## 3 Results
### Reduced Dimension Clustering to Identify Demand Patterns  
The development of sensor technologies and network communication technologies, via smart home energy management systems, for example, have had an explosive impact on customer behavior data accumulation. Extracting useful information from the resulting high-frequent multivariate data, machine learning have enormous potential for efficient targeting and steering end-customer behavior [29]. Earlier work has applied various machine learning techniques for customer load curve typification, which can be divided into 5 method groups; partitioning, hierarchical, density-based, grid-based and model-based [39]. Although no single clustering method is always superior to the other, as they are used for specific applications, most commonly used are partitioning models such as k-means, fuzzy c-means clustering and hierarchical. Non-hierarchical clustering methods [40; 41] are preferred over hierarchical in order to prioritize the minimization of internal cluster variance and cluster similarity. Fuzzy c-means and probability neural networks have proven to be useful methods for identifying load customer patterns [42]; however for distinct cluster identification, k-means is often preferred for achieving efficient and scalable results [43]. Lastly, in the above context of increasingly large datasets, efficiency can be improved by combining machine learning methods via hybrid approaches [44]. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Price Sensitivity \(\boldsymbol{\phi}_{i}\)** \\ \hline Number of Household Occupants & 0.18 *** \\  & (0.02) \\ Building Age & 0.06 *** \\  & (0.02) \\ Building Size & 0.02 *** \\  & (0.0003) \\ Building Type & 0.20 *** \\  & (0.02) \\ Roof Insulation & \(-\)0.47 \\  & (0.06) \\ RTP * Number of Household Occupants & 0.33 *** \\  & (0.03) \\ RTP * Building Age & \(-\)0.22 *** \\  & (0.03) \\ RTP * Building Size & \(-\)0.02 *** \\  & (0.0004) \\ RTP * Building Type & \(-\)0.25 *** \\  & (0.02) \\ RTP * Roof Insulation & 0.29 \\  & (0.08) \\ Solar Influx & \(-\)0.01 *** \\  & (0.0002) \\ Constant & 2.08 *** \\  & (0.25) \\ Observations & 72,273 \\ \(N\) & 108 \\ \(R^{2}\) & 0.13 \\ Adjusted \(R^{2}\) & 0.13 \\ \(F\) Statistic & 803.61 *** (\(df=12\); 72,259) \\ \hline \hline \end{tabular} Note: *\(p<0.1\); **\(p<0.05\); ***\(p<0.01\).  
\end{table} 
Table 4: Regression coefficient (standard errors SSE) results of complete model with interaction on price sensitivity. We conduct such a hybrid approach, via a form of spectral relaxation clustering [45], with a kernel Principal Component Analysis (kPCA) combined with k-means, in order to find distinct groups of households for demand targeting by home energy management systems. This section gives a descriptive overview of the reasoning, for a more comprehensive description we refer to earlier work [46]. The analysis shows how applying machine learning techniques should ideally play a role in smart home EMS in order to target individual customers along the individual attributes and send tariff recommendations to the utility. Spectral relaxation clustering finds the eigenvectors of the data set, which are orthogonal, and aims at explaining the variability of the data in lower dimensionality. The first step involves building a similarity matrix and computing the first k eigenvectors. We apply kernel PCA to ensure an interior solution, in that this method renders the eigenvectors of the covariance matrix. As the principal components are the continuous solution of the cluster membership, the analysis allows for identifying groups in terms of their components, while the groups can be used in terms of regression clustering for optimal targeting purposes. In a second step the algorithm builds a new data matrix, where the column represents the eigenvectors. We interpret the rows of this matrix as our new data points and apply k-means clustering. The principal component analysis is conducted to identify the most powerful variables for the cluster analysis of our households.