②Therefore, the feature selection step is extremely important for complex medical image processing. Although sparse learning and dictionary learning have been used to extract features, their shallow architectures still limit their representation ability.

③The development of hardware promotes the improvement of deep learning in medical image analysis

④Categories of medical imaging analysis: classification, detection/localization, registration, and segmentation

⑤This survey mainly centers on brain disease

cardiac adj.心脏的;心脏病的 n.心脏病患者;强心剂;健胃剂

2.3. Deep Learning

2.3.1. Feed-Forward Neural Networks

①The function of FFNN:

$y_k(\boldsymbol{x};\boldsymbol{\theta})=f^{(2)}\left(\sum_{j=1}^Mw_{k,j}^{(2)}f^{(1)}\left(\sum_{i=1}^Nw_{j,i}^{(1)}x_i+b_j^{(1)}\right)+b_k^{(2)}\right)$

where the $\boldsymbol{x}$ is the input vector, $y_k$ is the output;

superscript denotes layer index, $M$ is the number of hidden units;

$b_j$ and $b_k$ are bias terms of input layer hidden layer respectively;

$f^{(1)}$ and $f^{(2)}$ denote non-linear activation function;

$\theta=\left\{w_{j}^{(1)},w_{k}^{(2)},b_{j}^{(1)},b_{k}^{(2)}\right\}$ represents parameter set

②Sketch map of (A) single and (B) multi layer neural networks:

2.3.2. Stacked Auto-Encoders

①Auto-encoder (AE), namely so called auto-associator, possesses the ability of encoding and decoding

②AE can be stacked as stacked auto-encoders (SAE) with better performance

③Sketch map of SAE:

where the blue and red dot boxes are encoder and decoder respectively

④To avoid being trapped in local optimal solution, SAE applies layer-wise pretraining methods

2.3.3. Deep Belief Networks

①By stacking multiple restricted Bolztman machines (RBMs), the Deep Belief Network (DBN) is constructed

②The joint distribution of DBN:

$P(v,h^{(1)},\ldots,h^{(L)})=P(v\mid h^{(1)})(\prod_{l=1}^{L-2}P(h^{(l)}\mid h^{(l+1)}))P(h^{(L-1)},h^{(L)})$

where $v$ denotes visible units and $h^{(1)},...,h^{(L)}$ denotes $L$ hidden layers

③Sketch map of (A) DBN and (B) DBM:

where the double-headed arrow denotes undirected connection and the single-headed arrow denotes directed connection

2.3.4. Deep Boltzmann Machine

①Futher stacking RBMs can get Deep Boltzmann Machine (DBM):

$\begin{gathered}P(v_i|\boldsymbol{h}^1)=\sigma(\sum_jW_{ij}^{(1)}h_j^{(1)})\quad\\\\P(h_k^{(l)}|\boldsymbol{h}^{(l-1)},\boldsymbol{h}^{(l+1)})=\sigma(\sum_mW_{m\boldsymbol{k}}^{(l)}\boldsymbol{h}_m^{(l-1)}+\sum_nW_{kn}^{(l+1)}h_n^{(l+1)})\quad\\\\P(h_t^{(L)}|\boldsymbol{h}^{(L-1)})=\sigma(\sum_sW_{st}^{(L)}\boldsymbol{h}_s^{(L-1)})\quad\end{gathered}$

2.3.5. Generative Adversarial Networks

①Simultaneously including generator $G$ and discriminator $D$ , Generative Adversarial Networks (GANs) achieves the task of training models with a small number of labeled samples:

$\begin{aligned}\min_G\max_DV(G,D)&=\mathbb{E}_{x-p_{data}(x)}\left[\log D(x)\right]\\&+\mathbb{E}_{x-p_z(z)}\left[\log(1-D(G(z)))\right]\end{aligned}$

②The framework of GAN:

2.3.6. Convolutional Neural Networks

①The framework of convolutional neural network (CNN):

2.3.7. Graph Convolutional Networks

①The framework of Graph Convolutional Networks (GCN):

which includes spectral-based and spatial-based methods

2.3.8. Recurrent Neural Networks

①As the extension of FFNN, recurrent neural network (RNN) ia able to learn features and long-term dependencies from sequential and time-series data

②Framework of (A) long-short-term memory (LSTM) and (B) Gated Recurrent Unit (GRU):

2.3.9. Open Source Deep Learning Library

①Some toolkits of deep learning:

2.4. Applications in Brain Disorder Analysis With Medical Images

2.4.1. Deep Learning for Alzheimer's Disease Analysis

①Introducing the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the classification method of patients

②Enumerating DGM based and CNN based methods, 2D CNN and 3D CNN

③Articles which applying DL in AD detection:

④Classification performance of these articles:

⑤Articles that applying DL to predict MCI:

⑥Prediction performance of artivles above:

2.4.2. Deep Learning for Parkinson's Disease Analysis

①Dataset example: Parkinson's Progression Markers Initiative (PPMI)

②Exampling some DL works on PD diagnosis

③Articles which applying DL in PD detection:

2.4.3. Deep Learning for Austism Spectrum Disorder Analysis

①Dataset: ABIDE I/II

②Particularizing AE/CNN/RNN based methods

③Articles that applying DL to ASD diagnosis:

2.4.4. Deep Learning for Schizophrenia Analysis

①There is no widely used SZ neuroimaging dataset available currently

②Dataset from challenge: The MLSP2014 (Machine Learning for Signal Processing) SZ classification challenge, with 75 NC and 69 SZ

③Articles which applying DL in SZ detection:

2.5. Discussion and Future Direction

①Hyper-parameters of DL:

model optimization parameters	the optimization method, learning rate, and batch sizes, etc.
network structure parameters	number of hidden layers and units, dropout rate, activation function, etc.

②Optimization of hyper-parameters:

manual	grid search and random search
automatic	Bayesian Optimization

③Deep learning still faces the challenges of weak interpretability, limited multi-modality and limited data in imaging studies

2.6. Conclusion

Medicine and computers will inevitably merge

3. Reference List

Zhang, L. et al. (2020) 'A Survey on Deep Learning for Neuroimaging-Based Brain Disorder Analysis', Front Neurosci. doi: 10.3389/fnins.2020.00779

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