2 D wavelet analysis , 487

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1 Index 2 2 D wavelet analysis , 487 A Absolute distance to the model Aligned Vectors All data are needed... 19, 32 Alternating conditional expectations (ACE) Alternative to block scaling Alternative to variable selection Approaches to estimate non linearity Approaches to MSPC Assignable causes , 189 Assumptions of PLS Asymmetric case , 208 Autocorrelation function...309, 312, 317, 322 Automatic transformation Criteria Automatic transformation criteria Autoregressive Auto scaling... 36, 244 Autoscaling B Bandpass of frequencies Base level model , 360, 369, 370, 371 Basic assumption of SPC , 284 Batch Cross validation rules Batch duration and synchronization Batch level...291, 296, 299, 301 Batch processes... 88, 173, 189, 288, 289, 473, 481, 490 Batch project Cross validation rules Batch statistical process control... 4, 171, 283, 287 Batch variable importance , 304 Batch vectors Battery scaling Benefits of transformation Best basis Bimodality Block scaling Multi- and Megavariate Data Analysis Index 493

2 Blocks of logically related variables Blocks of variables Block scaling Block scaling , 253 C CA Calculation PLS Trees Scaling weight Categorical variable... 18, 373, 377, 383 Causal relationship... 20, 295 Causation... 20, 32 Chained filters Challenges of multivariate data Class Scaling Classical methods of statistics Classification of observations , 194, 209 Classification rate Cluster analysis Hierarchical HCA Overview PLS Trees References Cluster based design , 474 CoeffC CoeffCS Coefficients Background CoeffC CoeffMLR Rotated Scaled and centered Unscaled Y Related Profiles CoeffMLR CoeffRot COMFA Compare PLS with OPLS/O2PLS Concept of a model... 17, 28, 407 Conceptual basis of semi empirical modeling Confidence intervals Confidence Intervals... 31, 73, 85, 408, 419, 424 Confounding and/or undesirable variation Continuous variables... 18, 383 Contribution plot , 361, 362 Contribution tool Contribution based diagnostics Control chart Nomenclature and notation Statistics Target and standard deviation Controlled factors Index Multi- and Megavariate Data Analysis

3 Coomans plot , 206, 208 Correction factor , 452 Correlation and causation... 20, 32 Correspondence analysis... 54, 251, 252 Cosine of the angles COST approach... 17, 21, 32 Criteria automatic transformation Critical distance to the model Cross validation What is Cross validation rules Batches Non Significant Significant component Cross correlation function , 322 Cross validation (CV) is a practical Cross validation is known to face problems Cumulative explained variation Curved (non linear) relationships CuSum chart...273, 276, 282, 394 CV ANOVA Background Cylindrical tolerance volume D Data correction and compression Data preparation and standardization... 4 DCrit Degrees of non linearity , 384 Dendrogram Background Derivation of principal properties Design of experiments... 13, 17, 20, 22, 239, 241, 295, 301, 376, 474 Deterministic component Deviating time points Diagnose the process upset Diagnosing and handling non linearity Digitization Dimensionality problem Discontinuity Discrete factor Discrete wavelet transform Discriminant analysis... 1, 4, 88, 192, 203, 206, 208, 210, 477, 481 Discriminant Analysis models Cluster Analysis Disjoint class modelling Disjoint principal component Distance to model Absolute Background DModX predictionset Normalized Distance to the model... 8, 47, 78, 180, 197, 209, 263, 293, 382 Distinction between strong and moderate outliers Multi- and Megavariate Data Analysis Index 495

4 Distribution of the residuals , 236 Diverse sub set DMod Absolute Normalized Predictionset D optimal design Double centering E Effect of mean centering EWMA chart , 282, 394 Expanded terms scaling Expansion of the X matrix , 239, 242, 385 Experimental objectives Expert systems Explained variance... 49, 81 Explained variation of a variable Exploring process memory Exploring time series properties of scores Exponentially decreasing weights Extensions of PLS External RMSEP External validation , 165, 384, 419, 423 F Factor analysis... 1, 54, 305 Feed back controllers Feedback process control Feed back systems Filtering of data Final conditions of new batches Finite duration process Finite impulse response (FIR) model , 320 First PLS component... 58, 64, 65, 77, 81, 247, 375 First order filter EWMA Fisher's Exact test Fit Methods background Formulas and descriptions Formulating rules of classification Four levels of PAT Four levels of pattern recognition , 469 Fractional factorial design Full rank... 1, 20 G Genetic algorithms (GA) Geometric interpretation of PCA Geometry of PLS... 57, 63, 484 GIFI PLS , 375, 377, 378, 379, 380, 381, 384, 385 GOLPE Goodness of fit... 50, 52, 82, 419 Goodness of prediction... 50, 52, 82, 155, Index Multi- and Megavariate Data Analysis

