Consider a data set consisting of 220 data vectors, where each vector has 32 components and each component is a 4-byte value. Suppose that vec- tor quantization is used for compression and that 216 prototype vectors are used. How many bytes of storage does that data set take before and after compression and what is the compression ratio?
What will be an ideal response?
Before compression, the data set requires 4 × 32 × 220 = 134, 217, 728 bytes.
After compression, the data set requires 4×32×216 = 8, 388, 608 bytes for the
prototype vectors and 2×220 = 2, 097, 152 bytes for vectors, since identifying
the prototype vector associated with each data vector requires only two bytes.
Thus, after compression, 10,485,760 bytes are needed to represent the data.
The compression ratio is 12.8.
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