# Explorative Multidimensional Analysis for Energy Efficiency: DataViz versus Clustering Algorithms

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## Abstract

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## 1. Introduction

#### 1.1. Motivation and Problem Identification

#### 1.2. Current Paper Aim and Structure

## 2. Large Scale Buildings Energy Monitoring Methods

#### 2.1. Data Visualization

#### 2.1.1. The Scatter Plot Matrix

#### 2.1.2. The Parallel Coordinates

#### 2.2. Data Clustering Algorithms

#### 2.2.1. Distance Metrics

#### 2.2.2. Evaluation

- (i)
- The within-cluster sum of square [54]$${Q}_{T}=\frac{1}{k}\sum _{j=1}^{k}{\sigma}_{j}=\frac{1}{k}\sum _{j=1}^{k}\sum _{i=1}^{|{Z}_{j}|}\frac{d({x}_{i}^{j},{c}_{j})}{|{Z}_{j}|}$$
- (ii)
- The Davies–Bouldin index [55]$$DB=\frac{1}{k}\sum _{i=1}^{k}\underset{i\ne j}{max}\left(\right)open="("\; close=")">\frac{{\sigma}_{i}+{\sigma}_{j}}{d\left(\right)open="("\; close=")">{c}_{i},{c}_{j}}$$
- (iii)
- The silhouette index [56]$$S=\frac{1}{k}\sum _{j=1}^{k}{S}_{j}=\frac{1}{k}\sum _{j=1}^{k}\frac{1}{|{Z}_{j}|}\sum _{i=1}^{|{Z}_{j}|}\frac{{b}_{i}^{j}-{a}_{i}^{j}}{max\left(\right)open="["\; close="]">{a}_{i}^{j},{b}_{i}^{j}}$$$${a}_{i}^{j}=\frac{1}{|{Z}_{j}|}\sum _{l=1,l\ne i}^{|{Z}_{j}|}d\left(\right)open="("\; close=")">{x}_{i},{x}_{l}$$

#### 2.2.3. Clustering Algorithms

## 3. Methodology

#### 3.1. Dataset and Indices Description

#### 3.2. k-Means Algorithm

## 4. Results

#### 4.1. Cluster Identification

#### 4.1.1. Cluster Hypothesis

#### 4.1.2. Data Visualization Techniques

#### 4.1.3. Clustering Algorithm

#### 4.1.4. Comparison between DataViz and k-Means Clusters

#### 4.2. Setting Thresholds

#### 4.3. Monitoring Trends

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

## List of Abbreviations

GHG | Greenhouse Gas |

HVAC | Heating, ventilating and conditiong |

TRNSYS | Transient System Simulation Tool |

EEI | Energy Efficiency Index |

DataViz | Data Visualization |

TOE | Tonne of oil equivalent |

kWh | Kilowatt hour |

WSS | Within-Cluster Sum of Square |

$X,A,B$ | Multidimensional Dataset |

n | Number of elements in dataset X |

m | Number of attributes/dimensions of dataset X |

${x}_{i}$ | Observation i of dataset X |

${x}_{ij}$ | Real value of attribute j of observation i |

$i,l$ | Observation subscript |

${D}_{il}$ | Minkowski (or Mahalanobis) distance between observation i and l |

p | Minkowski order |

${J}_{\delta}\left(\right)open="("\; close=")">A,B$ | Jaccard Distance |

${Q}_{T}$ | Within-Cluster Sum of Square |

$DB$ | Davies-Bouldin Index |

S | Silhouette Index |

k | Number of Clusters |

${x}_{i}^{j}$ | Observation i lying in cluster j |

${c}_{x}$ | The centroid of the cluster x |

${\sigma}_{x}$ | Mean distance between any data in cluster x and the centroid of the cluster |

$|{Z}_{x}|$ | Number of points in cluster |

$d\left(\right)open="("\; close=")">{x}_{i},{x}_{j}$ | distance between points ${x}_{i}$ and ${x}_{j}$ |

${x}_{min,j},{x}_{max,j}$ | Alert thresholds for attribute j |

$EE{I}_{year,kWh,night/day}$ | Annual night/day Electrical Energy Efficiency Index |