5 GRID Group contribution plot H Hard block scaling HCA , 431 Hierarchical CA Cluster Analysis Hierarchical Cluster Analysis Hierarchical modelling Hierarchical PCA and PLS... 88, 355 Hierarchical PLS and PCA Higher order components... 43, 51, 66, 165, 185 Horseshoe problem Hotelling s T 2 tolerance ellipse Hotelling's T Hotelling's T2Range Calculation How many PLS components are really necessary I Identification of transfer function model Identifying contribution from variables Identifying the time series model Implementing CuSum Implementing EWMA Implicit non linear latent variable regression, INLR Implicit non linear latent variable regression, INLR , 376 Inclusion/exclusion of variables Increased interpretability Information scaling , 262 Inner relation... 64, 69, 77, 86, 88, 141, 184, 318, , 379, 382, 385, 415, 489 Inspection of time series properties Inspection of univariate statistics Intelligently selected observations... 1 Interpret the score plot Interpretation of refined model interpreting deviations intrinsic molecular properties Introduction to GIFI PLS Iterative nature of MVDA , 424 J Jack knifing K Karhunen Loeve expansion K dimensional space... 1, 28, 33, 37, 39 L Lag Scaling Multi- and Megavariate Data Analysis Index 497

6 Vectors Latent structure , 242 Latent variable (LV) regression Latent variable models... 2, 88, 149 Latent variable regression... 2, 73, 240, 376, 470 Lead optimization Leave one out approach Leverage... 46, 189, 253 Leverages Limitations of traditional calibration Linear combinations... 30, 53, 70, 85, 87, 312, 414 Linear discriminant analysis... 1, 213 Lipophilicity... 86, 132, 134, 138, 142, 473 Log transformation... 77, 233, 375, 410 Low dimensional plane M Main steps of GIFI PLS , 384 Main steps of multivariate calibration , 151 Main steps of multivariate characterization , 144 Main steps of MVDA Matrix of dummy variables , 209 Maximum covariance... 69, 414 Maximum variance direction Maximum variance least squares projection Mean centering... 34, 37, 38, 52, 57, 58, 63, 84, 153, 209, 233, 244, 246, 249, 253 Megavariate analysis... 1, 96, 118, 330, 356 Membership significance level Memory of the process Method of quantifying discrete changes Mild non linearity , 385 Missing data... 1, 7, 20, 22, 32, 56, 140, 171, 252, 257, 265, 288, 304, 370, 410 Missing value Correction factor Missing values correction factor Model concept... 28, 32 Model diagnostics... 50, 76, 82 Model plane... 27, 41, 43, 47, 164, 180 Model systems , 137 Model transparency Modeling power , 454 Moderate outliers... 46, 53, 78, 87, 173, 177, 179, 184, 189, 415 Modifications, GIFI I GIVI IV, of the methodology Monitoring Monitoring the state of the process Mother wavelet MPow , 454 MPow weighted DMod , 454 MPowX , 454 MTSA... 4, 307, 312, 314, 315, 317, 321 Multicollinearity... 20, 23, 32, 88, 135, 213 Multidimensional space... 23, 25, 32, 41 Multiple linear regression... 1, 20, 22, 87 Multiple responses Index Multi- and Megavariate Data Analysis

7 Multiplicative signal correction (MSC Multiresolution analysis Multivariate adaptive regression splines (MARS) Multivariate calibration... 2, 13, 37, 56, 57, 77, 88, 147, 152, 161, 163, 166, 171, 233, 246, 255, 256, 322, 373, 469, 474, 481, 485, 490 Multivariate characterization... 1, 2, 131, 137, 143, 171, 203, 248, 476, 484 Multivariate classification... 1, 4, 208 Multivariate CuSum charts Multivariate data analysis cycle Multivariate design , 139, 144, 423, 474, 479 Multivariate EWMA charts Multivariate normality Multivariate process modelling... 4, 171, 174, 189, 265 Multivariate Shewhart charts Multivariate statistical process control... 4, 171, 265, 269, 287, 483 Multivariate time series analysis... 4, 307, 322 Multi way techniques N Necessary condition for PLS DA Negative logarithm... 29, 234 Negatively (inversely) correlated Neural networks (NN) NIPALS... 56, 257 No scaling... 37, 243, 253 Nomenclature Control charts Non Significant component Non linear PLS... 88, 374, 375, 385, 471, 484 Non linear PLS , 375, 385 Non linearity Non linearity between X and Y... 77, 414 Normal distribution... 31, 234 Normal probability plot of residuals Normalized DMod Notation control charts Notation used in PCA Number of CV groups O O2PLS Background Hierarchical approach Orthogonal component Predictive component References with hierarchical Objectives of classification , 230 Observable group similarity , 231 Observation diagnostics... 46, 76 Observation Risk Observations Risk Observations and Loadings vectors Multi- and Megavariate Data Analysis Index 499

