New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

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32 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS in some of our test cases they alter the relative peak intensities where subsequent analyses rely on (e.g. to obtain the relative compound concentrations correctly). This has also been found by by others (e.g. (Li et al., 2007)). Our preliminary experiments have shown that non-parametric techniques are more appropriate. Out of these approaches a wavelet shrinkage approach (for a review see (Taswell, 2000); a nice introduction can be found here (Louis et al., 1998)) has performed best on artificial data and data from spiked experiments where we knew the peak positions and intensities. This wavelet shrinkage approach has been reported to be very well suited for denoising of mass spectrometry data (see e.g. (Ojanen et al., 2004; Liu, Sera, Matsubara, Otsuka and Terabe, 2003; Coombes et al., 2005)). Opposed to other denoising algorithms, such as moving average or lowpass filter (e.g. Savitzky-Golay), this approach utilizes the multi-scale nature of the signal and therefore has better energy conservation properties, that is, the amplitude of the signal decreases less through denoising. The multi-scale method used here is based on a time-invariant discrete orthogonal wavelet transformation (Nason and Silverman, 1995) because orthogonal wavelets can give the most compact representation of a signal. During the wavelet transform at each scale high- and low-pass filters are applied to the signal. The output from a high-pass filter is recorded as the wavelet coefficients and represents the details of the signal. The low-pass filter extracts the low-frequency components which are used in the next stage where another set of high- and low-pass filters is employed. Wavelet shrinkage denoising does involve non-linear soft thresholding (shrinking) in the wavelet transform domain (Donoho, 1995). It is based on the assumption that wavelet coefficients of the true signal have high amplitude, opposed to the lowest magnitude coefficients that represent the noise (see Figure 3.3.5 for an example). Thus, by eliminating coefficients that are smaller than a predetermined threshold this noise can be removed. Summarized, it is a three step process: a linear forward wavelet transform, a non-linear shrinkage denoising of the resulting coefficients and a linear inverse wavelet transform. None of these steps needs a-priori parameterization of a particular model. We now give a more formal definition. We assume we are given a noisy signal (the raw data) X consisting of m (noisy) samples X(t) = S(t) + ɛ(t), t = 1 . . . m This raw signal X is assumed to contain the real signal S with additive noise ɛ. Let W(·) denote the forward and W −1 (·) the inverse wavelet transform operators and Ds(·, λ) be the denoising operator with a data adaptive soft threshold λ. Our aim is to denoise X to estimate ˆ S which should be as close as possible to the original signal S. The three step process mentioned above is then: � Linear forward wavelet transform: Y = W(X). This results in m noisy wavelet coefficients yj,k. � Non-linear shrinkage denoising, that is thresholding the wavelet coefficients which includes estimating the threshold λ = {λ1, . . . , λj} for each level j (see below) – λ = d(Y ) – Z = Ds(Y, λ)
3.3. PREPROCESSING 33 Figure 3.3.5: Noisy signal (top) and its discrete wavelet transform (using a Symmlet- 10) at level L = 6. The wavelet coefficients are shown as spikes for the levels (−6 . . .− 10). The size and direction a spike (coefficient) represent its magnitude and sign. � Linear inverse wavelet transform: ˆ S = W −1 (Z) Obviously, selecting the threshold λ is key to successful denoising. A global, non-adaptive λ to remove white noise is proposed by (Donoho, 1995): λ = σ · � 2 · log(m), σ = MAD 0.6745 where m is the length of the signal and MAD an estimator of the noise level determined by the median absolute deviation in the first scale (the constant 0.6745 makes the estimate unbiased for the normal distribution.). From the tested shrinkage schemas (VisuShrink universal, Minimax, Stein’s Unbiased Risk Estimate (SURE) and Minimum Description Length) the SURE approach (Stein, 1981; Donoho and Johnstone, 1995) was found to deliver the best results. It determines a threshold for each resolution level (scale) by the principle of minimizing the Stein Unbiased Estimate of Risk. This approach is smoothness-adaptive and has some interesting properties when used for the MALDI-TOF spectra that can contain spiky as well as smooth peaks: if the unknown signal S contains jumps, the reconstruction ˆ S does also and if S contains smooths regions ˆ S will be as smooth as the basis functions will allow. Figure 3.3.6 shows an example of this shrinkage applied to a usual MALDI- TOF spectrum. Experiments have shown, that de-noising the signal improves classification accuracy of spectra (at the final stage of our pipeline, see section 3.8.5) by 4-5% on average, given all other parameters being equal. This is in good accordance with other studies, for example (Li et al., 2007) who achieve an improvement of 3-8% on similar SELDI-TOF serum data. 3.3.5 Baseline Correction A baseline correction is performed to remove this rather low-frequency noise from the spectrum. Following (Breen et al., 2000; Sauve and Speed, 2004; Gröpl et al., 2005) we use a morphological TopHat filter (Zeng et al., 2006).
Page 1 and 2: New Statistical Algorithms for the
Page 3 and 4: Contents Acknowledgments . . . . .
