Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using n log n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using n log n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a n log n processor PRAM, butterfly, or tree. Keywords. Hierarchical clustering, pattern analysis, parallel algorithm, butterfly network, PRAM algorithm. 1 In...

The recent and continuing construction of multi- and hyper-spectral imagers will provide detailed data cubes with information in both the spatial and spectral domain. This data shows great promise for remote sensing applications ranging from environmental and agricultural to national security interests. The reduction of this voluminous data to useful intermediate forms is necessary both for downlinking all those bits and for interpreting them. Smart on-board hardware is required, as well as sophisticated earth-bound processing. A segmented image (in which the multispectral data in each pixel is classified into one of a small number of categories) is one kind of intermediate form which provides some measure of data compression. Traditional image segmentation algorithms treat pixels independently and cluster the pixels according only to their spectral information. This neglects the implicit spatial information that is available in the image. We will suggest a simple approach --- a varian...

We present a parallel algorithm for performing multidimensional fast Hartley transforms (FHTs) on hypercube SIMD computers with unshared local memory. The flexibility of the algorithm derives from the partition of the dimensions of the hypercube in subsets associated with each of the dimensions of the transform, the pure binary processor indexing, and the consecutive distribution of data in the processors' local memory, which facilitates the parallel performance of unidimensional FHTs. The complexity of the algorithm and the associated data redundancy are analysed. Keywords: hypercube computer, parallel algorithm, FHT. 1 Introduction The Fourier transform is the operation upon which spectral analysis, signal processing and all their applications are based. For efficiency, it has for many years invariably been performed by some variant of the algorithm known as the fast Fourier transform (FFT). However, compared with the Hartley transform devised by Hartley in 1942 [1], the Fourier tr...

In this work we present a study on the parallelization of code segments that are typical of clustering algorithms. In order to approach this problem from a practical point of view we have considered the parallelization on the three types of architectures currently available from parallel system manufacturers: vector computers, shared memory multiprocessors and distributed memory multicomputers. We have selected the FC (Fuzzy Covariance) and AD (Affinity Decompositions) algorithms as representative of the different computational structures found in clustering algorithms. We present a comparative study of the results obtained from running these algorithms on three systems: VP2400/10, KSR-1 and AP1000. 1 Introduction The automatic classification of data is one of the basic tasks in pattern recognition. Given its iterative nature and high computational cost (CPU time), the most adequate solution for its numerical treatment is to use concurrent techniques in order to reduce the execution ...