**Lloyd-Max**

In computer science and electrical engineering, Lloyd’s algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces, and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition, and then re-partitions the input according to which of these centroids is closest. However, Lloyd’s algorithm differs from k-means clustering in that its input is a continuous geometric region rather than a discrete set of points. Thus, when re-partitioning the input, Lloyd’s algorithm uses Voronoi diagrams rather than simply determining the nearest center to each of a finite set of points as the k-means algorithm does. Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd’s algorithm can be used to construct close approximations to centroidal Voronoi tessellations of the input, which can be used for quantization, dithering, and stippling. Other applications of Lloyd’s algorithm include smoothing of triangle meshes in the finite element method.

➚ “Compressive K-means” … **Distributed Stream Processing Engines (DSPE)**

Distributed stream processing engines (DSPEs) are a new emergent family of MapReduce inspired technologies that address this issue. These engines allow to express parallel computation on streams, and combine the scalability of distributed processing with the efficiency of streaming algorithms. Examples of these engines include Storm, S4, and Samza. … **Robust Multiple Signal Classification (MUSIC)**

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on the observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: 1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and 2) under the assumption of spherically contoured noise distribution, the noise subspace can be determined from the eigendecomposition of the MT-covariance. Furthermore, we derive a new robust measure-transformed minimum description length (MDL) criterion for estimating the number of signals, and extend the MT-MUSIC framework to the case of coherent signals. The proposed approach is illustrated in simulation examples that show its advantages as compared to other robust MUSIC and MDL generalizations. …

# If you did not already know

**09**
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Aug 2017

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