Skip to main content

Table 1 Time complexity in training and test phases (for one input sample)

From: DeConFuse: a deep convolutional transform-based unsupervised fusion framework

PhaseStepsTime complexityDimension description
Training phase1. Convolution layers\(\mathcal {O}(P_{\ell } D_{\ell } M_{\ell } C)\) 
 2. Fully-connected (f.-c.) layer\(\mathcal {O}(I^{2} C^{2})\)\(S^{(c)} \in \mathbb {R}^{K\times D}\)
 3. Frobenius norm on conv. layers\(\mathcal {O}\left (P_{\ell } M_{\ell } C\right)\)\(T_{\ell }^{(c)}\in \mathbb {R}^{P_{\ell }\times M_{\ell }}\)
 4. Frobenius norm on f.-c. layer\(\mathcal {O}(I^{2} C^{2})\)\(\text {flat}(X^{(c)})\in \mathbb {R}^{K\times I}\)
 5. log-det on conv. layers\(\mathcal {O}(P_{\ell }^{2} M_{\ell } C)\)\(\widetilde {T_{c}} \in \mathbb {R}^{I \times O}\)
 6. log-det on f.-c. layer\(\mathcal {O}(I^{3}C^{2})\) 
Testing phaseStep 1. + Step 2.Step 1. + Step 2. 
  1. D = input sample size – K = num. of samples – C = num. of channels – L = num. of layers
  2. P = filter size at layer M = num. of filters at layer D = output sample size at layer
  3. I=DLML is the num. of output features per sample at last convolution layer
  4. O=αIC (with α[0,1]) is the num. of output features per sample at the fully connected layer