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zeEW{OhCCq*MF0XVyi)X_I8L~mh4#*0vFTZC;TdXCNx#vZPH$Ta9o^*6T=~@WW6TXp z)0P}Q6&o#P+Va5=<|i~Fmg2tyjLGW|bagG2Pxej29tPB{TJOGMnl)HJM`;yjG?&od z%54=2z;)TEqLxG7P3P>^PTx)Y?2n)RX#zBTi-y8fDX4CG@eL1c9$o!XSGQ^YZd=&b b-{hIobiQFoLIh?`R#tX63JP&W3Aq0OGi{i9 diff --git a/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.tex b/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.tex index 4895642f..0c520c16 100644 --- a/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.tex +++ b/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.tex @@ -809,6 +809,170 @@ Problems that exist in obtaining user feedback include: However, these metrics are rarely as trustworthy as explicit feedback. \end{itemize} +\section{Collaborative Filtering} +\textbf{Content filtering} is based solely on matching content of items to user's information needs. +\textbf{Collaborative filtering} collects human judgements and matches people who share the same information needs \& tastes. +Users share their judgements \& opinions. +It echoes the ``word of mouth'' principle. +Advantages of collaborative filtering over content filtering include: +\begin{itemize} + \item Support for filtering / retrieval of items where contents cannot be easily analysed in an automated manner. + \item Ability to filter based on quality / taste. + \item Recommend items that do not contain content the user was expecting. +\end{itemize} + +This approach has been successful in a number of domains -- mainly in recommending books/music/films and in e-commerce domains, e.g. Amazon, Netflix, Spotify, ebay, etc. +It has also been applied to collaborative browsing \& searching. +In fact, it can be applied whenever we have some notion of ``ratings'' or ``likes'' or ``relevance'' of items for a set of users. +\\\\ +The data in collaborative filtering consists of \textbf{users} (a set of user identifiers), \textbf{items} (a set of item identifiers), \& \textbf{ratings by users of items} (numeric values in some pre-defined range). +We can usually view this as a user-by-item matrix. + +\begin{figure}[H] + \centering + \includegraphics[width=0.8\textwidth]{./images/userbyitemmatrix.png} + \caption{User-By-Item Matrix Example (ratings from 1 to 5; 0 indicates no rating)} +\end{figure} + +With \textbf{explicit ratings}, the user usually provides a single numeric value, although the user maybe unwilling to supply many explicit ratings. +\textbf{Universal queries} are when a gauge set of items is presented to the user for rating. +Choosing a good gauge set is an open question. +\textbf{User-selected queries} are when the user chooses which items to rate (often leaving a sparse ratings matrix with many null values). +\\\\ +\textbf{Implicit ratings} are when the user's recommendation is obtained from purchase records, web logs, time spent reading an item, etc. +This implicit rating is usually mapped to some numeric scale. +\\\\ +For \textbf{user-user recommendation} approaches, there are three general steps: +\begin{enumerate} + \item \textbf{Calculate user correlation:} Find how \textit{similar} each user is to every other user. + \item \textbf{Select neighbourhood:} form groups or \textit{neighbourhoods} of users who are similar. + \item \textbf{Generate prediction:} in each group, \textit{make recommendations} based on what other users in the group have rated. +\end{enumerate} + +\subsection{Step 1: Calculate User Correlation} +Some approaches for finding how similar each user is to every other user include: +\begin{itemize} + \item Pearson correlation. + \item Constrained Pearson correlation. + \item The Spearman rank correlation. + \item Vector similarity. +\end{itemize} + +\subsubsection{Pearson Correlation} +\textbf{Pearson correlation} is when a weighted average of deviations from the neighbour's mean is calculated. +\[ + w_{a,u} = \frac{\sum^m_{i=1} (r_{a,i} - \overline{r}_a) \times (r_{u,i} - \overline{r}_u)} + {\sqrt{\sum^m_{i=1} (r_{u,i} - \overline{r}_u)^2} \times \sqrt{\sum^m_{i=1}(r_{a,i} - \overline{r}_a})^2} +\] +where for $m$ items: +\begin{itemize} + \item $r_{a,i}$ is the rating of a user $a$ for an item $i$. + \item $r_a$ is the average rating given by