${E}_{i,kWh,day}$ | Electrical energy consumption during working day for month i |

${E}_{i,kWh,night}$ | Electrical energy consumption during night and weekend for month i |

## References

- Powell, J.B. Green Building Services. J. Int. Commer. Econ.
**2015**. [Google Scholar] - Wilkinson, P.; Smith, K.; Beevers, S.; Tonne, C.; Oreszczyn, T. Energy, energy efficiency, and the built environment. Lancet
**2007**, 370, 1175–1187. [Google Scholar] [CrossRef] - Newman, P. The environmental impact of cities. Environ. Urban.
**2006**, 18, 275–295. [Google Scholar] [CrossRef] - Staff, I.E.A. Transition to Sustainable Buildings: Strategies and Opportunities To 2050; Organization for Economic Cooperation and Development: Paris, France, 2013. [Google Scholar]
- Lombardi, P.; Trossero, E. Beyond energy efficiency in evaluating sustainable development in planning and the built environment. Int. J. Sustain. Build. Technol. Urban Dev.
**2013**, 4, 274–282. [Google Scholar] [CrossRef] - Brandon, P.S.; Lombardi, P.; Shen, G.Q. Future Challenges in Evaluating and Managing Sustainable Development in the Built Environment; John Wiley & Sons: Southern Gate, Chichester, UK, 2017. [Google Scholar]
- Ascione, F.; Bianco, N.; Stasio, C.D.; Mauro, G.M.; Vanoli, G.P. Addressing Large-Scale Energy Retrofit of a Building Stock via Representative Building Samples: Public and Private Perspectives. Sustainability
**2017**, 9, 940. [Google Scholar] [CrossRef] - Giuseppina, C.; Galatioto, A.; Ricciu, R. Energy and economic analysis and feasibility of retrofit actions in Italian residential historical buildings. Energy Build.
**2016**, 128, 649–659. [Google Scholar] - Bakar, N.N.A.; Hassan, M.Y.; Abdullah, H.; Rahman, H.A.; Abdullah, M.P.; Hussin, F.; Bandi, M. Sustainable energy management practices and its effect on EEI: A study on university buildings. In Proceedings of the Global Engineering, Science and Technology Conference, Dubai, UAE, 1–2 April 2013. [Google Scholar]
- Moghimi, S.F.A.; Mat, S.; Lim, C.; Salleh, E.; Sopian, K. Building energy index and end-use energy analysis in large-scale hospitals case study in Malaysia. Energy Effic.
**2014**, 7, 243–256. [Google Scholar] [CrossRef] - González, A.B.R.; Díaz, J.J.V.; Caamano, A.J.; Wilby, M.R. Towards a universal energy efficiency index for buildings. Energy Build.
**2011**, 43, 980–987. [Google Scholar] [CrossRef] - Ballarini, I.; Corgnati, S.P.; Corrado, V. Use of reference buildings to assess the energy saving potentials of the residential building stock: The experience of TABULA project. Energy Policy
**2014**, 68, 273–284. [Google Scholar] [CrossRef] - Andaloro, A.P.; Salomone, R.; Ioppolo, G.; Andaloro, L. Energy certification of buildings: A comparative analysis of progress towards implementation in European countries. Energy Policy
**2010**, 38, 5840–5866. [Google Scholar] [CrossRef] - Galatioto, A.; Ciulla, G.; Ricciu, R. An overview of energy retrofit actions feasibility on Italian historical buildings. Energy
**2017**, 137, 991–1000. [Google Scholar] [CrossRef] - Ciulla, G.; Lo Brano, V.; D’Amico, A. Modelling relationship among energy demand, climate and office building features: A cluster analysis at European level. Appl. Energy
**2016**, 183, 1021–1034. [Google Scholar] [CrossRef] - Yun, G.; Steemers, K. Behavioural, physical and socio economic factors in household cooling energy consumption. Appl. Energy
**2011**, 88, 2191–2200. [Google Scholar] [CrossRef] - Wu, L.-M.; Chen, B.-S. Modeling of energy efficiency indicator for semi-conductor industry. In Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management, Singapore, 2–4 December 2007; IEEE: Piscataway, NJ, USA, 2007. [Google Scholar]
- Ferrer-Balas, D.; Lozano, R.; Huisingh, D.; Buckland, H.; Ysern, P.; Zilahy, G. Going beyond the rhetoric: System-wide changes in universities for sustainable societies. J. Clean. Prod.
