benchmarks/models/itemknn/README.md

ItemKNN

For this approach item vectors are represented as user-frequency [num users]-dimensional vectors constructed from the user-item interaction matrix $UU$. $U_{ij}U\_\{ij\}$ indicates how many times user $ii$ interacted with the item $jj$.

Similarity Measurement

We employ cosine similarity to measure similarity between vectors: $score(use{r}_i,ite{m}_j)=\cos (V_i,U_j^{\mathrm{\top }})score(user\_i,\; item\_j)\; =\; \backslash cos(V\_i,\; U^\backslash top\_j)$

where:

• $UU$ [num user $\times \backslash times$ num items]: original user-item interaction matrix

• $VV$ [num users $\times \backslash times$ num users]: user embedding matrix, where each row is:

  $V_i={\sum }_{(t,k)\in A_i}{\tau }^{{\max }_t(i)-t}{U}_k^{\mathrm{\top }}V\_\{i\}\; =\; \backslash sum\_\{(t,\; k)\; \backslash in\; A\_i\}\; \backslash tau^\{\backslash max\_t(i)\; -\; t\}\; U^\backslash top\_\{k\}$

  • $A_{i}A\_i$: set of $ii$-th user's (interaction timestamp, item index) pairs
  • ${\max }_t(i)\backslash max\_t(i)$: last $ii$-th user's interaction timestamp
  • $\tau \backslash tau$: time decay coefficient (per second)

For instance, when $\tau \backslash tau$ is equal to 0 (which is the simplest case), Top-k recommendations are generated by retrieving the most closest (k) item embeddings to the latest user's representation.

Hyperparameters

Parameter hour defines the time period (in hours) associated with a decay factor of 0.9.

Implementation Note

For 5b-scale datasets, memory constraints arise when multiplying user-item interaction matrix $UU$ and the user embedding matrix making computations infeasible. Thus, results for these datasets are not provided.