# Low-Rate Non-Intrusive Load Disaggregation with Graph Shift Quadratic Form Constraint
## 3 Experiment and Results
### Experimental Results and Discussion
Unknown in the first column is defined as the difference between the measured aggregate power and the sum of the appliance's power in each individual circuit, while in the last two columns it denotes the difference between the sum of disaggregated power and the actual aggregate consumption. From Figure 5, we find that there are some appliances not involved in the particular house. This can be attributed to three aspects: the first one is the appliance is OFF during testing, the second is the appliance's energy consumption is too low, and the last is that the appliance is not present in the house. Analyzing the results in three houses, we observe that GSQF-APD achieves a better disaggregation performance than GLQF-APD with a closer _PCEC_ metric to the ground truth for most appliances. In House 1, the average absolute difference after decomposition using GSQF-APD algorithm is 3.26%, whereas the average value obtained by GLQF-APD is 4.30%. Similarly, for Houses 2 and 6, the average absolute differences produced by GSQF-APD are 0.90% and 2.12%, lower than the results 1.31% and 2.97% produced by GLQF-APD, respectively. Figure 4: Classification performance comparison of two GSP-based approaches for House 2. (**a**) Precision; (**b**) Recall; (**c**) F-Measure. Remarks: Solution 1 and Solution 2 are two approaches in Ref. [40], which are GLQF-APD. 3. Comparison with the state-of-the-art NILM approaches: First, a comparison of average classification accuracy of GSQF-APD with GLQF-APD and SVM-based approach for House 2 is shown in Figure 6. We can see that the two GSP-based algorithms, GSQF-APD and GLQF-APD, achieve higher accuracy than the SVM-based method, especially when the ratio of training data is small (under 8%), the difference of classification accuracy can exceed 20%. This observation demonstrates that the GSP-based approach reduces the dependence on training data compared with the SVM-based method. Furthermore, the GSQF-APD approach that uses the graph shift-based regularization term outperforms the GLQF-APD approach that introduces the Laplacian quadratic form as a regularization term. The classification accuracy gap between GSQF-APD and GLQF-APD varies from 2% to 13%. Note that the curve obtained by the SVM-based method presents a relatively obvious step-characteristic, which is due to the fact that training data in a certain interval contains the same number of useful labels. With respect to the training complexity, we adopted the average training time as a metric. When two days of data are used, comprising over \(N\) = 2800 samples, the average training time for REDD is about 7.64 s. It is faster than the sparse coding based method which disaggregates the same amount of data in about 25 s, as reported in Ref. [35]. Figure 5: Comparison of appliance contribution to the total energy in Houses 1, 2, and 6 for GSQF-APD and GLQF-APD. Remarks: GSQF and GLQF in the figure refer to GSQF-APD and GLQF-APD, respectively. Figure 6: Classification accuracy of House 2 using GSQF-APD, GLQF-APD, and SVM algorithms. Then, we compare our results, \(F_{MP}\), with those of the GLQF-APD algorithm, \(F_{ML}\), the HMM-based algorithm, \(F_{MH}\), as reported in [40], and the DT-based algorithm [25], \(F_{MDT}\). Tables 2-4 show the results for REDD Houses 1, 2, 6, respectively. It can be seen that the proposed GSQF-APD approach in general outperforms other three state-of-the-art NILM approaches across all three houses. The HMM-based method has good performance in disaggregating refrigerator, since its operation is continuous and sole (i.e., usually the only one running at night) and thus has large data availability for training and facilitating good models. However, for other devices especially kitchen appliances, namely stove, microwave, and kitchen outlet, which usually have a short operation time, the HMM-based method performs poor.