**2010**, 18, 607–610. [Google Scholar] [CrossRef] - Agdas, D.; Srinivasan, R.; Frost, K.; Masters, F. Energy Use Assessment of Educational Buildings: Toward a Campus-wide Sustainable Energy Policy. Sustain. Cities Soc.
**2015**, 17, 15–21. [Google Scholar] [CrossRef] - Chung, M.; Rhee, E. Potential opportunities for energy conservation in existing buildings on university campus: A field survey in Korea. Energy Build.
**2014**, 78, 176–182. [Google Scholar] [CrossRef] - Escobedo, A.; Briceño, S.; Juárez, H.; Castillo, D.; Imaz, M.; Sheinbaum, C. Energy consumption and GHG emission scenarios of a university campus in Mexico. Energy Sustain. Dev.
**2014**, 18, 49–57. [Google Scholar] [CrossRef] - Evans, J.; Jones, R.; Karvonen, A.; Millard, L.; Wendler, J. Living labs and co-production: University campuses as platforms for sustainability science. Curr. Opin. Environ. Sustain.
**2015**, 16, 1–6. [Google Scholar] [CrossRef] - Robinson, O.; Kemp, S.; Williams, I. Carbon management at universities: A reality check. J. Clean. Prod.
**2014**, 106, 109–118. [Google Scholar] [CrossRef] - Del Mar Alonso-Almeida, M.; Marimon, F.; Casani, F.; Rodriguez-Pomeda, J. Diffusion of sustainability reporting in universities: Current situation and future perspectives. J. Clean. Prod.
**2015**, 106, 144–154. [Google Scholar] [CrossRef] - Lauder, A.; Sari, R.F.; Suwartha, N.; Tjahjono, G. Critical review of a global campus sustainability ranking: GreenMetric. J. Clean. Prod.
**2015**, 108, 852–863. [Google Scholar] [CrossRef] - NBS. China Statistical Yearbook; Technical Report; China Statistics Press: Beijing, China, 2012. [Google Scholar]
- Shriberg, M. Institutional assessment tools for sustainability in higher education: Strengths, weaknesses, and implications for practice and theory. Int. J. Sustain. High. Educ.
**2002**, 3, 254–270. [Google Scholar] [CrossRef] - Haas, R. Energy efficiency indicators in the residential sector: What do we know and what has to be ensured? Energy Policy
**1997**, 25, 789–802. [Google Scholar] [CrossRef] - Jollands, N.; Patterson, M. Four theoretical issues and a funeral: Improving the policy-guiding value of eco-efficiency indicators. Int. J. Environ. Sustain. Dev.
**2004**, 3, 235–261. [Google Scholar] [CrossRef] - Sonetti, G.; Lombardi, P.; Chelleri, L. True Green and Sustainable University Campuses? Toward a Clusters Approach. Sustainability
**2016**, 8. [Google Scholar] [CrossRef] - Yik, F.; Burnett, J.; Prescott, I. Predicting air-conditioning energy consumption of a group of buildings using different heat rejection methods. Energy Build.
**2001**, 33, 151–166. [Google Scholar] [CrossRef] - Howard, B.; Parshall, L.; Thompson, J.; Hammer, S.; Dickinson, J.; Modi, V. Spatial distribution of urban building energy consumption by end use. Energy Build.
**2012**, 45, 141–151. [Google Scholar] [CrossRef] - Yang, C.; Létourneau, S.; Guo, H. Developing Data-driven Models to Predict BEMS Energy Consumption for Demand Response Systems. In Modern Advances in Applied Intelligence; Ali, M., Pan, J.S., Chen, S.M., Horng, M.F., Eds.; Springer International Publishing: Cham, Switzerland, 2014; pp. 188–197. [Google Scholar]
- Hong, T.; Yang, L.; Hill, D.; Feng, W. Data and analytics to inform energy retrofit of high performance buildings. Appl. Energy
