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Dynamic Time Warping
In time series analysis, dynamic time warping (DTW) is an algorithm for measuring similarity between two temporal sequences, which may vary in speed. For instance, similarities in walking could be detected using DTW, even if one person was walking faster than the other, or if there were accelerations and decelerations during the course of an observation. DTW has been applied to temporal sequences of video, audio, and graphics data — indeed, any data that can be turned into a linear sequence can be analyzed with DTW. A well-known application has been automatic speech recognition, to cope with different speaking speeds. Other applications include speaker recognition and online signature recognition. It can also be used in partial shape matching applications. In general, DTW is a method that calculates an optimal match between two given sequences (e.g. time series) with certain restriction and rules: * Every index from the first sequence must be matched with one or more indices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hirschberg's Algorithm
In computer science, Hirschberg's algorithm, named after its inventor, Dan Hirschberg, is a dynamic programming algorithm that finds the optimal sequence alignment between two strings. Optimality is measured with the Levenshtein distance, defined to be the sum of the costs of insertions, replacements, deletions, and null actions needed to change one string into the other. Hirschberg's algorithm is simply described as a more space-efficient version of the Needleman–Wunsch algorithm that uses divide and conquer. Hirschberg's algorithm is commonly used in computational biology to find maximal global alignments of DNA and protein sequences. Algorithm information Hirschberg's algorithm is a generally applicable algorithm for optimal sequence alignment. BLAST and FASTA are suboptimal heuristics. If ''x'' and ''y'' are strings, where length(''x'') = ''n'' and length(''y'') = ''m'', the Needleman–Wunsch algorithm finds an optimal alignment in O(''nm'') time, using O(''nm'') space. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levenshtein Distance
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after the Soviet mathematician Vladimir Levenshtein, who considered this distance in 1965. Levenshtein distance may also be referred to as ''edit distance'', although that term may also denote a larger family of distance metrics known collectively as edit distance. It is closely related to pairwise string alignments. Definition The Levenshtein distance between two strings a, b (of length , a, and , b, respectively) is given by \operatorname(a, b) where : \operatorname(a, b) = \begin , a, & \text , b, = 0, \\ , b, & \text , a, = 0, \\ \operatorname\big(\operatorname(a),\operatorname(b)\big) & \text a = b \\ 1 + \min ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Analysis
Power analysis is a form of side channel attack in which the attacker studies the power consumption of a cryptographic hardware device. These attacks rely on basic physical properties of the device: semiconductor devices are governed by the laws of physics, which dictate that changes in voltages within the device require very small movements of electric charges (currents). By measuring those currents, it is possible to learn a small amount of information about the data being manipulated. Simple power analysis (SPA) involves visually interpreting power ''traces'', or graphs of electrical activity over time. Differential power analysis (DPA) is a more advanced form of power analysis, which can allow an attacker to compute the intermediate values within cryptographic computations through statistical analysis of data collected from multiple cryptographic operations. SPA and DPA were introduced to the open cryptography community in 1998 by Paul Kocher, Joshua Jaffe and Benjami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have '' optimal substructure''. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Warp Edit Distance
Time Warp Edit Distance (TWED) is a measure of similarity (or dissimilarity) for discrete time series matching with time ' elasticity'. In comparison to other distance measures, (e.g. DTW ( dynamic time warping) or LCS (longest common subsequence problem)), TWED is a metric. Its computational time complexity is O(n^2), but can be drastically reduced in some specific situations by using a corridor to reduce the search space. Its memory space complexity can be reduced to O(n). It was first proposed in 2009 by P.-F. Marteau. Definition \delta_(A^p_1,B^q_1) = Min \begin \delta_(A^_1,B^q_1) + \Gamma(a^_p \to \Lambda) & \rm \\ \delta_(A^_1,B^_1) + \Gamma(a^_p \to b^_q) & \rm\\ \delta_(A^_1,B^_1) + \Gamma(\Lambda \to b^_q) & \rm \end whereas \Gamma(\alpha^_p \to \Lambda) = d_(a^_, a^_) + \nu \cdot (t_ - t_) + \lambda \Gamma(\alpha^_p \to b^_q) = d_(a^_p, b^_q) + d_(a^_, b^_) + \nu \cdot (, t_ - t_, + , t_ - t_, ) \Gamma(\Lambda \to b^_q) = d_(b^_, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
