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  1. He captured it in a formula that calculates the minimum number of bits — a threshold later called the Shannon entropy — required to communicate a message.[1]
  2. The term “entropy” is borrowed from physics, where entropy is a measure of disorder.[1]
  3. A cloud has higher entropy than an ice cube, since a cloud allows for many more ways to arrange water molecules than a cube’s crystalline structure does.[1]
  4. In an analogous way, a random message has a high Shannon entropy — there are so many possibilities for how its information can be arranged — whereas one that obeys a strict pattern has low entropy.[1]
  5. Shannon entropy allows to estimate the average minimum number of bits needed to encode a string of symbols based on the alphabet size and the frequency of the symbols.[2]
  6. The concepts of entropy, as used in information theory and in various scientific disciplines, are now countless (Shannon, 1948).[3]
  7. Based on this fact, Shannon proposed measuring the average of this flux of information called entropy.[3]
  8. (7.79) can be a log 2 or an ln, with the entropy units in bits (binary units) or nats (natural units), respectively.[3]
  9. In general, the probability distribution for a given stochastic process is not known, and, in most situations, only small datasets from which to infer the entropy are available.[3]
  10. Shannon entropy, also known as information entropy or the Shannon entropy index, is a measure of the degree of randomness in a set of data.[4]
  11. The more characters there are, or the more proportional are the frequencies of occurrence, the harder it will be to predict what will come next - resulting in an increased entropy.[4]
  12. Apart from information theory, Shannon entropy is used in many fields.[4]
  13. In the Shannon entropy equation, p i is the probability of a given symbol.[5]
  14. The number of bits per character can be calculated from this frequency set using the Shannon entropy equation.[5]
  15. Shannon entropy provides a lower bound for the compression that can be achieved by the data representation (coding) compression step.[5]
  16. Shannon entropy makes no statement about the compression efficiency that can be achieved by predictive compression.[5]
  17. For anyone who wants to be fluent in Machine Learning, understanding Shannon’s entropy is crucial.[6]
  18. A little more formally, the entropy of a variable is the “amount of information” contained in the variable.[6]
  19. The analogy results when the values of the random variable designate energies of microstates, so Gibbs formula for the entropy is formally identical to Shannon's formula.[7]
  20. Entropy has relevance to other areas of mathematics such as combinatorics and machine learning.[7]
  21. The definition can be derived from a set of axioms establishing that entropy should be a measure of how "surprising" the average outcome of a variable is.[7]
  22. In this case a coin flip has an entropy of one bit.[7]
  23. Some details: We treat Shannon (discrete) and differential (continuous) entropy separately.[8]
  24. For example, you wouldn’t calculate nutrition in the same way you calculate entropy in thermodynamics.[9]
  25. Shannon entropy for imprecise and under-defined or over-defined information.[9]
  26. In the general case Arithmetic coding results in a near optimal encoding of messages that is very close to the number obtained from the Shannon entropy equation.[10]
  27. Statistical entropy was introduced by Shannon as a basic concept in information theory measuring the average missing information in a random source.[11]
  28. Extended into an entropy rate, it gives bounds in coding and compression theorems.[11]
  29. The relevance of entropy beyond the realm of physics, in particular for living systems and ecosystems, is yet to be demonstrated.[11]
  30. My goal is to really understand the concept of entropy, and I always try to explain complicated concepts using fun games, so that’s what I do in this post.[12]
  31. In colloquial terms, if the particles inside a system have many possible positions to move around, then the system has high entropy, and if they have to stay rigid, then the system has low entropy.[12]
  32. The molecules in ice have to stay in a lattice, as it is a rigid system, so ice has low entropy.[12]
  33. The molecules in water have more positions to move around, so water in liquid state has medium entropy.[12]
  34. In physics, the word entropy has important physical implications as the amount of "disorder" of a system.[13]
  35. But what properties single out Shannon entropy as special?[14]
  36. Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the "information loss", or change in entropy, associated with a measure-preserving function.[14]
  37. Shannon entropy then gives the only concept of information loss that is functorial, convex-linear and continuous.[14]
  38. The entropy H is correspondingly reduced in the posterior relative to the prior distribution.[15]
  39. In this case a measurement yields a posterior PDF with no change in the expected value but a significant increase in the spread and in the Shannon entropy.[15]
  40. 2.6 Entropy Rate Revisited . . . . . . . . . . . . . . . . . . . . . . .[16]
  41. 105 5.4 Limiting Entropy Densities 5.5 Information for General Alphabets . . . . . . . . . . . . . . . . .[16]
  42. Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the “information loss”, or change in entropy, associated with a measure-preserving function.[17]
  43. Thus, whenever you pick something out, you have absolutely no doubt (entropy is zero for Container 3) that it will be a circle.[18]
