# A Review of Data Mining with Big Data towards Its Applications in the Electronics Industry
## Data Mining with Big Data
### Performance Indicators
\begin{table}
\begin{tabular}{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 & \(D=\frac{\min_{1\leq k\leq n}d(k)}{\min_{1\leq k\leq n}d(k)}\) & \(d(i,j)\) 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 & \(QE=\frac{1}{N}\sum\limits_{i=1}^{N}\left|\left|x_{i}-r_{\beta}\right|\right|\) & \(TE=\frac{1}{N}\sum\limits_{i=1}^{N}u(x_{i})\) & \(N\) 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 5: The performance indicators for the association function. Accuracy (ACC), precision, sensitivity or recall, specificity, and so forth, given in Figure 2, are the commonly employed indicators. Meanwhile, the receiver operating characteristic curve (ROC) created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings is always taken to illustrate the diagnostic ability of a binary classifier system as its discrimination threshold is varied. The performance indicators for prediction mainly include the mean absolute percentage error (MAPE), the mean squared error (MSE), the mean absolute error (MAE), the root-mean-square error (RMSE), the root absolute error (RAE), the mean error (ME), the variance of errors (VARE), the relative error (RE), the goodness of fit (R\({}^{2}\)), the index of agreement (IA), and so on. Typical objective functions to assess the quality of clustering include internal and external criteria. The internal criterion for the quality of a clustering can be evaluated by the Davies-Bouldin index (DBI), Dunn index (DI), and so on, while the most used external criteria includes purity, normalized mutual information (NMI), rand index (RI), \(F\) measure, and so on. Meanwhile, some indicators like the quantization error (QE) and the topographic error (TE) are for a special algorithm like self-organizing map (SOM). The support, confidence, lift, and conviction are pervasive performance indicators for association. The outlier detection can be taken as a binary classification, and the performance indicators for classification can be used to evaluate the results. Time series analysis can be used for clustering, classification, and anomaly detection, as well as forecasting, and therefore, the related performance can be verified by the corresponding indicators for clustering, classification, and prediction.