naturally represented as a tensor X of size I × J × K. In order to avoid overloading the term “dimension”, we call an I × J × K tensor a three “mode” tensor, where “modes” are the numbers of indices used to index ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.