  44. As you can see, entropy (doubt, surprise, uncertainty) for Container 1 is less (56%), but more for Container 2 (99%).[18]
  45. For Container 3, there is no (0%) entropy - you have 100% chance to pick a circle.[18]
  46. The electroencephalographic Shannon entropy increased continuously over the observed concentration range of desflurane.[19]
  47. Recently, approximate entropy, a measure of the “amount of order” of the electroencephalographic signal has been shown to correlate well with the concentration of desflurane at the effect site.[19]
  48. The Shannon entropy 2 is a standard measure for the order state of sequences and has been applied previously to DNA sequences.[19]
  49. In this investigation, we applied the Shannon entropy to electroencephalographic data from anesthetized patients and correlated the concentration of anesthetic agent and entropy value.[19]
  50. KEYWORDS: Monte Carlo, keff, convergence, Shannon entropy, MCNP 1.[20]
  51. Line-plots of Shannon entropy vs. batch are easier to interpret and assess than are 2D or 3D plots of the source distribution vs. batch.[20]
  52. When running criticality calculations with MCNP5, it is essential that users examine the convergence of both keff and the fission source distribution (using Shannon entropy).[20]
  53. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations.[21]
  54. Shannon’s concept of entropy can now be taken up.[22]
  55. Thus, the bound computed using entropy cannot be attained with simple encodings.[22]
  56. This is better than the 2.0 obtained earlier, although still not equal to the entropy.[22]
  57. Because the entropy is not exactly equal to any fraction, no code exists whose average length is exactly equal to the entropy.[22]
  58. Pintacuda, N.: Shannon entropy: A more general derivation.[23]
  59. In this Letter, we report a comparative analysis of the Shannon entropy and qTIR using model series and real-world heartbeats.[24]
  60. We find that the permutation-based Shannon entropy (PEn) and time irreversibility (PYs) detect nonlinearities in the model series differently according to the surrogate theory.[24]
  61. In classical physics, the entropy of a physical system is proportional to the quantity of energy no longer available to do physical work.[25]
  62. In quantum mechanics, von Neumann entropy extends the notion of entropy to quantum systems by means of the density matrix.[25]
  63. In the theory of dynamical systems, entropy quantifies the exponential complexity of a dynamical system or the average flow of information per unit of time.[25]
  64. The term entropy is now used in many other sciences (such as sociology), sometimes distant from physics or mathematics, where it no longer maintains its rigorous quantitative character.[25]
  65. Shannon (the man, not the entropy) was one of those annoying people that excels at everything he touches.[26]
  66. Like the number of questions we need to arrive at the correct suit, Shannon Entropy decreases when order is imposed on a system and increases when the system is more random.[26]
  67. Once the (p)’s are known, Zorro simply implements the Shannon Entropy equation and returns the calculated value for (H), in bits.[26]
  68. A fair coin has an entropy of one bit.[27]
  69. However, if the coin is not fair, then the uncertainty is lower (if asked to bet on the next outcome, we would bet preferentially on the most frequent result), and thus the Shannon entropy is lower.[27]
  70. A long string of repeating characters has an entropy of 0, since every character is predictable.[27]
  71. Additivity The amount of entropy should be the same independently of how the process is regarded as being divided into parts.[27]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Quanta Magazine
  2. ↑ Shannon entropy calculator — Real example how to calculate and interpret information entropy
  3. ↑ 3.0 3.1 3.2 3.3 Shannon Entropy - an overview
  4. ↑ 4.0 4.1 4.2 Shannon Entropy Calculator
  5. ↑ 5.0 5.1 5.2 5.3 Shannon Entropy
  6. ↑ 6.0 6.1 The intuition behind Shannon’s Entropy
  7. ↑ 7.0 7.1 7.2 7.3 Entropy (information theory)
  8. ↑ What are the units of entropy of a normal distribution?
  9. ↑ 9.0 9.1 Shannon Entropy
  10. ↑ Shannon Entropy
  11. ↑ 11.0 11.1 11.2 Shannon entropy: a rigorous notion at the crossroads between probability, information theory, dynamical systems and statistical physics
  12. ↑ 12.0 12.1 12.2 12.3 Shannon Entropy, Information Gain, and Picking Balls from Buckets
  13. ↑ Entropy -- from Wolfram MathWorld
  14. ↑ 14.0 14.1 14.2 Shannon Entropy from Category Theory
  15. ↑ 15.0 15.1 On Some Shortcomings of Shannon Entropy as a Measure of Information Content in Indirect Measurements of Continuous Variables
  16. ↑ 16.0 16.1 Entropy and
  17. ↑ The n-Category Café
  18. ↑ 18.0 18.1 18.2 What is the role of the logarithm in Shannon's entropy?
  19. ↑ 19.0 19.1 19.2 19.3 Shannon Entropy Applied to the Measurement of the Electroencephalographic Effects of Desflurane
  20. ↑ 20.0 20.1 20.2 Physor-2006, ans topical meeting on reactor physics
  21. ↑ Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams
  22. ↑ 22.0 22.1 22.2 22.3 information theory - Entropy
  23. ↑ On Shannon's entropy, directed divergence and inaccuracy
  24. ↑ 24.0 24.1 Shannon entropy and quantitative time irreversibility for different and even contradictory aspects of complex systems
  25. ↑ 25.0 25.1 25.2 25.3 Scholarpedia
  26. ↑ 26.0 26.1 26.2 Shannon Entropy: A Genius Gambler’s Guide to Market Randomness
  27. ↑ 27.0 27.1 27.2 27.3 Information

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