Global convergence and empirical consistency of the generalized Lloyd algorithm

Sabin, Michael J.; Gray, Robert M.

doi:10.1109/tit.1986.1057168

Cited by 114 publications

(79 citation statements)

References 11 publications

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“…일반적인 데이터 압축 기술은 코드북 학습을 위해 서 Generalized Lloyd Algorithm (GLA)을 사용한다 [10] . 이 알고리즘은 N개의 centroid들을 임의로 분포시키 의 centroid로 선언하고, centroid를 2의 자승으로 분할 하면서 GLA를 수행하게 된다 [11] .…”

Section: 기존 양자화 방식unclassified

Quantization of LPC Coefficients Using a Multi-frame AR-model

Jung¹,

Kim²

2012

The Journal of the Acoustical Society of Korea

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For speech coding, a vocal tract is modeled using Linear Predictive Coding (LPC) coefficients. The LPC coefficients are typically transformed to Line Spectral Frequency (LSF) parameters which are advantageous for linear interpolation and quantization. If multidimensional LSF data are quantized directly using VectorQuantization (VQ), high rate-distortion performance can be obtained by fully utilizing intra-frame correlation. In practice, since this direct VQ system cannot be used due to high computational complexity and memory requirement, Split VQ (SVQ) is used where a multidimensional vector is split into multilple sub-vectors for quantization. The LSF parameters also have high inter-frame correlation, and thus Predictive SVQ (PSVQ) is utilized. PSVQ provides better rate-distortion performance than SVQ. In this paper, to implement the optimal predictors in PSVQ for voice storage devices, we propose Multi-Frame AR-model based SVQ (MF-AR-SVQ) that considers the inter-frame correlations with multiple previous frames. Compared with conventional PSVQ, the proposed MF-AR-SVQ provides 1 bit gain in terms of spectral distortion without significant increase in complexity and memory requirement.

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Section: 기존 양자화 방식unclassified

Quantization of LPC Coefficients Using a Multi-frame AR-model

Jung¹,

Kim²

2012

The Journal of the Acoustical Society of Korea

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“…It is a descent algorithm [13], i.e., it reduces the average distortion of the codebook with every iteration. However, the GLA is not guaranteed to find the global optimal codebook for non-convex distortion functions [15], since it may get trapped in a local minimum.…”

Section: A Codebook Designmentioning

confidence: 99%

Feedback Compression for Correlated Broadcast Channels

Simon

Francisco

Slock

et al. 2007

2007 14th IEEE Symposium on Communications and Vehicular Technology in the Benelux

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Abstract-In this paper we apply Predictive Vector Quantization (PVQ) to quantize time-correlated broadcast channels. PVQ exploits the time-correlation of the channel to reduce the quantization error of the channels, and thus to improve the sum rate of the system. PVQ predicts the actual channel based on a number of previous channels, and then quantizes the difference between the prediction and the true channel. In this paper we show how the corresponding codebooks can be designed, and we present a prediction strategy. The performance of PVQ for a broadcast system is depicted through numerical simulations.

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“…However, it is important to realize that the corollary does not imply that the underlying partitioning {π (t) j } k j=1 converges. We refer the reader interested in more general convergence results to Pollard (1982) and Sabin and Gray (1986).…”

Section: Spherical K-meansmentioning

confidence: 99%

Untitled

2001

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Abstract. Unlabeled document collections are becoming increasingly common and available; mining such data sets represents a major contemporary challenge. Using words as features, text documents are often represented as high-dimensional and sparse vectors-a few thousand dimensions and a sparsity of 95 to 99% is typical. In this paper, we study a certain spherical k-means algorithm for clustering such document vectors. The algorithm outputs k disjoint clusters each with a concept vector that is the centroid of the cluster normalized to have unit Euclidean norm. As our first contribution, we empirically demonstrate that, owing to the high-dimensionality and sparsity of the text data, the clusters produced by the algorithm have a certain "fractal-like" and "selfsimilar" behavior. As our second contribution, we introduce concept decompositions to approximate the matrix of document vectors; these decompositions are obtained by taking the least-squares approximation onto the linear subspace spanned by all the concept vectors. We empirically establish that the approximation errors of the concept decompositions are close to the best possible, namely, to truncated singular value decompositions. As our third contribution, we show that the concept vectors are localized in the word space, are sparse, and tend towards orthonormality. In contrast, the singular vectors are global in the word space and are dense. Nonetheless, we observe the surprising fact that the linear subspaces spanned by the concept vectors and the leading singular vectors are quite close in the sense of small principal angles between them. In conclusion, the concept vectors produced by the spherical k-means algorithm constitute a powerful sparse and localized "basis" for text data sets.

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Global convergence and empirical consistency of the generalized Lloyd algorithm

Cited by 114 publications

References 11 publications

Quantization of LPC Coefficients Using a Multi-frame AR-model

Quantization of LPC Coefficients Using a Multi-frame AR-model

Feedback Compression for Correlated Broadcast Channels

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