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Explain and Demonstrate Non-Shannon Entropy

See attached, or read [url removed, login to view] job explaining Kapur, Renyi, and Harvda/Charvat entropy

This job requires two things.

First

An explanation of these three types of entropy calculations. You can base it on [url removed, login to view]

Essentially, the following expressions must be explained in about 600 words each.

There is an image in the word document here.

The writing must be in academic style using third person. It is desired to reference other sources and provide the reference information. No direct quotes. No plagiarism, this will be carefully checked.

Second

Short and simple C source code. For Shannon entropy, the following was written.

int Frequencies[256];

void CountFrequencies(unsigned char *pDataSet, int nLength)

{

int i;

// Zero the frequency buffer.

for (i = 0; i < 256; i++)

{

Frequencies[i] = 0;

}

// Loop through each data element of the data set.

for (i = 0; i < nLength; i++)

{

// Increment the frequency for this data value.

Frequencies[pDataSet[i]]++;

}

}

double CalculateShannonEntropy(unsigned char *pDataSet, int nLength)

{

int i;

double dEntropy = 0, dTemp;

// Call the function that counts the frequencies.

CountFrequencies(pDataSet, nLength);

for (i = 0; i < 256; i++)

{

if (Frequencies[i] == 0)

{

continue;

}

dTemp = (double)Frequencies[i] / (double)nLength;

dEntropy -= ( dTemp * log2(dTemp) );

}

return(dEntropy);

}

Deliverables

Three pieces of text in word document, each approximately 600 words. They should explain the three types of entropy: Renyi, Kapur, and Harvda/Charvat. They should be professionally written in a third person voice, and exhibit the quality of an academic writer. References to sources are desired.

Three pieces of C code in a text file, each one similar to the Shannon entropy code above.

double CalculateRenyiEntropy(unsigned char *pDataSet, int nLength);

double CalculateKapurEntropy(unsigned char *pDataSet, int nLength);

double CalculateHarvdaCharvatEntropy(unsigned char *pDataSet, int nLength);

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