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Table 11 Frequently used notations

From: Improving session-based recommendation with contrastive learning

Notation Description
\({\Theta }\) Parameters in PIE-CL
\({\mathcal {F}}\) Activation function
B The batch size
T The session’s length
K K value in objective evaluations
L Clip value for session truncation
N The size of the memory bank
\({\mathcal {S}}/ x_i \) Session set / i-th item
\({\mathcal {V}}/ v_i\) Item embedding set / i-th item
t The last time step of the session
n The total number of items in the item set \({\mathcal {V}}\)
\(\mathbf {e}_i\) The embedding of i-th item
\(\mathbf {p}_i\) The embedding of position for i-th item
\({\mathcal {A}}\) The affinity matrix for importance extraction
\(\mathbf {Q}\) The query matrix for importance extraction
\(\mathbf {K}\) The key matrix for importance extraction
d The dimensionality of hidden state
\(\alpha _i\) The attention weight of i-th item
\(\mathbf {z}_l\) The long-term preference
\(\mathbf {z}_s\) The short-term preference
\(\mathbf {z}\) The individual preference
\({\hat{z}}_i\) The matching score with a certain item
\({\hat{y}}_i\) The matching probability with a certain item
\({\mathcal {L}}\) The cross-entropy loss
\({\mathcal {L}}_{CL}^i\) The proposed contrastive learning loss for i-th record
\(\mathbf {z}_i^+\) The mean vector of positive session representation
\(\mathbf {z}_i^-\) The mean vector of negative session representation
\(\mathbf {x}_{it}\) The target representation for i-th record
M The sum of contrastive samples
x The simplified representation for target item
\(x^+\) The simplified representation for matching score
\(x^-\) The simplified representation for non-matching score
\(\tau \) The temperature parameter
\(\lambda \) The hyper-parameter for losses compromise
  1. Vectors are denoted by boldface lowercase letters, Matrices are denoted by boldface uppercase letters