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

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82 CHAPTER 4. (BIO-)MEDICAL APPLICATIONS (a) Classification of class 1. (b) Classification of class 2. (c) Classification of both classes. Figure 4.3.5: A screenshot of a classification result. The green and red vertical bars reflect the value range of each feature in the respective green or red class. The boxes within this range show the 20% range around the average value (mid-point). Diamonds reflect the actual values (here peak heights) of a feature in a particular spectrum and lines connect the feature values for the same spectrum. For visualization purposes the lines are also dyed in the color of the class represented.
4.3. STUDY RESULTS 83 � kNN (gen.): Nearest-neighbor-like algorithm using non-nested generalized exemplars. (For more details see (Martin, 1995).) � ADTree: Class for generating an alternating decision tree. The basic algorithm is based on: (Freund and Mason, 1999). � Rand. Forest: Class for constructing a forest of random trees. (For more details see (Breiman, 2001).) � Bayes Net: Bayesian Network learning using the K2 hill climbing search algorithm. As mentioned earlier, other algorithms (more recent and/or complicated) could have been used as well. The main reason for using more established algorithms is that they are well studied and their properties are well understood. Each of these classification technique builds a particular model and optimizes the structure and parameters of this model using the 10-fold crossvalidation approach (see section 4.2.5). If the optimal structure / parameter set is found, this classifier is evaluated on the full data-set. This evaluation results in a quality value stating how many spectra were classified correctly. To ensure a statistical relevance we also create confidence intervals as described in section 4.2.5. 4.3.3 Fingerprints for Clustering The previous section introduced classification of unknown spectra based on fingerprint features. That is, based on a given set of peaks the classification algorithm assigns a probability value to each possible class the spectrum might stem from (e.g. “female” or “male”). The class having the highest probability values is then assigned to the spectrum. An implicit assumption here is that all spectra having assigned the same class have very similar features. While this is generally the case, further analyses show that a class can often be divided in smaller sub-classes, based on their feature similarity. This clustering approach often reveals groups of patients that have other common properties not explained by the actual class membership, such as age class, disease status or other medical treatment influencing blood proteins. Thus, we want to discover something about the nature of the class from which a sample arose - to discover whether the overall class is, in fact, heterogeneous. The next sections will first introduce some notations and presents a short overview of two widely used clustering methods, with a special emphasis on structural properties and implicit mathematical assumptions intrinsic for each of the methods. Subsequently, we show that for clustering high-dimensional spectra low-dimensional fingerprints are needed to achieve meaningful results. Cluster Distance Functional Let x ∈ X ⊂ R n be the observed n-dimensional data. In our case x would be a spectrum’s fingerprint, that is, a vector containing heights of n particular peaks. Our main goal is to partition data into K distinct groups (clusters) characterized by K distinct sets with a-priori unknown cluster parameters θ1, . . . , θK ∈ Ω ⊂ R d , (4.3.2)
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New Statistical Algorithms for the
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Contents Acknowledgments . . . . .
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New Statistical Algorithms for the
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Extended Abstract English Version M
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German Version Das Gebiet der Prote
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Chapter 1 Introduction and Survey 1
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1.2. GOALS, OBJECTIVES AND TASKS 7
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1.2. GOALS, OBJECTIVES AND TASKS 9
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Chapter 2 Preliminaries 2.1 Topic O
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2.1. TOPIC OVERVIEW 13 Figure 2.1.1
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2.1. TOPIC OVERVIEW 15 completeness
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2.2. AN EXAMPLE 17 (a) Opera A (b)
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2.2. AN EXAMPLE 19 Figure 2.2.6: Tw
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2.2. AN EXAMPLE 21 successes. We ca
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Chapter 3 Mathematical Modeling and
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3.2. INTRODUCTION TO MALDI TOF MS 2
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Page 73 and 74: 4.1. DATA USED 67 4.1.2 Serum Data
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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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