What does the parameter $\alpha$ do in the Jaccard method for binaryRatingsMatrix in R recommenderlab? What is the role of the parameter 'alpha' in the recommenderlab R package's use of Jaccard method in the recommender model for boolean user-preferences matrix?
i.e. method="Jaccard",param=list(...,alpha=0.5) ?
I saw the code for IBCF ("Item-Based Collaborative Filtering") and they used a dissimilarity function. But the function is not defined in the official CRAN PDF for the recommenderlab package.
Could someone please help?
 A: To the best of my knowledge, the Jaccard similarity coefficient does not require $\alpha$ or any other additional parameter.
The jaccard-methods used in recommenderlab can be found in the package proxy and arules as stated here help("dissimilarity",package="recommenderlab").
I stepped through the documentation in both linked packages and examples, but none used an  $\alpha$ when applying jaccard. So I'd ask the author of the code you have seen directly since a non-standard version is used (maybe he/she created a new version of jaccard, it is possible to use a custom similarity function additional to the ones in the package).
Edit 15:28 CEST
In a second step through the package documentation I found the  $\alpha$. I am sorry, you were right, see recommenderRegistry$get_entries(dataType = "binaryRatingMatrix"). 
In the package vignette various papers are linked as source. In An improved collaborative ﬁltering approach for predicting cross-category purchases based on binary market basket data by Mild and Reutterer an  $\alpha$ is used to exclude item-predictors in order to reduce the topseller / popular items bias and to find more discriminatory items. The similarity calculation via jaccard is not influenced. Details can be found on page 5-6. 
However, it is still unclear whether it is this alpha and whether it is exactly used as described in the paper. I suspect that $\alpha=0.5$ means to use standard IBCF, so $z_{1-\alpha}$ is used instead of $z_{1-\frac{\alpha}{2}}$(documentation is lacking here or I just can't find it). As I have written before, contacting the author of the package may help.
Regarding your question about the k parameters:
To recommend a item, only the top k most similar predictor-items are used to make a prediction (instead of all), so a nearest-neighorhood-approach is applied here. This is described in vignette of recommenderlab page 6-7.
Some remarks regarding the paper by Mild and Reutterer


*

*The $CF_{raw}$ method uses an arbitrary decision threshold (0.5), meanwhile the a priori approach $APPROB$ always returns the top 8 recommends. No wonder the $CF_{raw}$ has a lesser precision than $APPROB$. The recall rate is mentioned but not reported.

*Binary basket data reflects implicit preferences, i.e. customer has not bought an item may mean "don't know, but will like as soon as" instead of "don't like". Hence an discrimination approach may be problematic

*Grocery data (and as it seems from an offline store) is a specific domain. Based on my own experiences, the results cannot be easily transferred to other domains like books, fashion etc., where "not bought" can often mean "has bought elsewhere".


One has to note that the paper has been written in a very early stage of recommender system research (2002).
