## 1 Introduction
### Novel Hybrid UAC-NFC Model
\[\overline{x}_{i}^{l}(q+1)=\overline{x}_{i}^{l}(q)-\eta[\frac{f(\vec{x}^{p})-\vec{y}^ {p}}{\sum_{i=1}^{M}\Pi_{i=1}^{N}\exp(-(\frac{\vec{x}_{i}-\overline{y}^{p}}{\vec{ \sigma}_{i}^{l}}))}][\overline{y}(q)-f(\vec{x}^{p})][\prod_{i=1}^{n}\exp(-( \frac{\vec{x}_{i}-\overline{y}^{p}}{\vec{\sigma}_{i}^{l}})^{2})][\frac{2(\frac{ \vec{x}_{i}-\overline{y}^{p}}{\vec{\sigma}_{i}^{l}}(q))}{\sigma_{i}^{l}(q)}] \tag{6}\]  
\[f(\mathbf{x})=\frac{\sum_{l=1}^{M}\overline{y}^{l}[\prod_{i=1}^{n}\exp(-(\frac{x_{ i}-\overline{y}_{i}^{l}}{\sigma_{i}^{l}})^{2})]}{\sum_{l=1}^{M}\left[\prod_{i=1}^{n} \exp(-(\frac{x_{i}-\overline{y}_{i}^{l}}{\sigma_{i}^{l}})^{2})\right]} \tag{2}\]0  
The procedure of the novel hybrid UAC-NFC model proposed in this article is summarized in \[f(\mathbf{x})=\frac{\sum_{l=1}^{M}\overline{y}^{l}[\prod_{i=1}^{n}\exp(-(\frac{x_{ i}-\overline{y}_{i}^{l}}{\sigma_{i}^{l}})^{2})]}{\sum_{l=1}^{M}\left[\prod_{i=1}^{n} \exp(-(\frac{x_{i}-\overline{y}_{i}^{l}}{\sigma_{i}^{l}})^{2})\right]} \tag{2}\]1  
The intelligent-particle swarm optimization technique in [PERSON] et al. (2016) can be conducted in the second stage of the proposed hybrid UAC-NFC model and be used to fine tune the adjustable parameters of the constructed NFC. Sampling is biased if it systematically favors some observations over others. Sampling bias is sometimes called systematic bias. For load classification as predictive \begin{table}
\begin{tabular}{l} _Inputs_: \\ D = \(\{x^{1},x^{2},x^{3},\ldots,x^{p},\ldots,x^{N}\}\) // \(N\) input-output data pairs to be clustered automatically \\ \(r\) // radius \\ _Output_: \\ K // Set of k clusters \\ _Run_ the UAC process: \\ K\({}_{1}\) = \(\{x^{1}\}\). // the first cluster initialized by \(x^{1}\) \\ _Add_\({}_{1}\) to K. \\ \(k\) = 1. \\ \end{tabular} \
\begin{tabular}{l} _for_\(i=2\) to \(N\)**Do** // for \(\vec{x}^{2},x^{3},\ldots,x^{p},\ldots,x^{N}\) \\ _Find_ data point \(\vec{x}^{m}\) in cluster K\({}_{m}\)\(\subset\) K, where _dist_(\(\vec{x}^{m},\vec{x}^{i}\)), the Euclidean distance between \(\vec{x}^{m}\) and \(\vec{x}^{i}\), is the smallest. \\ **if**_dist_(\(\vec{x}^{m},\vec{x}^{i}\)) \(<\) \(r\), then \\ \(\mathrm{K}_{m}\) = K\({}_{m}\)\(\cup\)\(\{\vec{x}^{i}\}\). // the same cluster updated \\ **else** \\ \(k\) = \(k\) + 1. \\ \(\mathrm{K}_{k}\) = \(\{x^{i}\}\). // a new cluster created \\ _Add_\({}_{1}\) to K. \\ **End for** \\ \end{tabular}
\begin{tabular}{l} _Initialize the adjustable parameters, \(\overline{y}^{l}(0),\overline{x}_{i}^{l}(0)\), and \(\sigma_{i}^{l}(0)\), of the NFC of Equation (2) based on the clustering results obtained through the UAC process above and described in Section 2.2._ \\ _Stage 2. Execute the GD process [22; 23; 24; 25; 26] to train the UAC-NFC model constructed in Stage 1_ \\ **Do** \\ **for**_\(q=0\) to \(q_{max}\)**Do** \\ **for**_\(p=1\) to \(N\)**Do** \\ _Present_ the _pth_ input-output data pair (\(\vec{x}^{p},\vec{y}^{p}\)), and _compute_ the output of the NFC associated with the present data pair at the \(q\)th iteration of the training process in the forward propagation of the training process. _Update_ the adjustable parameters of the NFC according to Equations (5)–(7), in the backward propagation of the training process. \\ **End for** \\ _Obtain_ total error \(\Sigma\) \(|f(\vec{x}^{p})-y^{p}|\) with \(p=p+1\). \\ **End for** \\ **While** The NFC is not satisfactory with a high total error \\ \end{tabular}
\end{table} 
Table 1: The hybrid Unsupervised Automatic Clustering-integrated Neuro-Fuzzy Classification (UAC-NFC) model proposed in this article. modeling in DSM/home energy management, data being sampled through data acquisition, and then analyzed via feature extraction, evolve over time with a systematic bias between separate training and test datasets. Thus, a cross-validation procedure [21] was conducted to deal with data sampled with systematic errors.