njit-etd2003-081 - New Jersey Institute of Technology

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291 •"The Component Variances (Third Output)" •"Hotelling's T2 (Fourth Output)" The Principal Components (First Output) The first output of the princomp function, pcs, contains the 15 principal components. These are the linear combinations of the original variables that generate the new variables. 6. Let's look at the first three principal component vectors. >> p3=pcs(:,1:3) P3 = 0.2167 -0.1183 -0.1847 0.2066 -0.1977 -0.4588 0.2000 -0.2014 -0.4580 -0.2819 -0.3377 0.1507 -0.3001 0.1087 -0.3137 -0.2786 -0.3063 -0.1575 -0.2915 -0.0762 0.2091 -0.2585 0.3470 0.0879 -0.2663 0.3242 -0.1213 -0.3025 -0.3570 0.0794 -0.2793 0.1323 -0.3511 -0.2737 -0.2694 -0.2520 -0.2049 -0.3636 0.2074 -0.2168 0.2623 -0.0036 -0.2592 0.1920 -0.3122 >> The largest weights in the first column (first principal component) are the first and second elements, corresponding to the variables respiration and heart rate. To show the orthogonality of the principal components, note that premultiplying them by their transpose yields the identity matrix. >> I = p3'*p3
292 I= 1.0000 -0.0000 -0.0000 -0.0000 1.0000 -0.0000 -0.0000 -0.0000 1.0000 The Component Scores (Second Output) The second output, newdata, is the data in the new coordinate system defined by the principal components. This output is the same size as the input data matrix. 7. A plot of the first two columns of newdata shows the ratings data projected onto the first two principal components. >> plot(newdata(:,1),newdata(:,2),'+') >> xlabel('lst Principal Component'); >> ylabel('2nd Principal Component'); 8. The function gname is useful for graphically identifying a few points in a plot like this. You can call gname with a string matrix containing as many case labels as points in the plot. The string matrix names works for labeling points with the subject names. >> gname(names) Move your cursor over the plot and click once near each point at the top right. As you click on each point, MATLAB labels it with the proper row from the names string matrix. When you are finished labeling points, press the Return key. The labeled subjects are the normal subjects in data set. Perhaps one should consider them as a completely separate group. If gname is called without arguments, it labels each point with its row number. 9. One can create an index variable containing the row numbers of all the chosen normal subjects.
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Copyright Warning & Restrictions Th
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ABSTRACT TIME-FREQUENCY INVESTIGATI
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TIME-FREQUENCY INVESTIGATION OF HEA
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APPROVAL PAGE TIME-FREQUENCY INVEST
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BIOGRAPHICAL SKETCH (Continued) D.A
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ACKNOWLEDGMENT The author wishes to
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TABLE OF CONTENTS Chapter Page 1 IN
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TABLE OF CONTENTS (Continued) Chapt
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LIST OF FIGURES Figure Page 2.1 The
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LIST OF FIGURES (Continued) Figure
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LIST OF FIGURES (Continued) Figure
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ABBREVIATIONS A ABP Arterial Blood
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ABBREVIATIONS (Continued) P PID Pro
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2 mortality and sudden death. [2] B
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4 1) Patients with severe pulmonary
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6 examined for determining the inte
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8 identified using principal compon
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1 0 1. Present the application of t
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12 1.3 Outline of the Dissertation
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CHAPTER 2 PHYSIOLOGY BACKGROUND Bio
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16 Figure 2.2 The systemic and pulm
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18 illustrated in Figure 2.3. The i
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20 2.2 Blood Pressure The force tha
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22 2.4 The Nervous System Human beh
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24 The sympathetic nerve fibers lea
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26 Without these sympathetic and pa
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28 center in the medulla, which con
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30 Figure 2.6 Autonomic innervation
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32 average heart rate was measured
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34 However, they do note that there
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Figure 2.9 The placement of the pos
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38 female. While more men suffer fr
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40 Stage II: Moderate COPD - Worsen
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CHAPTER 3 ENGINEERING BACKGROUND Th
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44 Two common types of time-frequen
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46 STFT: Short-Time Fourier Transfo
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48 3.3 The Analytic Signal and Inst
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50 The advantage of using equation
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52 3.5 Covariance and Invariance Th
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where H(f), S(f) are Fourier transf
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56 Another shortcoming of the spect
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58 should take the kernel of the WD
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60 called the cross Wigner distribu
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62 3.6.3 The Choi-Williams (Exponen
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64 Figure 3.3 Performance of the Ch
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66 [-Ω,Ω ], then its STFT will be
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68 This condition forces that the w
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70 where c is a constant. Thus, the
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Figure 3.5 The time-frequency plane
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74 The measure dadb used in the tra
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76 and the wavelet transform repres
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78 Figure 3.6 Figure depicting the
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80 The final step to obtain the pow
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82 It should be noted that if the w
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84 The normal respiration rate can
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Figure 3.12 Power spectrum of BP II
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RR similar manner to give: When com
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90 when there is significant correl
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92 3.12 Partial Coherence Analysis
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94 after removal of the effects of