8 Observations are paired Occurrence of a special event , 284 One or several response variables One variable at a time On line PAT On line predictions... 15, 187, 304 OOC plot OPLS... 89, 90, 96, 97, 98, 100, 101, 107, 108, 112, 113, 114, 115, 117, 118, 119, 120, 122, 123, 125, 126, 128, 130, 427 OPLS/O2PLS Background Orthogonal component Predictive component References with hierarchical OPLS DA... 89, 215, 216 Optimal model dimensionality Orientation of the model plane Orientation of the obtained plane ORisk Orthogonal components , 112, 113, 114, 130 Orthogonal PLS Orthogonal PLS... 89, 117 Orthogonal PLS modeling Background Orthogonal component Predictive component References with hierarchical Orthogonal signal correction, OSC Out Of Control Summary Outlier handling P PARAFAC (parallel factor analysis Parametric release , 334 Pareto scaling , 246, 253 Partial least squares projections to latent structures... 5, 55, 255, 489 Partial Least Squares Projections to Latent Structures Path models Pattern recognition... 6, 192, 469, 486 PCA PCA diagnostics PCA for data overview PCR Peptide QSAR , 378, 380 Philosophy of local modelling Philosophy of model building PLS Time series analysis Trees Vs. OPLS/O2PLS What is? PLS prediction procedure Index Multi- and Megavariate Data Analysis

9 PLS regression coefficients...72, 207, 310, 313 PLS score plots... 67, 76, 141, 328, 385 PLS time series analysis...307, 310, 319, 321 PLS vs OPLS and O2PLS PLS weights... 56, 66, 70, 74, 141, 186, 245, 257, 292, 302, 318, 321, 328, 375, , 415 PLS with multiple responses PLS DA... 88, 203 PLS Trees Calculation What is? Positively correlated... 20, 42, 292 Practical rank... 2, 87 Prediction intervals in PLS Predictions for new observations Predictions of new observations , 424 Predictionset DMod Predictive component Predictive EWMA Predictive residual sum of squares... 52, 84, 420 Predictive validation , 419, 423 Preference mapping Pre processing of data... 57, 209, 252 Pre requisites of PAT Preserving batch direction Preserving variable direction Pre treatment of data Principal Component Analysis... 1, 4, 5, 26, 33, 53, 87, 89, 117, 131, 137, 323, 1, 425, 469, 478, 487 Principal component loadings Principal Component modeling Principal component regression Principal component regression, PCR Principal component scores... 45, 307, 322 Principal components analysis... 6, 26, 477, 489 Principle of analogy Principles of projections... 17, 23, 28, 32 Problems of process data , 265, 282 Process analytical technology... 4 Process Analytical Technology , 331 Process modeling... 55, 66 Process modelling... 3, 7, 171, 174, 189, 194, 204, 208, 241, 244, 265, 304, 322, 373, 412, 419 Process monitoring and optimization Process state visualisation Process status visualization... 20, 172, 326 Process upset , 361, 362 Product attributes , 267 Projection co ordinate Projection Methods... 1, 4, 5, 17, 20, 23, 30, 32, 57, 88, 89, 117, 150, 323, 1 Projection to latent structures Projections in higher dimensional space Projections to Latent Structures... 1, 4, 5, 55, 89, 117, 255, 323, 355 Properties of GIFI PLS Pure profile Pure spectral profiles , 106, 111 Multi- and Megavariate Data Analysis Index 501

