| AN . | Meaning . | First appearance . | AN . | Meaning . | First appearance . |
|---|---|---|---|---|---|
| |$a^{(l)}_j(\boldsymbol {x})$| | the output of the jth node in the lth layer for an input x | Section 4.1 | ap | an atmospheric parameter log Teff, log g or [Fe/H] | Section 7 |
| |$b^{(l)}_j$| | the bias of the jth node in the (l + 1)th layer | Section 4.1 | β | a regularized parameter in the objective function J(·, ·) | Section 4.1 |
| BSE | basic structure element | Abstract | DCP | description by convolution and pooling | Section 5.2 |
| f(·) | an estimation method | Section 6 | g(·) | an activation function of an autoencoder | Section 4.1 |
| hW, b | the mapping of an autoencoder | Section 4.1 | J(·, ·) | the objective function of an autoencoder | Section 4.1 |
| KL( · ∥ · ) | relative entropy of the average output of a hidden node and its expected output | Section 4.1 | λ | a weight decay parameter in the objective function J(·, ·) | Section 4.1 |
| |$\hat{\lambda }$| | optimized value for λ. |$\hat{\beta }$|, |$\hat{\rho }$|, |$\hat{n}$|, |$\hat{N}_p$|, |$\hat{n}^{\rm BP}_{\rm hl}$| and |$\hat{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| are defined similarly | Section 7 | m | number of nodes in the input layer of an autoencoder | Section 4.1 |
| n | number of nodes in the hidden layer of an autoencoder | Section 4.1 | |$n^{\rm BP}_{\rm hl}$| | number of hidden layers in a BP network | Section 6 |
| |$\tilde{n}^{\rm BP}_{\rm hl}$| | initialized value of |$n^{\rm BP}_{\rm hl}$| | Section 7 | |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | number of nodes in the hidden layers of a BP network | Section 6 |
| |$\tilde{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| | an initialization of |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | Section 7 | N | number of samples in a data set S or Str depending on its context | Section 4.1 |
| Np | number of pools | Section 5.2 | ρ | an desired activation level | Section 4.1 |
| |$\bar{\rho }_j$| | the average activation of the jth hidden node of an autoencoder | Section 4.1 | RRλ | restricted (search) range for λ. RRβ, RRρ, RRn, |$RR_{{N}_p}$|, |$RR_{{n}^{\rm BP}_{\rm hl}}$| and |$RR_ {{\boldsymbol {n}}^{\rm BP}_{\rm nhl}}$| are defined similarly | Section 7 |
| S | a data set with spectra and atmospheric parameters | Section 6 | SBSE | a set of BSEs | Section 4.2 |
| Str | a training set of stellar spectra | Section 4.2 | |$S^{\rm tr\_ae}$| | a training set for an autoencoder, consists of some spectral patches | Section 4.1 |
| |$v^{(j)}_q$| | the maximum convolution response with the jth BSE in the qth pool | Section 5.2 | w | description by convolution and pooling (DCP) | Section 5.2 |
| |$W^{(1)}_{j\cdot }$| | the jth BSE | Section 4.1 | |$W^{(l)}_{ji}$| | a weight between the ith node in the lth layer and the jth node in the (l + 1)th layer | Section 4.1 |
| x | a spectrum or a spectral patch for an autoencoder depending on its context | Section 2.3 | |$\bar{\boldsymbol {x}}$| | a normalized spectrum | Section 2.3 |
| y | output of an autoencoder | Section 4.1 | z | a convolution response of a spectrum with BSEs | Section 5.1 |
| AN . | Meaning . | First appearance . | AN . | Meaning . | First appearance . |
|---|---|---|---|---|---|
| |$a^{(l)}_j(\boldsymbol {x})$| | the output of the jth node in the lth layer for an input x | Section 4.1 | ap | an atmospheric parameter log Teff, log g or [Fe/H] | Section 7 |
| |$b^{(l)}_j$| | the bias of the jth node in the (l + 1)th layer | Section 4.1 | β | a regularized parameter in the objective function J(·, ·) | Section 4.1 |
| BSE | basic structure element | Abstract | DCP | description by convolution and pooling | Section 5.2 |
| f(·) | an estimation method | Section 6 | g(·) | an activation function of an autoencoder | Section 4.1 |
| hW, b | the mapping of an autoencoder | Section 4.1 | J(·, ·) | the objective function of an autoencoder | Section 4.1 |
| KL( · ∥ · ) | relative entropy of the average output of a hidden node and its expected output | Section 4.1 | λ | a weight decay parameter in the objective function J(·, ·) | Section 4.1 |
