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Median of medians finds an approximate median in linear time. Using this approximate median as an improved pivot, the worst-case complexity of quickselect reduces from quadratic to linear, which is also the asymptotically optimal worst-case complexity of any selection algorithm. In other words, the median of medians is an approximate median ...
The median of medians method partitions the input into sets of five elements, and uses some other non-recursive method to find the median of each of these sets in constant time per set. It then recursively calls itself to find the median of these n / 5 {\displaystyle n/5} medians.
One can combine basic quickselect with median of medians as fallback to get both fast average case performance and linear worst-case performance; this is done in introselect. Finer computations of the average time complexity yield a worst case of n ( 2 + 2 log 2 + o ( 1 ) ) ≤ 3.4 n + o ( n ) {\displaystyle n(2+2\log 2+o(1))\leq 3.4n+o(n ...
MATLAB datafiles with one 16384 times 5000 matrix per camera per acquisition. 30,000 Images and .mat files Authentication 2012 [183] S. Voloshynovskiy, et al. PharmaPack Dataset 1,000 unique classes with 54 images per class. Class labeling, many local descriptors, like SIFT and aKaZE, and local feature agreators, like Fisher Vector (FV). 54,000
This relates directly to the k-median problem which is the problem of finding k centers such that the clusters formed by them are the most compact with respect to the 2-norm. Formally, given a set of data points x , the k centers c i are to be chosen so as to minimize the sum of the distances from each x to the nearest c i .
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic , being more resilient to outliers in a data set than the standard deviation . In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it.
The median can thus be applied to school classes which are ranked but not numerical (e.g. working out a median grade when student test scores are graded from F to A), although the result might be halfway between classes if there is an even number of classes. (For odd number classes, one specific class is determined as the median.)
Some people use "spectral centroid" to refer to the median of the spectrum. This is a different statistic, the difference being essentially the same as the difference between the unweighted median and mean statistics. Since both are measures of central tendency, in some situations they will exhibit some similarity of behaviour.