using the binary matrix of recommendations one of the interesting conclusions from the netflix challenge was one of those obvious-in-hindsight ideaswe can learn lot about you just from knowing which movies you ratedeven without looking at which rating was giveneven with binary matrix where we have rating of where user rated movie and where they did notwe can make useful predictions in hindsightthis makes perfect sensewe do not choose movies to watch completely randomlybut instead pick those where we already have an expectation of liking them we also do not make random choices of which movies to ratebut perhaps only rate those we feel most strongly about (naturallythere are exceptionsbut on an average this is probably truewe can visualize the values of the matrix as an image where each rating is depicted as little square black represents the absence of rating and the grey levels represent the rating value we can see that the matrix is sparse--most of the squares are black we can also see that some users rate lot more movies than others and that some movies are the target of many more ratings than others the code to visualize the data is very simple (you can adapt it to show larger fraction of the matrix than is possible to show in this book)as followsfrom matplotlib import pyplot as plt imagedata reviews[: : todense(plt imshow(imagedatainterpolation='nearest'the following screenshot is the output of this code