10 Q Q , 449 Q2V , 449 Qualitative variable Quality control... 2, 9, 174, 419 Quantitative relation between X and Y... 70, 414 Quantitative sequence activity modelling Quantitative structure activity relationships... 56, 470, 483 Quantitative variable R R2V R2Vadj R2X R2Xadj R2Y R2Yadj Rationale of multivariate characterization Red in Transform page References Cluster analysis OPLS/O2PLS PLS time series Refined modelling with PCA or PLS Representative experiments , 239, 376 Representative set of observations... 30, 133, 135 Residual observation variance... 48, 80 Residual variable variance... 50, 81 Residual variable variation... 50, 81 Residual vector... 59, 62, 312 Response contour plot , 241, 328 Response contour plotting Response permutation and cross validation Response permutation testing , 422 Ridge regression Risk of spurious results RMSEcv RMSEE RMSEP , 458 Root cause Root mean square error of prediction Rotated coefficients Rotated regression coefficients , 106, 111, 112 Rotated regression coefficients... 97, 120 RR RSD S Savitsky Golay smoothing Scalability Scale page Background Lags Index Multi- and Megavariate Data Analysis

11 Scaling After changing observation selection Classes Expanded terms Lags Transformed variables Weight calculation Scaling and centering Scaling of data...34, 233, 243, 254 Scaling to unit variance... 36, 39, 53, 57, 63, 209, 233, 243, 245, 247, 253 Scope of SPC Score Vectors Score vector ua Score vectors ta Second PLS component... 65, 71, 83, 247 Secondary variation in X... 90, 113 Semi empirical modeling Sensitive to scaling Sequence data Set point , 374 Shewhart chart , 272, 276, 277, 413 Signal compression...233, 255, 257, 260 Signal correction... 57, 157, 233, 255, 407, 410, 474, 488, 490 Signal correction and compression...255, 256, 262, 410 Significance level membership Significant component SIMCA... 2, 47, 48, 52, 57, 69, 70, 97, 113, 118, 120, 121, 165, 196, 238, 258, 291, 300, 354, 389, 399, 411, 433 SIMCA method SIMCA methodology SIMCA offline SIMCA control SIMCA online SIMCA online software Similarity and class Simplified the response function Skewness of each variable S line...215, 218, 220, 222 Soft block scaling Soft independent modeling of class analogy Space filling designs Spectral data... 14, 61, 71, 153, 233, 255, 260 Spline PLS (SPLS) S plot...215, 220, 221, 468 Standard curve... 32, 147 Standard error Standard normal variate (SNV) correction State estimation Stationary , 144, 307, 309, 313, 318, 322 Statistical notes Steady state or dynamic conditions Step Response Plot Stochastic component Multi- and Megavariate Data Analysis Index 503

12 Strong non linearity Strong outliers... 46, 53, 161, 173, 177, 189, 253, 271, 320, 412 Structured noise , 104, 107 Structured noise Subgrouping , 282 Super variables Supervision of existing processes Support vector machines (SVM) SUS plot , 222, 403 T Target Control chart Target directed filtering Taylor series expansions Temporary process upsets... 48, 189 The asymmetric case , 208 Theoretical foundation... 31, 57, 407 Theoretical models Three factor mixture design Time Series Analysis References Time series data , 307, 310 Tolerance volume... 79, 85, 194, 205 Tolerance volumes... 78, 149, 194 Top level PLS model Training set selection , 139 Transfer function models Transform page coloring criteria Transformation of variables , 236, 242 Transformations... 34, 57, 204, 234, 238, 242, 262, 409 Transition from SPC to MSPC , 283 Trimming , 243, 252, 409 Two levels of batch modelling Types of data... 6, 16, 17, 190 Typical classification situations U Uncertainties Uncontrolled factors Uncorrelated responses... 73, 74, 416 Undesirable feature Unexplained variation Unified description of classical classification methods , 483 Unit variance (UV) scaling Univariate index Unrealistic model V Validate option in SIMCA Variable Importance Variable diagnostics... 49, 50, 76, Index Multi- and Megavariate Data Analysis

13 Variable influence on projection, VIP Variance covariance matrix... 1, 88 Vector Aligned Batch Function of component Function of lags Observations and Loadings Variables and scores Vectors available VIP Background Visualization of the correlation structure W Wavelet analysis , 255, 256, 474, 487 Wavelet packet transform Weighted averages... 53, 87, 269 Window into the three dimensional space Winsorizing...234, 243, 252, 409 X X and Y co ordinate systems X weight vectors wa Y Y orthogonal variation... 90, 115 Y Related Profiles Y weights ca Z Zeroing Zoom in/zoom out capability Zoom in/zoom out functionality Zooming in on highlighted samples Z scales Multi- and Megavariate Data Analysis Index 505