Detecting Multi-Resolution Pedestrians Using Group Cost-Sensitive Boosting with Channel Features

. 2019 Feb 14;19(4):780. doi: 10.3390/s19040780

Algorithm 1 Group Cost-Sensitive AdaBoost Algorithm

Input: Training set

{\{(x_{i}, y_{i})\}}_{i = 1}^{n}

where

x_{i}

is the feature vector of the sample and

y_{i} \in {1, - 1}

is the class label, costs

{C_{f n 1}, C_{f n 2}, \dots, C_{f n N}, C_{f p}}

for different groups, the set of weak learners

{\{g_{k} (x)\}}_{k = 1}^{K}

, and the number M of weak learners in the final classifier.

Output: Strong classifier

h (x)

for multi-resolution detectors.

1: Initialization: Set of uniformly distributed weights for each group:

ω_{i}^{(0)} = \frac{1}{2 | G_{+ 1} |}, \forall i \in G_{+ 1}; ω_{i}^{(0)} = \frac{1}{2 | G_{+ 2} |}, \forall i \in G_{+ 2}; \dots; ω_{i}^{(0)} = \frac{1}{2 | G_{+ N} |}, \forall i \in G_{+ N}; ω_{i}^{(0)} = \frac{1}{2 | G_{-} |}, \forall i \in G_{-}

3: for

m = {1, \dots, M}

4: for

k = {1, \dots, K}

5: Compute parameter values as in Equations (16), (17) with

g (x) = g_{k} (x)

;

6: Obtain the value of

α_{k}

by solving Equation (15);

7: Calculate the loss of the weak learner

(α_{k}, g_{k} (x))

as in Equation (18).

8: end for

9: Select the best weak learner

(α_{m}, g_{m} (x))

with the minimum loss as in Equation (19);

10: Update the weights

ω_{i}

according to Equation (20).

11: end for

12: return

h (x) = sgn [\sum_{m = 1}^{M} α_{m} g_{m} (x)]