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Soft memory errors Random bit flips, corrupting the content of the affected memory cells

Gabriel Moruz Goethe University. Resilient k-d Trees: k -Means in Space. Soft memory errors Random bit flips, corrupting the content of the affected memory cells Multiple causes, e.g. power failures, alpha particles, cosmic rays Memories tend to be more error-prone

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Soft memory errors Random bit flips, corrupting the content of the affected memory cells

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  1. Gabriel Moruz Goethe University Resilient k-d Trees: k-Means in Space • Soft memory errors • Random bit flips, corrupting the content of the affected memory cells • Multiple causes, e.g. power failures, alpha particles, cosmic rays • Memories tend to be more error-prone • Occurrence rates • Directly proportional to running time and memory used • Seldom in individual memories, a lot in large clusters • Increase dramatically with altitude • In space: much more frequent than at ground level • Adjusted rand index • Measure how good the clustering is • Value of 1: perfect accuracy • Value of 0: expected for random assignment of points to centers • k-dk-means • Build a k-d tree data structure on all points • Idea: use the k-d treecompute the closest center for potentially large groups of points at once • Behaves as bad as k-means on corrupted data • Resilient k-dtree • A k-d tree guaranteed to behave well in spite of memory corruptions • Split the tree in a top tree and many leaf structures (as in [2]) • Top tree: heavily replicated • Leaf structures only contain points • Top tree • Top tree • Leaf structures • Classical k-means • Given n input points, group them in k clusters • Idea: Maintain k centers – each center is the mean of points close to it • Image clustering: a cluster contains all pixels of a color, compress images • Motivation: data communication between space and earth is expensive Resilient k-d k-means maintains accuracy • Resilient k-dk-means • k-dk-means using a resilient k-d tree • Theoretically guaranteed to behave well on corrupted data [1] I. Finocchi and G. F. Italiano. Sorting and searching in faulty memories. In ACM STOC’04, 101–110. [2] G.S. Brodal, R. Fagerberg, I. Finocchi, F. Grandoni, G.F. Italiano, A. Jørgensen, G. Moruz, and T. Mølhave. Optimal resilient dictionaries. In ESA'07, 347-358. [3] F. Gieseke, G. Moruz, and J. Vahrenhold. Resilient K-d Trees: K-Means in Space Revisited. In ICDM ’10. • k-means in image clustering • k-means in image clustering MADALGO – Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation

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