**2014**, 126, 90–106. [Google Scholar] [CrossRef] - Yalcintas, M. An energy benchmarking model based on artificial neural network method with a case example for tropical climates. Int. J. Energy Res.
**2006**, 30, 1158–1174. [Google Scholar] [CrossRef] - Yalcintas, M.; Ozturk, U.A. An energy benchmarking model based on artificial neural network method utilizing US Commercial Buildings Energy Consumption Survey (CBECS) database. Int. J. Energy Res.
**2007**, 31, 412–421. [Google Scholar] [CrossRef] - Fan, C.; Xiao, F.; Wang, S. Development of prediction models for next-day building energy consumption and peak power demand using data mining techniques. Appl. Energy
**2014**, 127, 1–10. [Google Scholar] [CrossRef] - Inselberg, A. Multidimensional Detective. In Proceedings of the IEEE Symposium on Information Visualization, Phoenix, AZ, USA, 20–21 October 1997. [Google Scholar]
- Card, S.K.; Mackinlay, J.; Shneiderman, B. Readings in Information Visualization: Using Vision to Think; Morgan Kaufman: San Francisco, CA, USA, 1999. [Google Scholar]
- NIST-SEMATECH. E-Handbook of Statistical Methods; NIST: Gaithersburg, MD, USA, 1997.
- Bostock, M.; Ogievetsky, V.; Heer, J. D3: Data-Driven Documents. IEEE Trans. Vis. Comput. Graph.
**2011**, 12, 2301–2309. [Google Scholar] [CrossRef] [PubMed] - Bezanson, J.; Edelman, A.; Karpinski, S.; Shah, V.B. Julia: A fresh approach to numerical computing. arXiv, 2014; arXiv:1411.1607. [Google Scholar]
- Keim, D. Visual Techniques for Exploring Databases; Technical Report; NIST: Gaithersburg, MD, USA, 2003. [Google Scholar]
- Inselberg, A. The plane with parallel coordinates. Vis. Comput.
**1985**, 1, 69–97. [Google Scholar] [CrossRef] - Feiner, S.; Beshers, C. Worlds within worlds: Metaphors for exploring n-dimensional virtual worlds. In Proceedings of the 3rd Annual ACM SIGGRAPH Symposium on User Interface Software and Technology, Snowbird, UT, USA, 3–5 October 1990; pp. 76–83. [Google Scholar]
- Cleveland, W. Visualizing Data; Hobart Press: Summit, NJ, USA, 1993. [Google Scholar]
- Borg, I.; Groenen, P.J.F. Modern Multidimensional scaling: Theory and Applications. Vis. Comput.
**2005**, 2, 276–278. [Google Scholar] [CrossRef] - Keller, P.R.; Keller, M.M. Visual Cues-Practical Data Visualization. IBM Syst. J.
**1993**, 33. [Google Scholar] [CrossRef] - Ariaudo, F.; Balsamelli, L.; Corgnati, S.P. Il Catasto Energetico dei Consumi come strumento di analisi e programmazione degli interventi per il miglioramento dell’efficienza energetica di ampi patrimoni edilizi. In Proceedings of the 48th International Conference AICARR, Baveno, VCO, Italy, 22–23 September 2011; pp. 547–559. [Google Scholar]
- Cottafava, D.; Gambino, P.; Baricco, M.; Tartaglino, A. Multidimensional analysis tools for energy efficiency in large building stocks. In Proceedings of the 12th Conference on Sustainable Development of Energy, Water and Environment Systems, Dubrovnik, Croatia, 4–8 October 2017. [Google Scholar]
- Jain, A.; Dubes, R. Algorithms for Clustering Data; Prentice-Hall: Upper Saddle River, NJ, USA, 1988. [Google Scholar]
- Xu, R.; Wunsch, D. Survey of clustering algorithms. IEEE Trans. Neural Netw.
**2005**, 16, 645–678. [Google Scholar] [CrossRef] [PubMed] - Xu, D.; Tian, Y. A Comprehensive Survey of Clustering Algorithms. Ann. Data Sci.
**2015**, 2, 165–193. [Google Scholar] [CrossRef] - Kassambara, A. Practical Guide To Cluster Analysis in R; CreateSpace: North Charleston, SC, USA, 2017. [Google Scholar]
- Maulik, U.; Bandyopadhyay, S. Performance evaluation of some clustering algorithms and validity indices. IEEE Trans. Pattern Anal. Mach. Intell.
**2002**, 24, 1650–1654. [Google Scholar] [CrossRef] - Starczewski, A.; Krzyżak, A. Performance Evaluation of the Silhouette Index. In Artificial Intelligence and Soft Computing; Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., Eds.; Springer International Publishing: Cham, Switzerland, 2015; pp. 49–58. [Google Scholar]
- Rand, W.M. Objective Criteria for the Evaluation of Clustering Methods. J. Am. Stat. Assoc.
**1971**, 66, 846–850. [Google Scholar] [CrossRef] - Kosub, S. A note on the triangle inequality for the Jaccard distance. arXiv, 2016; arXiv:1612.02696. [Google Scholar]
- Fowlkes, E.B.; Mallows, C.L. A Method for Comparing Two Hierarchical Clusterings. J. Am. Stat. Assoc.
