# Deep Active Learning for Computer Vision Tasks: Methodologies, Applications, and Challenges
## 2 Candidate Selection Strategies in Active Learning
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Strategies** & **Methodologies** & **Typical Works** \\ \hline Random selection & \(\rhd\)**Random sampling** is to use random numbers to select samples from the unlabeled dataset for labeling. & N.A. \\ \hline \multirow{6}{*}{\(\rhd\)****Least confidence**} & \(\rhd\)**Least confidence** is to select the sample with the smallest probability of the top1 predicted class. In practice, the opposite of the maximum predicted probability is often taken as the uncertainty score of the sample. & [PERSON] et al. [10] \\  & \(\rhd\)**\(\mathbb{X}=\underset{x\in U}{\operatorname*{arg\,max}}[1-P(\hat{y}\mid x)]= \underset{x\in U}{\operatorname*{arg\,min}}P(\hat{y}\mid x)\)** & [PERSON] et al. [11; 12] \\ \cline{2-3}  & \(\rhd\)**Margin sampling** is to calculate the difference between the probabilities of the top1 and the top2 predicted class.Then the samples with the smallest difference are defined as hard-to-classify samples for labeling. [PERSON] et al. [13] \\ Uncertainty-based selection & \(\rhd\)**Multi-class level uncertainty** is to select the two samples that are the farthest from the classification hyperplane of multi-class and take their distance difference as the score. [PERSON] et al. [15] \\  & \(\rhd\)**Maximize entropy** is to utilize the methodology that larger entropy denotes higher uncertainty. The sample with the largest entropy is selected as candidate. [PERSON] et al. [17] \\  & \(\rhd\)**\(\mathbb{X}=\underset{x\in U}{\operatorname*{arg\,max}}\;E_{x}=\underset{x\in U}{ \operatorname*{arg\,min}}\Big{\{}\sum_{i=1}^{Y}P(y_{i}\mid x)\times\log P(y_{ i}\mid x)\Big{\}}\)** [PERSON] et al. [18] \\ \hline \multirow{6}{*}{\(\rhd\)**Mayers-based selection**} & \(\rhd\)**Angle-based** measurement is to measure diversity by calculating the undirected angles between the induced hyper-planes. [PERSON] et al. [19] \\  & \(\rhd\)**Redundancy-based** measurement is to measure the diversity as the redundancy between unlabeled points via symmetric KL divergence [20] between the two vectors of probability values. [PERSON] et al. [21] \\  & \(\rhd\)**\(R(x_{i},x_{j})=\sum_{y}^{|Y|}\big{[}P(y\mid x_{i})-P(y\mid x_{j})\big{]}\log \big{[}P(y\mid x_{i})-P(y\mid x_{j})\big{]}\)** & [PERSON] et al. [22] \\ \hline \multirow{6}{*}{Committee-based selection [23]} & \(\rhd\)**Vote entropy-based** measurement is to select the hard sample voted by the Committee. The models in the committee distinguish samples into different classes. The predicted results toward one sample with the largest entropy is classified as hard sample and needs to vote for labeling. & [PERSON] et al. [24] \\  & \(\rhd\)**\(\mathbb{X}=\underset{x\in U}{\operatorname*{arg\,min}}\Big{\{}-\frac{1}{N} \sum_{i=1}^{Y}\big{[}Vote(y_{i})\log\frac{Vote(y_{i})}{N}\big{]}\Big{\}}\)** & [PERSON] et al. [25] \\ \cline{2-3}  & \(\rhd\)**Average KL divergence–based** measurement is to measure the deviation of those unlabeled samples via calculating the average KL divergence of the committee \(\mathcal{C}\). & [PERSON] et al. [25] \\ \cline{2-3}  & \(\mathbb{X}=\underset{x\in U}{\operatorname*{arg\,max}}\;\frac{1}{N}\sum_{i=1} ^{N}KL\big{(}P_{\mathcal{M}_{i}}\|P_{\mathcal{C}}\big{)}=\underset{x\in U}{ \operatorname*{arg\,max}}\;\frac{1}{N}\sum_{i=1}^{N}\sum_{j}^{|Y|}P_{\mathcal{ M}_{j}}\big{(}y_{j}\mid x\big{)}\log\frac{P_{\mathcal{M}_{j}}(y_{j}|x)}{P_{ \mathcal{C}}(y_{j}|x)}\) \\ \hline \hline \end{tabular} Note: \(\mathbb{X}\) represents the selected sample, \(U\) is the unlabeled data pool, \(y_{1}\) is the predicted class with max probability, \(P(y_{1}\mid x)\) is the conditional probability where the input is \(x\), and the predicted class is \(y_{1}\). \(\hat{y}_{2}\) denotes the top2 predicted class. \(D(x,y)\) represents the distance from the sample \(x\) to the classification hyperplane of class \(y\). \(\phi(x_{i})\) is the normalization function, \(k\big{(}x_{i},x_{j}\big{)}=\big{\langle}\phi(x_{i}),\phi(x_{j})\big{\rangle}\) is the kernel function. \(|Y|\) is the total number of classes, \(P(y\mid x)\) is the conditional probability where the input is \(x_{i}\), and the predicted class is \(y\). \(Vote(y_{i})\) denotes the number of models that voted for the current class \(y_{i}\), and \(\sum_{i=1}^{|Y|}Vote(y_{i})=N\). \(\mathcal{M}_{i}\) represents a specific model in the committee. \(KL(P_{i}\|P_{2})\) is the KL divergence between two distributions \(P_{1}\) and \(P_{2}\).  
\end{table}