Algorithm 1 Training algorithm for L-Tree.
	Input $\overline{\overline{\mathrm{X}}}$: the training image set which consist of $\{{\mathrm{X}}_1,{\mathrm{X}}_2,\dots ,{\mathrm{X}}_N\}$ (an $N\times W\times H$ matrix) $\mathrm{Y}$: the labels of training image set (an $N\times 1$ matrix) s: the ratio between local area and original image ($W_s=\mathrm{s}·W$, $H_s=\mathrm{s}·H$) K: the number of neurons in one SOM ($K=K_r\times K_c$) $\{L_1,L_2,\dots ,L_C\}$: the set of class labels
	Output: a single L-Tree
	Build a L-Tree $(\overline{\overline{\mathrm{X}}})$ 1:Extract random local-area position $(x_{st},y_{st})$ 2:Normalize by subtracting the mean, ${\overline{\overline{\mathrm{x}}}}^{{}^{\prime }}$ 3:Node learning (${\overline{\overline{\mathrm{x}}}}^{{}^{\prime }}$) 4:Split $\overline{\overline{\mathrm{X}}}$ into subset ${\overline{\overline{\mathrm{X}}}}_1,{\overline{\overline{\mathrm{X}}}}_2,\dots ,{\overline{\overline{\mathrm{X}}}}_K$ according to the similarity with K trained neurons. 5:Calculate class probability from relative frequency of each samples and save it to the neurons. 6:For $j=1,2,\dots ,K$ inspect a $\mathbf{terminal}\mathbf{criteria}$ 7:If 6 satisfying stop the node learning, else then Build a L-Tree (${\overline{\overline{\mathrm{X}}}}_j$).
	Node learning $({\overline{\overline{\mathrm{x}}}}^{\prime })$ 1:Generate new K neurons weight $\mathrm{W}(t=0)$ and initialize with random values before learning 2:do 3:  Select randomly $n(=\sqrt{N})$ samples from ${\overline{\overline{\mathrm{x}}}}^{{}^{\prime }}$ 4:  ${\mathrm{w}}_i(t+1)={\mathrm{w}}_i\left(t\right)+h_{c,i}({\mathrm{x}}_j-{\mathrm{w}}_i\left(t\right))$          ▹ Update a neuron’s weights 5:  $\alpha \left(t\right)=\alpha \left(t\right)exp\left(-\frac{1}{\tau }\right)$                   ▹ Update a learning rate 6:  $t=t+1$ 7:while until $\mathrm{W}\left(t\right)\ne \mathrm{W}(t-1)$