**1983**, 78, 553–569. [Google Scholar] [CrossRef] - Nagpal, A.; Jatain, A.; Gaur, D. Review based on data clustering algorithms. In Proceedings of the 2013 IEEE Conference on Information Communication Technologies, Thuckalay, Tamil Nadu, India, 11–12 April 2013; pp. 298–303. [Google Scholar]
- Ahmad, A.; Dey, L. A K-mean Clustering Algorithm for Mixed Numeric and Categorical Data. Data Knowl. Eng.
**2007**, 63, 503–527. [Google Scholar] [CrossRef] - Macqueen, J. Some methods for classification and analysis of multivariate observations. In Proceedings of the 5-th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA, 21 June–18 July 1967; pp. 281–297. [Google Scholar]
- Park, H.; Jun, C. A simple and fast algorithm for K-medoids clustering. Expert Syst. Appl.
**2009**, 36, 3336–3341. [Google Scholar] [CrossRef] - Kaufman, L.; Rousseeuw, P. Partitioning around Medoids (Program Pam); Wiley: Hoboken, NJ, USA, 1990; pp. 126–160. [Google Scholar]
- Ng, R.T.; Jiawei, H. CLARANS: A method for clustering objects for spatial data mining. IEEE Trans. Knowl. Data Eng.
**2002**, 14, 1003–1016. [Google Scholar] [CrossRef] - Kaufman, L.; Rousseeuw, P. Partitioning around Medoids (Program Pam); Wiley: Hoboken, NJ, USA, 1990; pp. 68–120. [Google Scholar]
- Guha, S.; Rastogi, R.; Shim, K. CURE: An Efficient Clustering Algorithm for Large Data sets. In Proceedings of the ACM SIGMOD Conference, Seattle, WA, USA, 2–4 June 1998. [Google Scholar]
- Zhang, T.; Ramakrishnan, R.; Livny, M. BIRCH: An efficient data clustering method for very large databases. In Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD), Montreal, QC, Canada, 4–6 June 1996; pp. 103–114. [Google Scholar]
- Karypis, G.; Han, E.H.; Kumar, V. Chameleon: Hierarchical clustering using dynamic modeling. Computer
**1999**, 32, 68–75. [Google Scholar] [CrossRef] - Ketchen, J.D.; Shook, C.L. The application of cluster analysis in strategic management reasearch: An analysis and critique. Strateg. Manag. J.
**1996**, 17, 441–458. [Google Scholar] [CrossRef] - Thorndike, R.L. Who belongs in the family? Psychometrika
**1953**, 18, 267–276. [Google Scholar] [CrossRef] - Pollard, K.S.; Van Der Laan, M.J. A method to identify significant clusters in gene expression data. In Proceedings of the SCI (World Multiconference on Systemics, Cybernetics and Informatics), Orlando, FL, USA, 14–18 July 2002; Volume 2, pp. 318–325. [Google Scholar]
- Tibshirani, R.; Walther, G.; Hastie, T. Estimating the number of clusters in a data set via the gap statistic. J. R. Stat. Soc. Ser. B (Stat. Methodol.)
**2001**, 63, 411–423. [Google Scholar] [CrossRef] - Sheikholeslami, G.; Chatterjee, S.; Zhang, A. Wavecluster: A Multi-Resolution Clustering Approach for Very Large Spatial Databases. VLDB
**1998**, 98, 428–439. [Google Scholar] - Smyth, P. Clustering Using Monte Carlo Cross-Validation. In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, KDD’96, Portland, Oregon, 2–4 August 1996; Volume 1, pp. 26–133. [Google Scholar]
- Monti, S.; Tamayo, P.; Mesirov, J.; Golub, T. Consensus clustering: A resampling-based method for class discovery and visualization of gene expression microarray data. Mach. Learn.
**2003**, 52, 91–118. [Google Scholar] [CrossRef] - Roth, V.; Lange, T.; Braun, M.; Buhmann, J. A resampling approach to cluster validation. In Compstat; Springer: Heidelberg, Germany, 2002; pp. 123–128. [Google Scholar]
- Wang, J. Consistent selection of the number of clusters via crossvalidation. Biometrika
**2010**, 97, 893–904. [Google Scholar] [CrossRef] - Cottafava, D.; Gambino, P.; Baricco, M.; Tartaglino, A. Energy efficiency in a large university: The UniTo experience. In Proceedings of the Sustainable Built Environment. Towards Post Carbon Cities, Turin, Italy, 18–19 February 2016; pp. 92–101. [Google Scholar]

