Let a and q be two units of Zp, q not a root of unity, and let Vq be the closure of the set {aqn | n = 0, 1, 2, ..}. K is a non-archimedean valued field, K contains Qp, and K is complete for the valuation |.|, which extends the p-adic valuation. C(Vq → K) is the Banach space of continuous functions from Vq to K, equipped with the supremum norm. Let E and Dq be the operators on C(Vq → K) defined...

Vector quantization (VQ) is an efficient data compression technique for low bit rate applications. However, the major disadvantage of VQ is that its encoding complexity increases dramatically with bit rate and vector dimension. Even though one can use a modified VQ, such as the tree-structured VQ, to reduce the encoding complexity, it is practically infeasible to implement such a VQ at a high b...

Proteins containing the FxxxVQxhTG or VQ motif interact with WRKY transcription factors. Although VQ proteins have been reported in several plants, knowledge about their structures, functions and evolution is still very limited. Here, we report structural and functional analysis of the VQ protein family from soybean. Like Arabidopsis homologues, soybean VQ proteins bind only Group I and IIc WRK...

A low bit rate still image compression scheme by compressing the indices of Vector Quantization (VQ) and generating residual codebook is proposed. The indices of VQ are compressed by exploiting correlation among image blocks, which reduces the bit per index. A residual codebook similar to VQ codebook is generated that represents the distortion produced in VQ. Using this residual codebook the di...

Vector quantization (VQ) is an efficient technique for image compression. However, one of the most serious problems of VQ is the heavily computational load for searching the closest codeword to the input vector in the codebook. To overcome this problem, we propose a simple and fast partial distance search algorithm for VQ codebook by using the sum-norm pyramid structure of codewords. The propos...

VQ = {(q, a) ∈ Z : gcd(q, a) = 1, max{|a|, |q|} ≤ Q}. Then the Jarńık polygon PQ is the unique (up to translation) convex polygon whose sides are precisely the vectors in VQ. In other words, PQ is the polygon whose vertices can be obtained by starting from an arbitrary point in R and adding the vectors in VQ one by one, traversing those vectors in a counterclockwise direction. For example, the ...

In this paper, we present local image descriptor using VQ-SIFT for more effective and efficient image retrieval. Instead of SIFT's weighted orientation histograms, we apply vector quantization (VQ) histogram as an alternate representation for SIFT features. Experimental results show that SIFT features using VQ-based local descriptors can achieve better image retrieval accuracy than the conventi...

This letter proves the equivalence between vector quantization (VQ) classifiers and circular backpropagation (CBP) networks. The calibrated prototypes for a VQ schema can be plugged in a CBP feedforward structure having the same number of hidden neurons and featuring the same mapping. The letter describes how to exploit such equivalence by using VQ prototypes to perform a meaningful initializat...