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ID3 Algorithm
In decision tree learning, ID3 (Iterative Dichotomiser 3) is an algorithm invented by Ross QuinlanQuinlan, J. R. 1986. Induction of Decision Trees. Mach. Learn. 1, 1 (Mar. 1986), 81–106 used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm, and is typically used in the machine learning and natural language processing domains. Algorithm The ID3 algorithm begins with the original set S as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S and calculates the entropy \Eta or the information gain IG(S) of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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ID3 Algorithm Decision Tree
ID3 is a metadata container most often used in conjunction with the MP3 audio file format. It allows information such as the title, artist, album, track number, and other information about the file to be stored in the file itself. ID3 is a ''de facto'' standard for metadata in MP3 files; no standardization body was involved in its creation nor has such an organization given it a formal approval status. It competes with the APE tag in this area. There are two unrelated versions of ID3: ID3v1 and ID3v2. In ID3v1, the metadata is stored in a 128-byte segment at the end of the file. In ID3v2, an extensible set of "frames" located at the start of the file is used. Sub-variants of both versions exist. ID3v1 When the MP3 standard was published in 1995, it did not include a method for storing file metadata. In 1996 Eric Kemp proposed adding a 128-byte suffix to MP3 files, which would store useful information such as an artist's name or a related album title. Kemp deliberately placed t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Empty Set
In mathematics, the empty set or void set is the unique Set (mathematics), set having no Element (mathematics), elements; its size or cardinality (count of elements in a set) is 0, zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called ''non-empty''. In some textbooks and popularizations, the empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty). Notation Common notations for the empty set include "", "\emptyset", and "∅". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø () in the Danish orthography, Danish and Norwegian orthography, Norwegian a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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] |
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Backtracking
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Greedy Algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure. Specifics Greedy algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Local Optimum
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative'' extrema) or on the entire domain (the ''global'' or ''absolute'' extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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ID3 Decision Tree- Splicing
ID3 is a metadata container most often used in conjunction with the MP3 audio file format. It allows information such as the title, artist, album, track number, and other information about the file to be stored in the file itself. ID3 is a ''de facto'' standard for metadata in MP3 files; no standardization body was involved in its creation nor has such an organization given it a formal approval status. It competes with the APE tag in this area. There are two unrelated versions of ID3: ID3v1 and ID3v2. In ID3v1, the metadata is stored in a 128-byte segment at the end of the file. In ID3v2, an extensible set of "frames" located at the start of the file is used. Sub-variants of both versions exist. ID3v1 When the MP3 standard was published in 1995, it did not include a method for storing file metadata. In 1996 Eric Kemp proposed adding a 128-byte suffix to MP3 files, which would store useful information such as an artist's name or a related album title. Kemp deliberately placed t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Node (computer Science)
A node is a basic unit of a data structure, such as a linked list or Tree (data structure), tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by Pointer (computer programming), pointers. Nodes and trees Nodes are often arranged into tree structures. A node represents the information contained in a single data structure. These nodes may contain a value or condition, or possibly serve as another independent data structure. Nodes are represented by a single parent node. The highest point on a tree structure is called a root node, which does not have a parent node, but serves as the parent or 'grandparent' of all of the nodes below it in the tree. The height of a node is determined by the total number of edges on the path from that node to the furthest leaf node, and the height of the tree is equal to the height of the root node. Node depth is determined by the distance between that particular node and the root node. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Maximum
In mathematical analysis, the maximum and minimum of a function (mathematics), function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given Interval (mathematics), range (the ''local'' or ''relative'' extrema) or on the entire domain of a function, domain (the ''global'' or ''absolute'' extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set (mathematics), set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. Definition A real-valued Function (mathematics), function ''f'' defined on a Domain of a function, domain ''X'' has a global (or absolute) m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Minimum
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative'' extrema) or on the entire domain (the ''global'' or ''absolute'' extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Posterior Distribution
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating. In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density interval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |