Figure $2$

Figure $3$ represents the SVD of the matrix from Fig. $2.$ Suppose Leslie assigns rating $3$ to Alien

and rating $4$ to Titanic, giving us a representation of Leslie in "movie space" of $0,3,0,0,4.$

Find the representation of Leslie in concept space. What does that representation predict

about how well Leslie would like the other movies appearing in our example data?

[1110033004400555000004400055

00022]

$0$

$0$

$0$

$5$

$4$

$0$

$0$

$0$

$5$

$4$

$3=\left[\begin{array}{cccccccc}\mathrm{.}14& 0& 0& 0& 0& \mathrm{.}60& \mathrm{.}75& \mathrm{.}30\end{array}\right]$

$0$

$0$

$0$

$\mathrm{.}70$

$\mathrm{.}56$

$\mathrm{.}42\left[\begin{array}{ccc}12\mathrm{.}4& 0& 9\mathrm{.}5\end{array}\right]$

$0\left[\begin{array}{ccccccccc}\mathrm{.}58& \mathrm{.}58& \mathrm{.}58& 0& 0& 0& 0& \mathrm{.}71& \mathrm{.}71\end{array}\right]$

$0$

$M$

$U$

$$

$V^T$

Figure $3$