Page 5 and 6: New Statistical Algorithms for the
Page 7 and 8: Extended Abstract English Version M
Page 9 and 10: German Version Das Gebiet der Prote
Page 11 and 12: Chapter 1 Introduction and Survey 1
Page 13 and 14: 1.2. GOALS, OBJECTIVES AND TASKS 7
Page 15 and 16: 1.2. GOALS, OBJECTIVES AND TASKS 9
Page 17 and 18: Chapter 2 Preliminaries 2.1 Topic O
Page 19 and 20: 2.1. TOPIC OVERVIEW 13 Figure 2.1.1
Page 21 and 22: 2.1. TOPIC OVERVIEW 15 completeness
Page 23 and 24: 2.2. AN EXAMPLE 17 (a) Opera A (b)
Page 25 and 26: 2.2. AN EXAMPLE 19 Figure 2.2.6: Tw
Page 27 and 28: 2.2. AN EXAMPLE 21 successes. We ca
Page 29 and 30: Chapter 3 Mathematical Modeling and
Page 31 and 32: 3.2. INTRODUCTION TO MALDI TOF MS 2
Page 37: 3.3. PREPROCESSING 31 mix (external
Page 41 and 42: 3.3. PREPROCESSING 35 Figure 3.3.7:
Page 43 and 44: 3.4. HIGHLY SENSITIVE PEAK DETECTIO
Page 49 and 50: 3.5. PEAK DETECTION IN 2D MAPS 43
Page 51 and 52: 3.6. PEAK REGISTRATION (ALIGNMENT)
Page 57 and 58: 3.7. IDENTIFYING POTENTIAL FEATURES
Page 63 and 64: 3.8. EXTRACTING FINGERPRINTS 57 Fig
Page 65 and 66: 3.8. EXTRACTING FINGERPRINTS 59 FID
Page 67 and 68: 3.8. EXTRACTING FINGERPRINTS 61 Dim
Page 69 and 70: 3.9. COMPLEXITY ANALYSIS 63 3.9 Com
Page 71 and 72: Chapter 4 (Bio-)Medical Application
Page 73 and 74: 4.1. DATA USED 67 4.1.2 Serum Data
Page 75 and 76: 4.2. STATISTICAL REMARKS 69 1. Vali
Page 77 and 78: 4.2. STATISTICAL REMARKS 71 Molar v
Page 79 and 80: 4.2. STATISTICAL REMARKS 73 � Fir
Page 81 and 82: 4.2. STATISTICAL REMARKS 75 Let ˆ
Page 83 and 84: 4.2. STATISTICAL REMARKS 77 the boo
Page 85 and 86: 4.3. STUDY RESULTS 79 Figure 4.3.3:
Page 87 and 88: 4.3. STUDY RESULTS 81 Figure 4.3.4:
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4.3. STUDY RESULTS 83 � kNN (gen.
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4.3. STUDY RESULTS 85 d(x, θi) =
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4.3. STUDY RESULTS 87 pairs of obje
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4.3. STUDY RESULTS 89 � “Peptid
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4.4. IDENTIFICATION OF PROTEOMIC FI
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4.6. BIOLOGICAL APPLICATIONS 101 4.
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Chapter 5 Computer Science Grid Str
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5.1. INTRODUCTION 105 � A node is
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5.1. INTRODUCTION 107 of and config
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5.1. INTRODUCTION 109 particular pr
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5.2. THE QUASI AD-HOC (QAD) GRID 11
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5.2. THE QUASI AD-HOC (QAD) GRID 11
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5.3. QAD GRID PLATFORM SERVER 115 F
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5.3. QAD GRID PLATFORM SERVER 117 j
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5.3. QAD GRID PLATFORM SERVER 119 (
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5.3. QAD GRID PLATFORM SERVER 121 p
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5.3. QAD GRID PLATFORM SERVER 123 D
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5.3. QAD GRID PLATFORM SERVER 125 F
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5.3. QAD GRID PLATFORM SERVER 127 t
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5.4. QAD GRID WORKER 129 field. A w
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5.4. QAD GRID WORKER 131 2. This re
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5.4. QAD GRID WORKER 133 Figure 5.4
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5.4. QAD GRID WORKER 135 Checkpoint
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5.4. QAD GRID WORKER 137 database b
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5.5. QAD GRID PLATFORM SERVICES 139
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5.6. QAD GRID WORKFLOWS 141 � Dat
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5.6. QAD GRID WORKFLOWS 143 Service
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5.6. QAD GRID WORKFLOWS 145 Figure
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5.7. RELATED WORK 147 to set-up sys
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5.7. RELATED WORK 149 Table 5.7.1 -
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Chapter 6 proteomics.net - Product-
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6.2. CASE STUDIES 153 6.2 Case Stud
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6.2. CASE STUDIES 155 Figure 6.2.2:
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6.2. CASE STUDIES 157 MASCOT and SE
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6.2. CASE STUDIES 159 The peak pick
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6.2. CASE STUDIES 161 first entry i
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6.2. CASE STUDIES 163 Approach Base
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6.2. CASE STUDIES 165 Figure 6.2.5:
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Chapter 7 Related Work In this chap
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Chapter 8 Conclusion and Future Dir
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8.3. FROM BIOMARKERS TO BIOPRINTS 1
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Appendix A Implementation Details T
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Appendix B Curriculum Vitae Name Ti
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References Aebersold, R. and Mann,
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REFERENCES 179 Breiman, L. (2001).
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REFERENCES 181 Downard, K. M. and M
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REFERENCES 183 Gillette, M. A., Man
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REFERENCES 185 Huyghe, E., Muller,
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REFERENCES 187 Kuijpens, J. L. P.,
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REFERENCES 189 McLachlan, S. M. and
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REFERENCES 191 Platt, J. C. (1999).
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REFERENCES 193 Stone, M. (1974). Cr
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REFERENCES 195 Washburn, M. P., Wol
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