| |$\hat{\lambda }$| | optimized value for λ. |$\hat{\beta }$|, |$\hat{\rho }$|, |$\hat{n}$|, |$\hat{N}_p$|, |$\hat{n}^{\rm BP}_{\rm hl}$| and |$\hat{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| are defined similarly | Section 7 | m | number of nodes in the input layer of an autoencoder | Section 4.1 |
| n | number of nodes in the hidden layer of an autoencoder | Section 4.1 | |$n^{\rm BP}_{\rm hl}$| | number of hidden layers in a BP network | Section 6 |
| |$\tilde{n}^{\rm BP}_{\rm hl}$| | initialized value of |$n^{\rm BP}_{\rm hl}$| | Section 7 | |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | number of nodes in the hidden layers of a BP network | Section 6 |
| |$\tilde{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| | an initialization of |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | Section 7 | N | number of samples in a data set S or Str depending on its context | Section 4.1 |
| Np | number of pools | Section 5.2 | ρ | an desired activation level | Section 4.1 |
| |$\bar{\rho }_j$| | the average activation of the jth hidden node of an autoencoder | Section 4.1 | RRλ | restricted (search) range for λ. RRβ, RRρ, RRn, |$RR_{{N}_p}$|, |$RR_{{n}^{\rm BP}_{\rm hl}}$| and |$RR_ {{\boldsymbol {n}}^{\rm BP}_{\rm nhl}}$| are defined similarly | Section 7 |
| S | a data set with spectra and atmospheric parameters | Section 6 | SBSE | a set of BSEs | Section 4.2 |
| Str | a training set of stellar spectra | Section 4.2 | |$S^{\rm tr\_ae}$| | a training set for an autoencoder, consists of some spectral patches | Section 4.1 |
| |$v^{(j)}_q$| | the maximum convolution response with the jth BSE in the qth pool | Section 5.2 | w | description by convolution and pooling (DCP) | Section 5.2 |
| |$W^{(1)}_{j\cdot }$| | the jth BSE | Section 4.1 | |$W^{(l)}_{ji}$| | a weight between the ith node in the lth layer and the jth node in the (l + 1)th layer | Section 4.1 |
| x | a spectrum or a spectral patch for an autoencoder depending on its context | Section 2.3 | |$\bar{\boldsymbol {x}}$| | a normalized spectrum | Section 2.3 |
| y | output of an autoencoder | Section 4.1 | z | a convolution response of a spectrum with BSEs | Section 5.1 |
| AN . | Meaning . | First appearance . | AN . | Meaning . | First appearance . |
|---|---|---|---|---|---|
| |$a^{(l)}_j(\boldsymbol {x})$| | the output of the jth node in the lth layer for an input x | Section 4.1 | ap | an atmospheric parameter log Teff, log g or [Fe/H] | Section 7 |
| |$b^{(l)}_j$| | the bias of the jth node in the (l + 1)th layer | Section 4.1 | β | a regularized parameter in the objective function J(·, ·) | Section 4.1 |
| BSE | basic structure element | Abstract | DCP | description by convolution and pooling | Section 5.2 |
| f(·) | an estimation method | Section 6 | g(·) | an activation function of an autoencoder | Section 4.1 |
| hW, b | the mapping of an autoencoder | Section 4.1 | J(·, ·) | the objective function of an autoencoder | Section 4.1 |
| KL( · ∥ · ) | relative entropy of the average output of a hidden node and its expected output | Section 4.1 | λ | a weight decay parameter in the objective function J(·, ·) | Section 4.1 |
| |$\hat{\lambda }$| | optimized value for λ. |$\hat{\beta }$|, |$\hat{\rho }$|, |$\hat{n}$|, |$\hat{N}_p$|, |$\hat{n}^{\rm BP}_{\rm hl}$| and |$\hat{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| are defined similarly | Section 7 | m | number of nodes in the input layer of an autoencoder | Section 4.1 |
| n | number of nodes in the hidden layer of an autoencoder | Section 4.1 | |$n^{\rm BP}_{\rm hl}$| | number of hidden layers in a BP network | Section 6 |
| |$\tilde{n}^{\rm BP}_{\rm hl}$| | initialized value of |$n^{\rm BP}_{\rm hl}$| | Section 7 | |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | number of nodes in the hidden layers of a BP network | Section 6 |
| |$\tilde{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| | an initialization of |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | Section 7 | N | number of samples in a data set S or Str depending on its context | Section 4.1 |
| Np | number of pools | Section 5.2 | ρ | an desired activation level | Section 4.1 |
