# A Review of Data Mining with Big Data towards Its Applications in the Electronics Industry
## Data Mining with Big Data
### Performance Indicators  
The knowledge extracted should be evaluated and interpreted correctly to obtain reliable results. The evaluation of the DM methods to reach a final decision requires a comparison of results obtained from various DM methods using several measures [4]. The performance indicators employed to evaluate classifiers based on a confusion matrix are illustrated in Figure 2. The indicators widely used for the measurement of prediction, clustering, and association of DM functions are summarized in Tables 3-5 respectively. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indictors** & **Equation** & **Description** \\ \hline DBI & \(DBI=\frac{1}{n}\sum\limits_{i=1}^{n}\max\limits_{j\
eq i}(\frac{\sigma_{i}+ \sigma_{j}}{d(c_{i},c_{j})})\) & \(n\) is the number of clusters, \(c_{x}\) is the centroid of cluster \(x\), \(\sigma_{x}\) is the average distance of all elements in cluster \(x\) to centroid \(c_{x}\), and \(d(c_{i},c_{j})\) is the distance between centroids \(c_{i}\) and \(c_{j}\). \\ \hline DI & \(D=\frac{\min_{1\leq i<j\leq n}d(i,j)}{\min_{1\leq k\leq n}d(k)}\) & \(d(i,j)\) represents the distance between clusters \(i\) and \(j\); \(d^{\prime}(k)\) measures the intra-cluster distance of cluster \(k\). \\ \hline Purity & \(Purity(\Omega,C)=\frac{1}{N}\sum\limits_{k}\max\limits_{j}\left|w_{k}\cap c_{j}\right|\) & \(\Omega=\left\{w_{1},w_{2},\ldots,w_{k}\right\}\) is the set of clusters, \(\mathbb{C}=\left\{c_{1},c_{2},\ldots,c_{j}\right\}\) is the set of classes, \(I\) is mutual information, and \(H\) is entropy. \\ \hline RI & \(RI=\frac{TP+TN}{TP+FP+FN+TN}\) & The definitions of _TP_, _TN_, _FP_, _FN_, precision, and recall are the same as the specifications given in Figure 2; \(\beta\) is the penalty coefficient. \\ \hline QE & \(QE=\frac{1}{N}\sum\limits_{i=1}^{N}\left|\left|x_{i}-r_{\beta}\right|\right|\) & \(N\) refers to the number of original data vectors, and \(r_{\beta}\) is the best matching unit of the data vector \(x_{i}\); \(u(x)\) gets the value of 1 if the best and the second best matching units of the input vector are non-adjacent, and 0 otherwise. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The performance indicators for the clustering function [24]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indictors** & **Equation** & **Indictors** & **Equation** \\ \hline MAPE & \(MAPE=\frac{1}{N}\sum\limits_{i=1}^{N}\left|\frac{\beta-y_{i}}{y_{i}}\right|\times 100\) & R\({}^{2}\) & \(R^{2}=\sum\limits_{i=1}^{N}\left(\theta_{i}-\overline{y}\right)^{2}/\sum\limits _{i=1}^{N}\left(y_{i}-\overline{y}\right)^{2}\) \\ MSE & \(MSE=\sum\limits_{i=1}^{N}\left(\theta_{i}-y_{i}\right)^{2}/N\) & ME & \(ME=\frac{1}{N}\sum\limits_{i=1}^{N}\frac{\left|y_{i}-\theta_{i}\right|}{y_{i}}\) \\ MAE & \(MAE=\sum\limits_{i=1}^{N}\left|\theta_{i}-y_{i}\right|/N\) & VARER & \(VARE=\frac{1}{n-1}\sum\limits_{k=1}^{N}\frac{\left(\left|y_{i}-\overline{y} \right|}{y_{i}}-ME\right)^{2}\) \\ RMSE & \(RMSE=\sqrt{\sum\limits_{i=1}^{N}\left(\theta_{i}-y_{i}\right)^{2}/N}\) & RE & \(RE=\frac{E\left(y_{i}-\theta_{i}\right)^{2}}{E\left(y_{i}-\overline{y}\right)^{ 2}}\) \\ RSE & \(RSE=\sqrt{\sum\limits_{i=1}^{N}\left(\theta_{i}-y_{i}\right)^{2}/N}\) & IA & \(IA=1-\) \\ RAE & \(RAE=\sqrt{\sum\limits_{i=1}^{N}\left|\theta_{i}-y_{i}\right|/N}\) & - & - \\ \hline \hline \multicolumn{3}{c}{Note: \(y_{i}\) and \(\hat{y_{i}}\) are the observed and predicted value of sample \(i\) respectively; \(\overline{y}\) is the average result of samples. \(\sum\limits_{i=1}^{N}\left(y_{i}-\overline{y}\right)^{2}\) is the total sum of squares, while \(\sum\limits_{i=1}^{N}\left(\hat{y}_{i}-\overline{y}\right)^{2}\) is the explained sum of squares. \(E\) is the expectation value.} \\ \end{tabular}
\end{table} 
Table 3: The performance indicators for the prediction function [23].