njit-etd2003-081 - New Jersey Institute of Technology
njit-etd2003-081 - New Jersey Institute of Technology njit-etd2003-081 - New Jersey Institute of Technology
121 variables will simultaneously contribute to the uncovering of meaningful patterns of Figure 3.19 Contour graph of a two-way joining clustering. (From Statistic Manual, the SAS Institute, 2001). For example, returning to the example of Figure 3.19 above, the medical researcher may want to identify clusters of patients that are similar with regard to particular clusters of similar measures of physical fitness. The figure shows the 13 physical fitness patterns on the y axis and the different heart cases in the x axis. The measures of similarity or distance values are indicated by using various color intensities. The difficulty with interpreting these results may arise from the fact that the similarities between different clusters may pertain to (or be caused by) somewhat different subsets of variables. Thus, the resulting structure (clusters) is by nature not homogeneous. This
122 may seem a bit confusing at first, and, indeed, compared to the other clustering methods described (Joining (Tree Clustering) and K- means Clustering), two-way joining is probably the one least commonly used. However, some researchers believe that this method offers a powerful exploratory data analysis tool (for more information refer to the detailed description of this method in Hartigan [52]). 3.15.19 K-means Clustering This method of clustering is very different from the Joining (Tree Clustering) and Twoway Joining. Suppose that one already has the hypotheses concerning the number of clusters in one's cases or variables. The computer may be told to form exactly 3 clusters that are to be as distinct as possible. This is the type of research question that can be addressed by the k- means clustering algorithm. In general, the k-means method will produce exactly k different clusters of greatest possible distinction. In the physical fitness example (in Two-way Joining), the medical researcher may have a "hunch" from clinical experience that her heart patients fall basically into three different categories with regard to physical fitness. One might wonder whether this intuition can be quantified, that is, whether a k-means cluster analysis of the physical fitness measures would indeed produce the three clusters of patients as expected. If so, the means on the different measures of physical fitness for each cluster would represent a quantitative way of expressing the researcher's hypothesis or intuition (i.e., patients in cluster 1 are high on measure 1, low on measure 2, etc.).
- Page 99 and 100: 70 where c is a constant. Thus, the
- Page 101 and 102: Figure 3.5 The time-frequency plane
- Page 103 and 104: 74 The measure dadb used in the tra
- Page 105 and 106: 76 and the wavelet transform repres
- Page 107 and 108: 78 Figure 3.6 Figure depicting the
- Page 109 and 110: 80 The final step to obtain the pow
- Page 111 and 112: 82 It should be noted that if the w
- Page 113 and 114: 84 The normal respiration rate can
- Page 115 and 116: Figure 3.12 Power spectrum of BP II
- Page 117 and 118: RR similar manner to give: When com
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- Page 121 and 122: 92 3.12 Partial Coherence Analysis
- Page 123 and 124: 94 after removal of the effects of
- Page 125 and 126: 96 The bulk of the theory and appli
- Page 127 and 128: 98 technique is measurement time. T
- Page 129 and 130: 100 usually attainable. The key poi
- Page 131 and 132: 102 variability exists in the propa
- Page 133 and 134: 104 eXogenous input (ARX) was used
- Page 135 and 136: 106 The baroreflex, an autonomic re
- Page 137 and 138: 108 the principal components are no
- Page 139 and 140: 110 The mathematical solution for t
- Page 141 and 142: 112 3.15 Cluster Analysis The term
- Page 143 and 144: 114 formed) one can read off the cr
- Page 145 and 146: 116 3.15.5 Squared Euclidian Distan
- Page 147 and 148: 118 Alternatively, one may use the
- Page 149: 120 Sneath and Sokal used the abbre
- Page 153 and 154: CHAPTER 4 METHODS The purpose of th
- Page 155 and 156: 126 4.1.2.1 Autonomic Testing. HR V
- Page 157 and 158: 128 of heart rate, blood pressure,
- Page 159 and 160: 130 The patients who underwent LVRS
- Page 161 and 162: 132 panel of the Correct.vi. It was
- Page 163 and 164: 134 4.2.3 Power Spectrum Analysis o
- Page 165 and 166: 136 weighted-average value of the c
- Page 167 and 168: 138 For each given scale a within t
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- Page 171 and 172: 142 4.2.8 System Identification Ana
- Page 173 and 174: 144 In this study a simpler approac
- Page 175 and 176: 146 Table 4.2 Parameters That Make
- Page 177 and 178: 148 4.2.11 Cluster Analysis The sam
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- Page 181 and 182: Figure 5.2 BPV analysis of a COPD s
- Page 183 and 184: Figure 5.3 HRV analysis of a normal
- Page 185 and 186: Figure 5.4.1 Comparison of the HRV
- Page 187 and 188: 158 5.2 Time Frequency Analysis One
- Page 189 and 190: Figure 5.5 Test signal with 3 sine
- Page 191 and 192: 162 Figure 5.6 (c) CWD of a signal
- Page 193 and 194: 164 Figure 5.7 (c) WT (dB4 wavelet)
- Page 195 and 196: 166 HRV more information about HRV
- Page 197 and 198: 168 Figure 5.9 (c) CWD plots of a n
- Page 199 and 200: Figure 5.10 CWT (Morlet) HRV plot o
121<br />
variables will simultaneously contribute to the uncovering <strong>of</strong> meaningful patterns <strong>of</strong><br />
Figure 3.19 Contour graph <strong>of</strong> a two-way joining clustering. (From Statistic Manual, the<br />
SAS <strong>Institute</strong>, 2001).<br />
For example, returning to the example <strong>of</strong> Figure 3.19 above, the medical<br />
researcher may want to identify clusters <strong>of</strong> patients that are similar with regard to<br />
particular clusters <strong>of</strong> similar measures <strong>of</strong> physical fitness. The figure shows the 13<br />
physical fitness patterns on the y axis and the different heart cases in the x axis. The<br />
measures <strong>of</strong> similarity or distance values are indicated by using various color intensities.<br />
The difficulty with interpreting these results may arise from the fact that the similarities<br />
between different clusters may pertain to (or be caused by) somewhat different subsets<br />
<strong>of</strong> variables. Thus, the resulting structure (clusters) is by nature not homogeneous. This
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