Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not hold for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains such as biology that require the use of Jaccard, Gower, or more complex distances. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm to achieve an O(k)-fold speedup in the second SWAP phase of the algorithm, but will still find the same results as the original PAM algorithm. If we slightly relax the choice of swaps performed (at comparable quality), we can further accelerate the algorithm by performing up to k swaps in each iteration. With the substantially faster SWAP, we can now also explore alternative strategies for choosing the initial medoids. We also show how the CLARA and CLARANS algorithms benefit from these modifications. It can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100, we observed a 200-fold speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets as long as we can afford to compute a distance matrix, and in particular to higher k (at k=2, the new SWAP was only 1.5 times faster, as the speedup is expected to increase with k)

On the Exact BER of Bit-Wise Demodulators for One-Dimensional Constellations

The optimal bit-wise demodulator for M-ary pulse amplitude modulation (PAM) over the additive white Gaussian noise channel is analyzed in terms of uncoded bit-error rate (BER). New closed-form BER expressions for 4-PAM with any labeling are developed. Moreover, closed-form BER expressions for 11 out of 23 possible bit patterns for 8-PAM are presented, which enable us to obtain the BER for 8-PAM with some of the most popular labelings, including the binary reflected Gray code and the natural binary code. Numerical results show that, regardless of the labeling, there is no difference between the optimal demodulator and the symbol-wise demodulator for any BER of practical interest (below 0.1)

Performance analysis of pre-equalized multilevel partial response schemes

In order to achieve high speed on electrical interconnects, channel attenuation at high frequencies must be dealt with by proper transceiver design. In this paper we investigate finite-complexity MMSE pre-equalization under an average transmit power constraint, to compensate for channel distortion in the case of both full-response and precoded partial response signaling with L-PAM mapping, and consider the resulting error performance for symbol-by-symbol detection and sequence detection. For a representative electrical interconnect, we point out that the constellation size (2-PAM or 4-PAM), the type of signaling (full response or partial response), the detection method (symbol-by-symbol detection or sequence detection) and the number of pre-equalizer taps should be carefully selected in order to achieve satisfactory error performance at high data rates. For several scenarios, precoded duobinary 4-PAM is found to yield the best error performance for given average transmit power

It’s about time we challenged the views of those who wrongly claim that only a handful of universities deliver social mobility

No one yet knows the full impact that the fee changes will have on many underrepresented communities. Pam Tatlow argues that the diversification of student bodies amidst fee changes must start with a challenge to the elitism that pervades the social mobility debate

Primary Amoebic (Naegleria fowleri) Meningoencephalitis Presenting as Status Epilepticus

Primary amebic meningoencephalitis (PAM) is a rare entity. Usual presenting features are fever, headache and seizures with meningeal signs and this disease carries high mortality rate. We present a case report of PAM presenting as status epilepticus

Arts & Social Change Grantmaking: Statistical Report

Provides additional charts and graphs with data summaries based on the survey of grantmakers conducted by Americans for the Arts and summarized in the report "Trend or Tipping Point: Arts & Social Change Grantmaking" (401 KOR)