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Network Coordinate System
A Network Coordinate System (NC system) is a system for predicting characteristics such as the latency or bandwidth of connections between nodes in a network by assigning coordinates to nodes. More formally, It assigns a coordinate embedding \vec c_n to each node n in a network using an optimization algorithm such that a predefined operation \vec c_a \otimes \vec c_b \rightarrow d_ estimates some directional characteristic d_ of the connection between node a and b. Uses In general, Network Coordinate Systems can be used for peer discovery, optimal-server selection, and characteristic-aware routing. Latency Optimization When optimizing for latency as a connection characteristic i.e. for low-latency connections, NC systems can potentially help improve the quality of experience for many different applications such as: * Online Games ** Forming game groups such that all the players are close to each other and thus have a smoother overall experience. ** Choosing servers as clos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Coordinate System
A Network Coordinate System (NC system) is a system for predicting characteristics such as the latency or bandwidth of connections between nodes in a network by assigning coordinates to nodes. More formally, It assigns a coordinate embedding \vec c_n to each node n in a network using an optimization algorithm such that a predefined operation \vec c_a \otimes \vec c_b \rightarrow d_ estimates some directional characteristic d_ of the connection between node a and b. Uses In general, Network Coordinate Systems can be used for peer discovery, optimal-server selection, and characteristic-aware routing. Latency Optimization When optimizing for latency as a connection characteristic i.e. for low-latency connections, NC systems can potentially help improve the quality of experience for many different applications such as: * Online Games ** Forming game groups such that all the players are close to each other and thus have a smoother overall experience. ** Choosing servers as clos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vivaldi Coordinates
Vivaldi Coordinate System is a decentralized Network Coordinate System, that allows for distributed systems such as peer-to-peer networks to estimate round-trip time (RTT) between arbitrary nodes in a network. Through this scheme, network topology awareness can be used to tune the network behavior to more efficiently distribute data. For example, in a peer-to-peer network, more responsive identification and delivery of content can be achieved. In the Vuze, Azureus application, Vivaldi is used to improve the performance of the distributed hash table that facilitates query matches. Design The algorithm behind Vivaldi is an optimization algorithm that figures out the most stable configuration of points in a euclidean space such that distances between the points are as close as possible to real-world measured distances. In effect, the algorithm attempts to Embedding space, embed the multi-dimensional space that is latency measurements between computers into a low-dimensional eucli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vuze
Vuze (previously Azureus) is a BitTorrent client used to transfer files via the BitTorrent protocol. Vuze is written in Java, and uses the Azureus Engine. In addition to downloading data linked to .torrent files, Azureus allows users to view, publish and share original DVD and HD quality video content. Content is presented through channels and categories containing TV shows, music videos, movies, video games, series and others. Additionally, if users prefer to publish their original content, they may earn money from it. Azureus was first released in June 2003 at SourceForge.net, mostly to experiment with the Standard Widget Toolkit from Eclipse. It later became one of the most popular BitTorrent clients. The Azureus software was released under the GNU General Public License, and remains as a free software application. It was among the most popular BitTorrent clients. However, the Vuze software added in more recent versions is proprietary and users are required to accept these m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Search
In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. The other approach is trust region. The line search approach first finds a descent direction along which the objective function f will be reduced and then computes a step size that determines how far \mathbf should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly or inexactly. Example use Here is an example gradient method that uses a line search in step 4. # Set iteration counter \displaystyle k=0, and make an initial guess \mathbf_0 for the minimum # Repeat: # Compute a descent direction \mathbf_k # Choose \displaystyle \alpha_k to 'loosely' minimize h(\alpha_k)=f(\mathbf_k+\alpha_k\mathbf_k) over \alpha_k\in\mathbb R_+ # &nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Gradient Descent
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data). Especially in high-dimensional optimization problems this reduces the very high computational burden, achieving faster iterations in trade for a lower convergence rate. While the basic idea behind stochastic approximation can be traced back to the Robbins–Monro algorithm of the 1950s, stochastic gradient descent has become an important optimization method in machine learning. Background Both statistical estimation and machine learning consider the problem of minimizing an objective function that has the form of a sum: : Q(w) = \frac\sum_^n Q_i(w), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loss Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Notation This article will use the following notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-negative Matrix Factorization
Non-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 is factorized into (usually) two matrices and , 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. Since the problem is not exactly solvable in general, it is commonly approximated numerically. NMF finds applications in such fields as astronomy, computer vision, document clustering, missing data imputation, chemometrics, audio signal processing, recommender systems, and bioinformatics. History In chemometrics non-negative matrix factorization has a long history under the name "self modeling curve resolution". In this framework the vectors in the right matrix are continuous curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inner Product Space
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in \langle a, b \rangle. Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or ''scalar product'' of Cartesian coordinates. Inner product spaces of infinite dimension are widely used in functional analysis. Inner product spaces over the field of complex numbers are sometimes referred to as unitary spaces. The first usage of the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898. An inner product naturally induces an associated norm, (denoted , x, and , y, in the picture); so, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Completion
Matrix completion is the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing data imputation in statistics. A wide range of datasets are naturally organized in matrix form. One example is the movie-ratings matrix, as appears in the Netflix problem: Given a ratings matrix in which each entry (i,j) represents the rating of movie j by customer i, if customer i has watched movie j and is otherwise missing, we would like to predict the remaining entries in order to make good recommendations to customers on what to watch next. Another example is the document-term matrix: The frequencies of words used in a collection of documents can be represented as a matrix, where each entry corresponds to the number of times the associated term appears in the indicated document. Without any restrictions on the number of degrees of freedom in the completed matrix this problem is underdetermined since the hidden entries could be assigned arbitrary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
