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Matrix Factorization (recommender Systems)
Matrix factorization is a class of collaborative filtering algorithms used in recommender systems. Matrix factorization algorithms work by decomposing the user-item interaction matrix into the product of two lower dimensionality rectangular matrices. This family of methods became widely known during the Netflix prize challenge due to its effectiveness as reported by Simon Funk in his 2006 blog post, where he shared his findings with the research community. The prediction results can be improved by assigning different regularization weights to the latent factors based on items' popularity and users' activeness. Techniques The idea behind matrix factorization is to represent users and items in a lower dimensional latent space. Since the initial work by Funk in 2006 a multitude of matrix factorization approaches have been proposed for recommender systems. Some of the most used and simpler ones are listed in the following sections. Funk MF The original algorithm proposed by Simo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collaborative Filtering
Collaborative filtering (CF) is, besides content-based filtering, one of two major techniques used by recommender systems.Francesco Ricci and Lior Rokach and Bracha ShapiraIntroduction to Recommender Systems Handbook, Recommender Systems Handbook, Springer, 2011, pp. 1–35 Collaborative filtering has two senses, a narrow one and a more general one. In the newer, narrower sense, collaborative filtering is a method of making automatic predictions (filtering) about a user's interests by utilizing preferences or taste information collected from many users (collaborating). This approach assumes that if persons ''A'' and ''B'' share similar opinions on one issue, they are more likely to agree on other issues compared to a random pairing of ''A'' with another person. For instance, a collaborative filtering system for television programming could predict which shows a user might enjoy based on a limited list of the user's tastes (likes or dislikes). These predictions are specific to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recommender System
A recommender system (RecSys), or a recommendation system (sometimes replacing ''system'' with terms such as ''platform'', ''engine'', or ''algorithm'') and sometimes only called "the algorithm" or "algorithm", is a subclass of information filtering system that provides suggestions for items that are most pertinent to a particular user. Recommender systems are particularly useful when an individual needs to choose an item from a potentially overwhelming number of items that a service may offer. Modern recommendation systems such as those used on large social media sites make extensive use of AI, machine learning and related techniques to learn the behavior and preferences of each user and categorize content to tailor their feed individually. Typically, the suggestions refer to various decision-making processes, such as what product to purchase, what music to listen to, or what online news to read. Recommender systems are used in a variety of areas, with commonly recognised ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end 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 . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Netflix Prize
The Netflix Prize was an open competition for the best collaborative filtering algorithm to predict user ratings for films, based on previous ratings without any other information about the users or films, i.e. without the users being identified except by numbers assigned for the contest. The competition was held by Netflix, a video streaming service, and was open to anyone who was neither connected with Netflix (current and former employees, agents, close relatives of Netflix employees, etc.) nor a resident of certain blocked countries (such as Cuba or North Korea). On September 21, 2009, the grand prize of was given to the BellKor's Pragmatic Chaos team which bested Netflix's own algorithm for predicting ratings by 10.06%. Problem and data sets Netflix provided a ''training'' data set of 100,480,507 ratings that 480,189 users gave to 17,770 movies. Each training rating is a quadruplet of the form . The user and movie fields are integer IDs, while grades are from 1 to 5 (inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latent Space
A latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge from the resemblances from the objects. In most cases, the dimensionality of the latent space is chosen to be lower than the dimensionality of the feature space from which the data points are drawn, making the construction of a latent space an example of dimensionality reduction, which can also be viewed as a form of data compression. Latent spaces are usually fit via machine learning, and they can then be used as feature spaces in machine learning models, including classifiers and other supervised predictors. The interpretation of the latent spaces of machine learning models is an active field of study, but latent space interpretation is difficult to achieve. Due to the black-box ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition#Matrix polar decomposition, polar decomposition. Specifically, the singular value decomposition of an m \times n complex matrix is a factorization of the form \mathbf = \mathbf, where is an complex unitary matrix, \mathbf \Sigma is an m \times n rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \mathbf V^* is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrix, orthogonal matrices; in such contexts, the SVD ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overfitting
In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitted model is a mathematical model that contains more parameters than can be justified by the data. In the special case where the model consists of a polynomial function, these parameters represent the degree of a polynomial. The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the Statistical noise, noise) as if that variation represented underlying model structure. Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. Underfitting would occur, for example, when fitting a linear model to nonlinear data. Such a model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularization (mathematics)
In mathematics, statistics, Mathematical finance, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the Problem solving, answer to a problem to a simpler one. It is often used in solving 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. These terms could be Prior probability, priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. * Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frobenius Norm
In the field of mathematics, norms are defined for elements within a vector space. Specifically, when the vector space comprises matrices, such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Preliminaries Given a field \ K\ of either real or complex numbers (or any complete subset thereof), let \ K^\ be the -vector space of matrices with m rows and n columns and entries in the field \ K ~. A matrix norm is a norm on \ K^~. Norms are often expressed with double vertical bars (like so: \ \, A\, \ ). Thus, the matrix norm is a function \ \, \cdot\, : K^ \to \R^\ that must satisfy the following properties: For all scalars \ \alpha \in K\ and matrices \ A, B \in K^\ , * \, A\, \ge 0\ (''positive-valued'') * \, A\, = 0 \iff A=0_ (''definite'') * \left\, \alpha\ A \right\, = \left, \alpha \\ \left\, A\right\, \ (''absolutely homogeneous'') * \, A + B \, \le \, A \, + \, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recommender Systems
A recommender system (RecSys), or a recommendation system (sometimes replacing ''system'' with terms such as ''platform'', ''engine'', or ''algorithm'') and sometimes only called "the algorithm" or "algorithm", is a subclass of information filtering system that provides suggestions for items that are most pertinent to a particular user. Recommender systems are particularly useful when an individual needs to choose an item from a potentially overwhelming number of items that a service may offer. Modern recommendation systems such as those used on large social media sites make extensive use of AI, machine learning and related techniques to learn the behavior and preferences of each user and categorize content to tailor their feed individually. Typically, the suggestions refer to various Decision-making process, decision-making processes, such as what product to purchase, what music to listen to, or what online news to read. Recommender systems are used in a variety of areas, with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cold Start (recommender Systems)
Cold start can refer to: * Cold start (automotive), the starting of a vehicle engine at a low temperature relative to its operating temperature. * Cold start (computing), a startup problem in computer information systems. * Cold Start (military doctrine), a military doctrine developed by the Indian Armed Forces. * Cold start (recommender systems), the problem of recommending items to users with insufficient data * "Cold Start" (''Pole to Pole with Michael Palin''), a 1992 television episode See also * Cold open, a narrative technique used in television and films {{dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
