# Ph.D. Thesis On Vector Quantization 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.The vector quantization carried out by three steps encoder, channel and decoder.

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The transformation is usually done by projection or by using a codebook.

In some cases, a codebook can be also used to entropy code the discrete value in the same step, by generating a prefix coded variable-length encoded value as its output.

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.

The set of discrete amplitude levels is quantized jointly rather than each sample being quantized separately.

Consider a k-dimensional vector form the vector space to which all the quantized vectors belong.

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.

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.

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