Dimensionality Reduction and Subspace Clustering in Mixed Reality for Condition Monitoring of High-Dimensional Production Data †
Abstract
:1. Introduction
- How can mixed reality be used to allow for quick insights into large datasets?
- How can more than three dimensions be visualized in a comprehensible manner?
- How can recommendations be automatically computed for the purpose to visually analyze industrial production systems more properly?
- Identification of clusters in the reduced dataset.
- Recognition of correlations between variables in the reduced dataset.
- the geometric structure of the objects,
- the configuration of the machine operator,
- measured values from sensors attached to the machine,
- and the quality report of the printed object.
2. Related Work
3. Fundamentals
3.1. Principal Component Analysis
- Subtraction of the average across each dimension
- Calculation of the covariance matrix
- Calculation of the eigenvectors and eigenvalues of the covariance matrix
- Definition of the number of components
- Calculation of the new and reduced dataset
3.2. Subspace Clustering
CLIQUE
4. Prototype
4.1. Dataset
- REQ1: High-dimensional datasets must be displayed in a way that existing clusters can be easily identified.
- REQ2: Data representation must be simplified as the application users are not necessarily data science experts.
- REQ3: A powerful overview feature must be provided to identify the relation between the datasets dimensions.
- REQ4: It must be possible to visualize more than three dimensions as well as to exchange dimensions in the visualization.
- REQ5: To enable REQ4 properly, the computational resources must be explicitly considered and well distributed.
- REQ6: Precise application feedback and easy input possibilities must be provided to accomplish an understandable data analysis workflow.
- REQ7: A recommender system should be provided that supports the decision making while accomplishing the complex process of identifying clusters.
4.2. The HoloLens
4.3. Graphical User Interface
- A negative variance is marked with a red edge.
- A positive variance is displayed with a green edge.
- The strength of a variable connection is visualized based on the opacity of each color, where the covariance intervals [0, 1] and [−1, 0] are mapped to the new opacity value in the range [0, 100%].
4.4. Backend
4.5. Automated Recommendations
4.5.1. Recommendations for Principal Component Analysis
Algorithm 1: Recommendation based on information loss. The information Loss is used to remove dimensions from the matrix. |
4.5.2. Recommendations for Subspace Clustering
- What is the largest cluster? This command highlights the clusters that cover the most units and lists all dimensions that are involved.
- How many clusters does {dimension} generate? This command searches the list of clusters and counts occurrences of clusters with respect to the selected dimension.
- What is the densest cluster? This command compares clusters in terms of data points in the cluster and reveals the one with the maximum number of points.
5. Discussion
6. Conclusions
Author Contributions
Conflicts of Interest
References
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Number of Jobs | 215 |
Mean of Number of Layers | 411,425 |
Variance of Number of Layers | 57,828 |
Data Format | XML |
Inertial Measurement Unit (IMU) | 1 |
Environmental Recognition Camera | 4 |
Depth Sensor | 1 |
RGB Camera | 2MP*1 |
Mixed-Reality Capture | 1 |
Microphone | 4(2*2) |
Ambient Light Sensor | 1 |
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Hoppenstedt, B.; Reichert, M.; Kammerer, K.; Probst, T.; Schlee, W.; Spiliopoulou, M.; Pryss, R. Dimensionality Reduction and Subspace Clustering in Mixed Reality for Condition Monitoring of High-Dimensional Production Data. Sensors 2019, 19, 3903. https://doi.org/10.3390/s19183903
Hoppenstedt B, Reichert M, Kammerer K, Probst T, Schlee W, Spiliopoulou M, Pryss R. Dimensionality Reduction and Subspace Clustering in Mixed Reality for Condition Monitoring of High-Dimensional Production Data. Sensors. 2019; 19(18):3903. https://doi.org/10.3390/s19183903
Chicago/Turabian StyleHoppenstedt, Burkhard, Manfred Reichert, Klaus Kammerer, Thomas Probst, Winfried Schlee, Myra Spiliopoulou, and Rüdiger Pryss. 2019. "Dimensionality Reduction and Subspace Clustering in Mixed Reality for Condition Monitoring of High-Dimensional Production Data" Sensors 19, no. 18: 3903. https://doi.org/10.3390/s19183903