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Hierarchical clustering of complex energy systems using pretopology

Loup-Noe Levy, Jeremie Bosom, Guillaume Guerard, Soufian Ben Amor, Marc Bui, Hai Tran

TL;DR

The paper tackles clustering of heterogeneous energy consumption profiles across large territories to optimize building energy management. It introduces a novel hierarchical clustering framework grounded in pretopology, leveraging pseudoclosure, seed-based subset generation, adjacency relations, and quasi-hierarchy construction, implemented in Python. The approach is validated on synthetic 2D and time-series benchmarks plus a real Enedis dataset, achieving perfect ARI on the benchmark and yielding meaningful clusters in real data. This multi-criteria, hierarchical clustering of complex energy systems promises more nuanced portfolio analysis and targeted energy optimization actions.

Abstract

This article attempts answering the following problematic: How to model and classify energy consumption profiles over a large distributed territory to optimize the management of buildings' consumption? Doing case-by-case in depth auditing of thousands of buildings would require a massive amount of time and money as well as a significant number of qualified people. Thus, an automated method must be developed to establish a relevant and effective recommendations system. To answer this problematic, pretopology is used to model the sites' consumption profiles and a multi-criterion hierarchical classification algorithm, using the properties of pretopological space, has been developed in a Python library. To evaluate the results, three data sets are used: A generated set of dots of various sizes in a 2D space, a generated set of time series and a set of consumption time series of 400 real consumption sites from a French Energy company. On the point data set, the algorithm is able to identify the clusters of points using their position in space and their size as parameter. On the generated time series, the algorithm is able to identify the time series clusters using Pearson's correlation with an Adjusted Rand Index (ARI) of 1.

Hierarchical clustering of complex energy systems using pretopology

TL;DR

The paper tackles clustering of heterogeneous energy consumption profiles across large territories to optimize building energy management. It introduces a novel hierarchical clustering framework grounded in pretopology, leveraging pseudoclosure, seed-based subset generation, adjacency relations, and quasi-hierarchy construction, implemented in Python. The approach is validated on synthetic 2D and time-series benchmarks plus a real Enedis dataset, achieving perfect ARI on the benchmark and yielding meaningful clusters in real data. This multi-criteria, hierarchical clustering of complex energy systems promises more nuanced portfolio analysis and targeted energy optimization actions.

Abstract

This article attempts answering the following problematic: How to model and classify energy consumption profiles over a large distributed territory to optimize the management of buildings' consumption? Doing case-by-case in depth auditing of thousands of buildings would require a massive amount of time and money as well as a significant number of qualified people. Thus, an automated method must be developed to establish a relevant and effective recommendations system. To answer this problematic, pretopology is used to model the sites' consumption profiles and a multi-criterion hierarchical classification algorithm, using the properties of pretopological space, has been developed in a Python library. To evaluate the results, three data sets are used: A generated set of dots of various sizes in a 2D space, a generated set of time series and a set of consumption time series of 400 real consumption sites from a French Energy company. On the point data set, the algorithm is able to identify the clusters of points using their position in space and their size as parameter. On the generated time series, the algorithm is able to identify the time series clusters using Pearson's correlation with an Adjusted Rand Index (ARI) of 1.

Paper Structure

This paper contains 26 sections, 5 theorems, 4 equations, 12 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Centroid-based clustering:
  4. Density-based clustering:
  5. Hierarchical clustering:
  6. Distribution-based clustering:
  7. Conclusion about clustering methods:
  8. Relevance of pretopology-based clustering:
  9. Pretopology
  10. Pretopological space
  11. Central definitions and propositions
  12. Hierarchical Clustering Algorithms
  13. Calculation of a family of elementary sets or seeds
  14. Construction of subsets by applying pseudoclosure
  15. Construction of the adjacency matrix
  16. ...and 11 more sections

Key Result

proposition thmcounterproposition

In a pretopological space of type $V$, the intersection of closures is a closure.

Figures (12)

  • Figure 1: Example of a pseudoclosure functionlaborde2019Pretopology
  • Figure 2: Closure of set $A$laborde2019Pretopology
  • Figure 3: Pseudoclosure function on a graphlaborde2019Pretopology
  • Figure 4: Filters vs Prefilterslaborde2019Pretopology
  • Figure 5: Neighborhood definition of a pretopologylaborde2019Pretopology
  • ...and 7 more figures

Theorems & Definitions (13)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • ...and 3 more