The smart meter roll-out in many countries leads to energy providers, energy value-added service providers, and grid operators having access to increasing amounts of high-resolution load profiles (e.g. 15-minute resolution) compared to only having one measurement per year as before. These load profiles will be analyzed within diverse data mining tasks such as classification, clustering, and forecasting. However, such lowly aggregated high-resolution load profiles are generally quite intermittent and have less structure to be exploited by standard data mining algorithms. If for instance point-wise distances, such as the Euclidean distance, are used to compare household load profiles, they may inflict a double-penalty if a spike has about the correct height, but is shifted slightly in time. To compare household load profiles, a local permutation invariant (LPI) distance measure was introduced as the adjusted p-norm error to assess household short-term load forecasts and forecasting models minimizing it have since been introduced. This talk will first introduce the characteristics of load profiles at low aggregation levels and introduce the LPI distance as well as the related Dynamic Time Warping (DTW) distance popular in the time series literature. It will discuss the problem of finding a sample mean under the DTW and LPI distances, and introduce approximate optimization methods based on subgradient descent. It will then show how the choice of the distance measure (and its sample mean) affect the results within typical data analytics use cases, namely short-term load forecasting, load profile clustering, and classification. A novel distance measure combining properties of the LPI and DTW, the local nearest neighbor alignment (LNNA) distance is introduced and discussed.