| |$\bar{\rho }_j$| | the average activation of the jth hidden node of an autoencoder | Section 4.1 | RRλ | restricted (search) range for λ. RRβ, RRρ, RRn, |$RR_{{N}_p}$|, |$RR_{{n}^{\rm BP}_{\rm hl}}$| and |$RR_ {{\boldsymbol {n}}^{\rm BP}_{\rm nhl}}$| are defined similarly | Section 7 |
| S | a data set with spectra and atmospheric parameters | Section 6 | SBSE | a set of BSEs | Section 4.2 |
| Str | a training set of stellar spectra | Section 4.2 | |$S^{\rm tr\_ae}$| | a training set for an autoencoder, consists of some spectral patches | Section 4.1 |
| |$v^{(j)}_q$| | the maximum convolution response with the jth BSE in the qth pool | Section 5.2 | w | description by convolution and pooling (DCP) | Section 5.2 |
| |$W^{(1)}_{j\cdot }$| | the jth BSE | Section 4.1 | |$W^{(l)}_{ji}$| | a weight between the ith node in the lth layer and the jth node in the (l + 1)th layer | Section 4.1 |
| x | a spectrum or a spectral patch for an autoencoder depending on its context | Section 2.3 | |$\bar{\boldsymbol {x}}$| | a normalized spectrum | Section 2.3 |
| y | output of an autoencoder | Section 4.1 | z | a convolution response of a spectrum with BSEs | Section 5.1 |
| AN . | Meaning . | First appearance . | AN . | Meaning . | First appearance . |
|---|---|---|---|---|---|
| |$a^{(l)}_j(\boldsymbol {x})$| | the output of the jth node in the lth layer for an input x | Section 4.1 | ap | an atmospheric parameter log Teff, log g or [Fe/H] | Section 7 |
| |$b^{(l)}_j$| | the bias of the jth node in the (l + 1)th layer | Section 4.1 | β | a regularized parameter in the objective function J(·, ·) | Section 4.1 |
| BSE | basic structure element | Abstract | DCP | description by convolution and pooling | Section 5.2 |
| f(·) | an estimation method | Section 6 | g(·) | an activation function of an autoencoder | Section 4.1 |
| hW, b | the mapping of an autoencoder | Section 4.1 | J(·, ·) | the objective function of an autoencoder | Section 4.1 |
| KL( · ∥ · ) | relative entropy of the average output of a hidden node and its expected output | Section 4.1 | λ | a weight decay parameter in the objective function J(·, ·) | Section 4.1 |
| |$\hat{\lambda }$| | optimized value for λ. |$\hat{\beta }$|, |$\hat{\rho }$|, |$\hat{n}$|, |$\hat{N}_p$|, |$\hat{n}^{\rm BP}_{\rm hl}$| and |$\hat{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| are defined similarly | Section 7 | m | number of nodes in the input layer of an autoencoder | Section 4.1 |
| n | number of nodes in the hidden layer of an autoencoder | Section 4.1 | |$n^{\rm BP}_{\rm hl}$| | number of hidden layers in a BP network | Section 6 |
| |$\tilde{n}^{\rm BP}_{\rm hl}$| | initialized value of |$n^{\rm BP}_{\rm hl}$| | Section 7 | |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | number of nodes in the hidden layers of a BP network | Section 6 |
| |$\tilde{\boldsymbol {n}}^{\rm BP}_{\rm nhl}$| | an initialization of |$\boldsymbol {n}^{\rm BP}_{\rm nhl}$| | Section 7 | N | number of samples in a data set S or Str depending on its context | Section 4.1 |
| Np | number of pools | Section 5.2 | ρ | an desired activation level | Section 4.1 |
| |$\bar{\rho }_j$| | the average activation of the jth hidden node of an autoencoder | Section 4.1 | RRλ | restricted (search) range for λ. RRβ, RRρ, RRn, |$RR_{{N}_p}$|, |$RR_{{n}^{\rm BP}_{\rm hl}}$| and |$RR_ {{\boldsymbol {n}}^{\rm BP}_{\rm nhl}}$| are defined similarly | Section 7 |
| S | a data set with spectra and atmospheric parameters | Section 6 | SBSE | a set of BSEs | Section 4.2 |
| Str | a training set of stellar spectra | Section 4.2 | |$S^{\rm tr\_ae}$| | a training set for an autoencoder, consists of some spectral patches | Section 4.1 |
| |$v^{(j)}_q$| | the maximum convolution response with the jth BSE in the qth pool | Section 5.2 | w | description by convolution and pooling (DCP) | Section 5.2 |
| |$W^{(1)}_{j\cdot }$| | the jth BSE | Section 4.1 | |$W^{(l)}_{ji}$| | a weight between the ith node in the lth layer and the jth node in the (l + 1)th layer | Section 4.1 |
| x | a spectrum or a spectral patch for an autoencoder depending on its context | Section 2.3 | |$\bar{\boldsymbol {x}}$| | a normalized spectrum | Section 2.3 |
| y | output of an autoencoder | Section 4.1 | z | a convolution response of a spectrum with BSEs | Section 5.1 |
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