**Figure 1.**Scatter plot matrix for the Unito’s buildings stock with respect to four attributes: type of building (1–9), the night/day energy efficiency index, the energy consumption per user and the energy consumption per square meter.

**Figure 2.**Parallel coordinates method for the Unito’s buildings stock for two building functions—(

**a**) Humanities Depts. and (

**b**) Agrarian Depts.—with respect to four attributes: type of building (1–9), the night/day energy efficiency index, absolute annual energy consumption and the energy consumption per square meter.

**Figure 3.**Elbow method. The plot shows within-cluster sum of square vs. k ($n.$ of clusters). The right k number is between 9 and 10.

**Figure 4.**Interactive data visualization tool to monitor historical trends based on the Parallel Coordinates method.

k | WSS | DB Index | Sil Index |
---|---|---|---|

3 | 0.597 | 2.165 | 0.407 |

4 | 0.426 | 1.985 | 0.505 |

5 | 0.321 | 1.966 | 0.479 |

6 | 0.271 | 1.726 | 0.466 |

7 | 0.228 | 1.701 | 0.490 |

8 | 0.213 | 1.694 | 0.411 |

9 | 0.146 | 1.501 | 0.680 |

10 | 0.140 | 1.539 | 0.531 |

Rand Index | Fowlkes Index |
---|---|

0.769 | 0.645 |

Building | kWh/year∗m${}^{2}$ | ${\mathit{EEI}}_{\mathit{night}/\mathit{day}}$ |
---|---|---|

Scientific Depts without lab | 30–50 | 0.8–1.1 |

Scientific Depts with lab | 70–110 | 1.1–1.9 |

Humanities Depts | <50 | 0.6–1.1 |

Agrarian Depts | 20–70 | 1.5–2.5 |

Medical Depts | 50–70 | 1.2–1.5 |

Administrative Offices | <50 | 0.4–1 |

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**MDPI and ACS Style**

Cottafava, D.; Sonetti, G.; Gambino, P.; Tartaglino, A.
Explorative Multidimensional Analysis for Energy Efficiency: DataViz versus Clustering Algorithms. *Energies* **2018**, *11*, 1312.
https://doi.org/10.3390/en11051312

**AMA Style**

Cottafava D, Sonetti G, Gambino P, Tartaglino A.
Explorative Multidimensional Analysis for Energy Efficiency: DataViz versus Clustering Algorithms. *Energies*. 2018; 11(5):1312.
https://doi.org/10.3390/en11051312

**Chicago/Turabian Style**

Cottafava, Dario, Giulia Sonetti, Paolo Gambino, and Andrea Tartaglino.
2018. "Explorative Multidimensional Analysis for Energy Efficiency: DataViz versus Clustering Algorithms" *Energies* 11, no. 5: 1312.
https://doi.org/10.3390/en11051312