Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Non-negative matrix factorizationNon-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered.
Symmetric matrixIn linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
LU decompositionIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.
Text editorA text editor is a type of computer program that edits plain text. Such programs are sometimes known as "notepad" software (e.g. Windows Notepad). Text editors are provided with operating systems and software development packages, and can be used to change files such as s, documentation files and programming language source code. Plain text and Rich text There are important differences between plain text (created and edited by text editors) and rich text (such as that created by word processors or desktop publishing software).
Text fileA text file (sometimes spelled textfile; an old alternative name is flatfile) is a kind of that is structured as a sequence of of electronic text. A text file exists stored as data within a . In operating systems such as CP/M and MS-DOS, where the operating system does not keep track of the file size in bytes, the end of a text file is denoted by placing one or more special characters, known as an (EOF) marker, as padding after the last line in a text file.
Multimodal sentiment analysisMultimodal sentiment analysis is a technology for traditional text-based sentiment analysis, which includes modalities such as audio and visual data. It can be bimodal, which includes different combinations of two modalities, or trimodal, which incorporates three modalities. With the extensive amount of social media data available online in different forms such as videos and images, the conventional text-based sentiment analysis has evolved into more complex models of multimodal sentiment analysis, which can be applied in the development of virtual assistants, analysis of YouTube movie reviews, analysis of news videos, and emotion recognition (sometimes known as emotion detection) such as depression monitoring, among others.
Tf–idfIn information retrieval, tf–idf (also TF*IDF, TFIDF, TF–IDF, or Tf–idf), short for term frequency–inverse document frequency, is a numerical statistic that is intended to reflect how important a word is to a document in a collection or corpus. It is often used as a weighting factor in searches of information retrieval, text mining, and user modeling. The tf–idf value increases proportionally to the number of times a word appears in the document and is offset by the number of documents in the corpus that contain the word, which helps to adjust for the fact that some words appear more frequently in general.
Unitary matrixIn linear algebra, an invertible complex square matrix U is unitary if its conjugate transpose U* is also its inverse, that is, if where I is the identity matrix. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger (†), so the equation above is written For real numbers, the analogue of a unitary matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve norms, and thus, probability amplitudes.
Plain textIn computing, plain text is a loose term for data (e.g. file contents) that represent only characters of readable material but not its graphical representation nor other objects (floating-point numbers, images, etc.). It may also include a limited number of "whitespace" characters that affect simple arrangement of text, such as spaces, line breaks, or tabulation characters.
Regularization (mathematics)In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem.
