# Biclustering of Smart Building Electric Energy Consumption Data
## 1 Introduction  
Energy consumption of buildings is receiving more and more attention in today's economies. As buildings represent substantial consumers of energy worldwide, with this trend increasing over the past few decades due to rising living standards, this issue has drawn considerable attention from various stakeholders (e.g., inhabitants, policy makers, and industry). As pointed out in [1], the energy consumption in buildings has experienced an increment of 1.5% per year in Europe and of 1.9% per year in North America. This increment is even more alarming in China, where it has experienced an increment of 10% in the last twenty years [2]. Moreover, as pointed out in [3], it is estimated that the world energy consumption will increase from 549 quadrillion Btu in 2012 to 629 quadrillion Btu in 2020 and then to 815 quadrillion Btu in 2040, a 48% increase (1.4%/year). Non-OECD Asian countries (including China and India) account for more than half of the increase. It follows that actions are required to improve the efficiency of energy consumption in buildings, in order to decrease both the costs associated to it and the environmental impact this consumption has. In fact, energy consumption is not only important on the economy level, but also for the repercussions that it has on the environment. For example, the European Union has recently issued a directive (European Directive 2009/28/EC [4]) that requires that all EU countries adopt a set of minimum energy efficiency requirements. More specifically, it stipulates a 20% reduction in energy consumption by 2020 relative to 1990 levels along with a 20% reduction in \(CO_{2}\) emissions as well as 20% of all energy be produced by renewable technologies. A relevant fraction of worldwide energy consumption is tightly related to indoor systems for residential, commercial, public, and industrial premises; it has been estimated that residential and commercial buildings account today for about 20% of the world's total energy consumption. In this domain, the energy bill due to environmental control, including heating, ventilation, and air conditioning (HVAC), is dominating, especially in the developed countries [3]. Thus, it is important to gain insights regarding the energy consumption of buildings, with the aim of improving their energy efficiency. In this sense, smart buildings [5], i.e., buildings that use sensors, actuators and microchips, to collect data and manage them according to a business functions and services, can help. In fact, such buildings can provide data regarding the electric energy consumption, which can then be used to both improve their efficiency and for automated fault detection and diagnostics. In the field of analysis of energy consumption of smart buildings, different data analysis techniques are usually applied to help manage them, including classification [6], forecasting [7; 8; 9] and clustering techniques [10; 11] of energy consumption patterns. In this sense, it is useful to analyse the data regarding the consumption of energy over a period of time in order to extract useful information. This kind of data is usually organised as a time series. Time series are a common data type and they are widely used in diverse application areas, such as finance, economics, communication, automatic control, and online services, among others [12]. A common analysis technique applied to time series is clustering [12; 13]. Clustering time series is to identify the homogeneous groups of time series data based on their similarity. It is an important and useful technique for exploratory study on the characteristics of various groups in a given time series dataset. However, in some domains, clustering in only one dimension may not be enough. For example, we may consider the energy consumption data of a set of buildings over a specific period of time. In this case, clustering can be applied in order to extract general buildings profiles, i.e., groups of buildings that present the same behaviour over the whole time interval considered.