# Ph.D. Thesis On Vector Quantization Another (simpler) method is LBG which is based on K-Means.The algorithm can be iteratively updated with 'live' data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples.In this algorithm we are assuming that brightness of a firefly is equal to objective function value. Step 5: If no firefly fitness value is better than the selected firefly then it moves randomly in search space according to Equation (5) Step 6: Repeat step 3 to step 5 until one of the termination criteria is reached.

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It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid.

For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm).

Vector quantization compresses the size of the image by using the optimization algorithm.

We can use FFA and ALO algorithm for the image compression system.

The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data.

Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error.

Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model and to sparse coding models used in deep learning algorithms such as autoencoder.

It is desirable to use a cooling schedule to produce convergence: see Simulated annealing.

Step 3: Once the mapping of all the input vectors to the initial code vectors is made, compute the centroids of the partition region found in step 2. We used firefly algorithm for vector quantization for LBG scheme.

FFA LBG vector quantization algorithm The basic principle of firefly algorithm is flashing pattern and characteristics of fireflies.

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