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96 The bulk of the theory and appli
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98 technique is measurement time. T
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100 usually attainable. The key poi
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102 variability exists in the propa
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104 eXogenous input (ARX) was used
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106 The baroreflex, an autonomic re
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108 the principal components are no
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110 The mathematical solution for t
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112 3.15 Cluster Analysis The term
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114 formed) one can read off the cr
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116 3.15.5 Squared Euclidian Distan
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118 Alternatively, one may use the
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120 Sneath and Sokal used the abbre
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122 may seem a bit confusing at fir
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CHAPTER 4 METHODS The purpose of th
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126 4.1.2.1 Autonomic Testing. HR V
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128 of heart rate, blood pressure,
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130 The patients who underwent LVRS
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132 panel of the Correct.vi. It was
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134 4.2.3 Power Spectrum Analysis o
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136 weighted-average value of the c
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138 For each given scale a within t
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140 frequency F to the wavelet func
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142 4.2.8 System Identification Ana
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144 In this study a simpler approac
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146 Table 4.2 Parameters That Make
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148 4.2.11 Cluster Analysis The sam
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150 viewing the time series of sequ
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Figure 5.2 BPV analysis of a COPD s
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Figure 5.3 HRV analysis of a normal
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Figure 5.4.1 Comparison of the HRV
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158 5.2 Time Frequency Analysis One
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Figure 5.5 Test signal with 3 sine
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162 Figure 5.6 (c) CWD of a signal
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164 Figure 5.7 (c) WT (dB4 wavelet)
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166 HRV more information about HRV
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168 Figure 5.9 (c) CWD plots of a n
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Figure 5.10 CWT (Morlet) HRV plot o
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172 The following figures show the
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174 Figure 5.15 CWT (Mexican Hat) H
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176 5.2.5 Best Wavelet Selection fo
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178 Table 5.1 Correlation Indices o
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180 5.2.6 Vagal Tone and Sympathova
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182 These figures basically show th
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184 Figure 5.20 Sympathetic and par
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188 5.2.7 Time-Frequency Analysis (
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190 Figure 5.29 3D and contour plot
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192 Figure 5.33 3D and contour plot
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Figure 5.44 Plot of raw respiration
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Figure 5.46 The LF partial coherenc
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Figure 5.48 HF partial coherence pl
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Table 5.2 Cross-Spectral Analysis o
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Table 5.3 Cross-Spectral Analysis o
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Figure 5.50 HF coherence of COPD (1
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212 For better presentation of the
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Figure 5.53 Coherence and partial c
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216 2. Interpretation of the transf
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218 covariances of the parameters,
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220 deviations are interpreted as A
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222 Figure 5.58 Bode plot of the HR
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224 In this section a simple model
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226 The data for all 47 COPD subjec
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228 Figure 5.60 Normal and COPD cla
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230 Figure 5.61 Normal and COPD cla
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232 Figure 5.62 Normal classificati
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234 5.7 Cluster Analysis The purpos
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236 Figure 5.64 Severity classifica
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238 both the normal and COPD subjec
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Page 271 and 272: APPENDIX A EXERCISE PHYSIOLOGY A.1
Page 273 and 274: 244 A.3 Figure Out Your Target Hear
Page 275 and 276: APPENDIX B ANALYSIS PROGRAM LISTING
Page 277 and 278: 248 4) Click on file, close to exit
Page 279 and 280: 250 • TN 11
Page 281 and 282: 252 B.1.2 Partial Coherence Between
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Page 285 and 286: 256 Block Diagram !rime of record K
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Page 289 and 290: 260 B.2.2 Time — Frequency Analys
Page 291 and 292: 262 This program provides the STFT
Page 293 and 294: 264 G(:j+1)=G(:,j+1)/(2*sum(G(:j+1)
Page 295 and 296: 266 T=(length(Signa)/sample)/(Times
Page 297 and 298: 268 subplot(3, 1,3), plot(T,E); xla
Page 299 and 300: 270 4. The program creates five out
Page 301 and 302: 272 B.2.3.4 Program to Generate Sym
Page 303 and 304: 274 ylabel('frequency'); title('Ins
Page 305 and 306: 276 The program will run and output
Page 307 and 308: 278 axis([0 1 0 2]); grid on; xlabe
Page 309 and 310: 280 vagal=sum(TFDs(HFC,1:k)); symto
Page 311 and 312: 282 plot(J,symtopar); %plot(A,symto
Page 313 and 314: 284 4. Remove the constant levels a
Page 315 and 316: 286 Make sure the agreement is quit
Page 317 and 318: 288 B.2.6 Principal Components Anal
Page 319: 290 Columns 12 through 15 'LF_pcoh_
Page 323 and 324: 294 variances = 3.4083 1.2140 1.141
Page 325 and 326: 296 B.2.7 Cluster Analysis Program
Page 327 and 328: 298 end [R,C]=size(Data); if length
Page 329 and 330: 300 B.2.8 Cross-correlation Program
Page 331 and 332: 302 C.3 Partial coherence of HR and
Page 333 and 334: 304 [13] Madwed, J., and R. Cohen.
Page 335 and 336: 306 [41] Mallat, S. G., "A Theory f
Page 337: [70] Tazebay, M.V., R.T. Saliba and
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