Practical methods for speeding-up the pairwise nearest neighbor method

Abstract

The pairwise nearest neighbor (PNN) method is a simple and well-known method for codebook generation in vector quantization. In its exact form, it provides a good-quality codebook but at the cost of high run time. A fast exact algorithm was recently introduced to implement the PNN an order of magnitude faster than the original O(N 3 K) time algorithm. The run time, however, is still lower bounded by O(N 2 K), and therefore, additional speed-ups may be required in applications where time is an important factor. We consider two practical methods to reduce the amount of work caused by the distance calculations. Through experiments, we show that the run time can be reduced to 10 to 15% that of the original method for data sets in color quantization and in spatial vector quantization.

An agglomerative clustering algorithm using a dynamic k-nearest-neighbor list

“…All computing is performed on an Intel Core 2 Quad 2.4 GHz PC with 2 GB of memory. In examples 2-6, the proposed algorithm DKNNA is compared with the FPNN [7] and the DLA [8] in terms of the number of distance calculations, computing time and mean square error using three different nearest-neighbor search algorithms: full search (FULL), PDS + MPS + Lazy [27] and fast search (FS) [18,21]. It should be noted that the proposed method will not generate exact the same results as those of Ward's method and the FPNN, although their differences are not significant any more.…”

“…Table 3 shows the mean square errors of the FPNN, DLA, and DKNNA using three different search algorithms: full search, MPS + PDS + Lazy [27] and fast search [18,21]. It can be seen from Table 3 that there is little difference between the mean square errors of the FPNN and DKNNA, since there are many cluster pairs with the same cluster distance in the early stage of a cluster merge.…”

“…The merging cost is defined as being the cluster distance between a cluster and its nearest neighbor. To study the effect of search algorithm on the proposed method, we use full search, MPS + PDS + Lazy [24,27], and fast search [18,21] algorithms to determine k nearest neighbors of a cluster. This paper is organized as follows.…”

“…Kaukoranta et al [12] presented the lazy pairwise nearest neighbor method (Lazy) to postpone some distance calculations in the process of the cluster merge. Virmajoki et al [27] proposed an algorithm, which combines partial distortion search (PDS) [2], mean-distance-ordered partial search (MPS) [24], and Lazy [12] to speed up the FPNN. This algorithm is referred to as FPNN + PDS + MPS + Lazy in this paper.…”

“…This data set is generated from a gray image ''Lena'' with N = 16384 and d = 16, where d is the data dimension.Some search algorithms, such as full search (FULL), fast search (FS)[18,21] and PDS + MPS + Lazy[27], can be used to determine a cluster's k nearest neighbors in steps (1.2), (2.3) and (3.6) of DKNNA. If a fast search and PDS + MPS + Lazy are used for DKNNA, the corresponding algorithms are referred to as DKNNA + FS and DKNNA + PDS + MPS + Lazy, respectively, in this paper.…”