Multidimensional Visualization and Clustering of Historical Process Data

Abstract

Multivariate statistical analysis using principal components can reveal patterns and structures within a data set and give insights into process performance and operation. The output medium is usually a two dimensional screen, however, so it is a challenge to visualize the multidimensional structure of a data set by means of a two-dimensional plot. A method of visualization is described in the form of a hierarchical classification tree that can be used to view the structure within a multivariate principal component model of three or more dimensions. The tree is generated from an unsupervised agglomerative hierarchical clustering algorithm which operates in the score space of the principal component model, and a recursive algorithm to draw the tree. It is readily adaptable to a wide range of multivariate analysis applications including process performance analysis and process or equipment auditing. Its application are illustrated with industrial data sets.

Integration of stochastic simulation with multivariate analysis: Short‐term facility fit prediction

“…Methods for principal component analysis have been widely documented. The method used in this article was derived from Thornhill et al and uses singular value decomposition. The output data from the simulations were first transformed by mean centering and stored as a comma separated variable file which was then imported.…”

“…re‐routing to larger tanks) and the Monte Carlo simulations were repeated with the improved process. The complexity of each dataset was then reduced using principal component analysis combined with clustering to reduce the dimensionality and eliminate noise . The results were compared to assess the impact of the process change.…”

“…Although PCA might reduce hundreds of datasets to a few principal components, it does not automatically identify clusters of batches with similar characteristics for further examination. Hence in this article, algorithms adapted from Thornhill et al are used to achieve hierarchical and k ‐means clustering of the datasets so as to identify significant clusters of batches. Multidimensional visualization of each cluster's characteristics in terms of the raw data (e.g.…”

Nearest neighbors method for detecting transient disturbances in process and electromechanical systems

“…Other measures reported in the literature include the cosine similarity [21] and related correlation measure [22], and Dynamic Time Warp (DTW) [23]. However, these measures have properties which are less desirable for the detection of transient disturbances.…”

Evaluating and Visualizing the Cost‐Effectiveness and Robustness of Biopharmaceutical Manufacturing Strategies

“…Stonier et al [13] describe work where a database -driven simulation tool is used to mimic the stochastic nature of industrial mAb manufacturing processes when transferred to large -scale facilities using Monte Carlo simulation. The complexity of each dataset was then reduced using PCA combined with clustering to reduce the dimensionality and eliminate noise [17] . The tool predicted an unacceptable likelihood of product loss upon the transfer.…”