SFFT: Sparse Fast Fourier Transform
Sparse Fast Fourier Transform : The discrete Fourier transform (DFT) is one of the most important and widely used computational tasks. Its applications are broad and include signal processing, communications, and audio/image/video compression. Hence, fast algorithms for DFT are highly valuable. Currently, the fastest such algorithm is the Fast Fourier Transform (FFT), which computes the DFT of an
Nearly Optimal Sparse Fourier Transform
We consider the problem of computing the k-sparse approximation to the discrete Fourier transform of an n-dimensional signal. We show: * An O(k log n)-time randomized algorithm for the case where the input signal has at most k non-zero Fourier coefficients, and * An O(k log n log(n/k))-time randomized algorithm for general input signals. Both algorithms achieve o(n log n) time, and thus improve ov
What is the expectation maximization algorithm? - Nature Biotechnology
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tokuronmain.dvi
2003 年 11 月 12 日 29 .....2.5..... 最尤法とその計算アルゴリズム ここでは，最尤推定値を数値計算で求める方法を 3 つ紹介する． 2.5.1 ニュート ン・ラプソン法 いま，g : R → R を 2 階微分可能な関数とし ，方程式 g (x) = 0 をみたす解 x = c をみつけ たい．そのために，c に近い x に対して，テーラー展開をする： 0 = g (c) ≈ g (x) + g (x)(x − c) ˙ ただし，g (x) = dg/dx である．g (x) = 0 のとき，これを c について解けば ˙ ˙ c≈x− g (x) g (x) ˙ を得る．初期値 x0 を取り，点列 {xn }∞ を逐次的に n=1 xn+1 = xn − g (xn ) , g (xn ) ˙ n = 0, 1, . . . (2.7
1
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Affinity Propagation | Frey Lab - Probabilistic and Statistical Inference Group
