CSCE 470 Lecture 25

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Just covered this stuf...

Root-Mean-Square Error (RMSE)

(See wikipedia:Root-mean-square deviation→)

Used for evaluating the effectiveness of a model/estimator (or in our case, a recommender based on ratings)

$RMSE={\sqrt {\frac {\sum \left({\mbox{predicted}}-{\mbox{actual}}\right)^{2}}{n}}}$

Given matrix of data:

${\begin{bmatrix}4&&3&\\3&4&2^{*}&\\3&5^{*}&5&\\&&4^{*}&5\\\end{bmatrix}}$

The starred items are not known to the algorithm. Suppose the algorithm gives the following scores:

${\begin{bmatrix}4&&3&\\3&4&3&\\3&2&5&\\&&1&5\\\end{bmatrix}}$

The RMSE is

${\sqrt {\frac {(3-2)^{2}+(2-5)^{2}+(1-4)^{2}}{3}}}\approx 2.516611478$

The goal is to minimize this value. If the value is 1, then our recommender was off by one for every single value.

Introspection

Does rating really equal enjoyment?

Well, ${\mbox{rating}}={\mbox{enjoyment}}({\mbox{context}})$

Recommender Systems

Collaborative Filtering

1. Take everybody, find average rating
2. Find KNN (see below) and take their rating

To find similarity (as in KNN), we need:

1. representation (usually a vector)
   • ratings
   • Watched-or-not (binary)
   • distance from average
2. a way to compare
   • manhattan
   • Euclidean
   • Cosine
   • Jaccard

Once we've found several similar users, how should we give score based on values?

• average
• max (optimistic)
• min (don't suck)
• weighted average

How could Clustering Help us?

Find groups of similar people that have similar tastes