An overview of Renyi Entropy and some potential applications

Beadle, E.; Schroeder, Jim; Moran, Bill; Suvorova, Sofia

doi:10.1109/acssc.2008.5074715

Cited by 21 publications

(12 citation statements)

References 19 publications

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“…The system diagram is shown in Figure 6.4. Figure 6.5 shows the training images (22,21,19 images per class, respectively) to illustrate the difficulty of the task.…”

Section: Case Study: Automatic Target Recognition (Atr) With Itlmentioning

confidence: 99%

“…(11.4)), but for values in the range given by the Silverman's rule different information is contained in CSD, because it is in fact using a different similarity metric. This may have applications in spectral estimation and detection theories, however, we and others [22] have just started to explore this relation.…”

Section: Definition the Generalized Covariance Function Called The mentioning

confidence: 99%

See 1 more Smart Citation

Information Theoretic Learning

Prı́ncipe¹

2010

Information Science and Statistics

758

170

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“…The system diagram is shown in Figure 6.4. Figure 6.5 shows the training images (22,21,19 images per class, respectively) to illustrate the difficulty of the task.…”

Section: Case Study: Automatic Target Recognition (Atr) With Itlmentioning

confidence: 99%

Section: Definition the Generalized Covariance Function Called The mentioning

confidence: 99%

Information Theoretic Learning

Prı́ncipe¹

2010

Information Science and Statistics

758

170

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“…It' s well know that entropy can be used to measure the average amount of information conveyed by random variable and it has been applied in image processing, coding theory, finance decisions and other various fields [4]. Keeping this idea in mind, our work try to find the relation between entropy and similarity and then build an alternative similarity measure based on Renyi's quadratic entropy for the audio signal processing.…”

Section: Introductionmentioning

confidence: 98%

Audio similarity measure based on Renyi's quadratic entropy

Pan

Yang

et al. 2010

2010 International Conference on Audio, Language and Image Processing

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Considering noise interference often exists in audio processing, it is not robust enough to calculate audio similarity by using distance measure directly. In this paper, basing on Renyi's quadratic entropy a novel scheme for audio similarity measure is proposed . In our work, we extract Mel Frequency Cepstral Coefficients (MFCCs) to represent each audio, and then calculate the similarity based on the entropy of audio samples by probability density function (pdf) of MFCCs which can be estimated by Parzen window. The experimental results show that: (a) our approach has better performance than the one based on Euclidean distance in the common SNR condition, (b) our approach can achieve 94.00% matching accuracy even when the signal to noise ratio (SNR) is 0db. In addition, our algorithm also can be applied in audio retrieval and musical cluster.

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“…For instance, the more delocalized is the electron distribution, the larger is the Shannon entropy (S) [3][4][5][6][7][8][9][10][11][12][13][14]. Moreover, Rényi entropy of order α (R α ) [15][16][17] and Tsallis entropy of order α (T α ) [18][19][20][21] are the one-parameter generalizations of Shannon entropy and offer extended descriptions. In addition, Onicescu Information Energy of order α (E O α ) [22,23] is related to the frequency moment of the electron density [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

2019

Atoms

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Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α .

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An overview of Renyi Entropy and some potential applications

Cited by 21 publications

References 19 publications

Information Theoretic Learning

Information Theoretic Learning

Audio similarity measure based on Renyi's quadratic entropy

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

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