a user $a$. + \item $r_{u,i}$ is the rating of user $u$ for item $i$. + \item $r_u$ is the average rating given by user $u$. +\end{itemize} + +\subsubsection{Vector Similarity} +\textbf{Vector similarity} uses the cosine measure between the user vectors (where users are represented by a vector of ratings for items in the data set) to calculate correlation. + +\subsection{Step 2: Select Neighbourhood} +Some approaches for forming groups or \textbf{neighbourhoods} of users who are similar include: +\begin{itemize} + \item \textbf{Correlation thresholding:} all neighbours with absolute correlations greater than a specified threshold are selected, say 0.7 if correlations in range 0 to 1. + \item \textbf{Best-$n$ correlations:} the best $n$ correlates are chosen. +\end{itemize} + +A large neighbourhood can result in low-precision results, while a small neighbourhood can result in few or now predictions. + +\subsection{Step 3: Generate Predictions} +For some user (the active user) in a group, make recommendations based on what other users inthe group have rated which the active user has not rated. +Approaches for doing so include: +\begin{itemize} + \item \textbf{Compute the weighted average} of the user rating using the correlations as the weights. + This weighted average approach makes an assumption that all users rate items with approximately the same distribution. + \item \textbf{Compute the weighted mean} of all neighbours' ratings. + Rather than take the explicit numeric value of a rating, a rating's strength is interpreted as its distance from a neighbour's mean rating. + This approach attempts to account for the lack of uniformity in ratings. + + \[ + P_{a,i} = \bar{r}_a + \frac{\sum^n_{u=1} (r_{u,i - \bar{r}_u}) \times w_{a,u}}{\sum^n_{u=1} w_{a,u}} + \] + where for $n$ neighbours: + \begin{itemize} + \item $\bar{r}_a$ is the average rating given by active user $a$. + \item $r_{u,i}$ is the rating of user $u$ for item $i$. + \item $w_{a,u}$ is the similarity between user $u$ and $a$. + \end{itemize} +\end{itemize} + +Note that the Pearson Correlation formula does not explicitly take into account the number of co-rated items by users. +Thus it is possible to get a high correlation value based on only one co-rated item. +Often, the Pearson Correlation formula is adjusted to take this into account. + +\subsection{Experimental Approach for Testing} +A known collection of ratings by users over a range of items is decomposed into two disjoint subsets. +The first set (usually the larger) is used to generate recommendations for items corresponding to those in the smaller set. +These recommendations are then compared to the actual ratings in the second subset. +The accuracy \& coverage of a system can thus be ascertained. + +\subsubsection{Metrics} +The main metrics used to test the predictions produced are: +\begin{itemize} + \item \textbf{Coverage:} a measure of the ability of the system to provide a recommendation on a given item. + \item \textbf{Accuracy:} a measure of the correctness of the recommendations generated by the system. +\end{itemize} + +\textbf{Statistical accuracy metrics} are usually calculated by comparing the ratings generated by the system to user-provided ratings. +The accuracy is usually presented as the mean absolute error (\textbf{MAE}) between ratings \& predictions. +\\\\ +Typically, the value of the rating is not that important: it is more important to know if the rating is a useful or a non-useful rating. +\textbf{Decision support accuracy metrics} measure whether the recommendation is actually useful to the user. +Many other approaches also exist, including: +\begin{itemize} + \item Machine learning approaches. + \begin{itemize} + \item Bayesian models. + \item Clustering models. + \end{itemize} + \item Models of how people rate items. + \item Data mining approaches. + \item Hybrid models which combine collaborative filtering with content filtering. + \item Graph decomposition approaches. +\end{itemize} + +\subsection{Collaborative Filtering Issues} +\begin{itemize} + \item \textbf{Sparsity of Matrix:} in a typical domain, there would be many users \& many items but any user would only have rated a small fraction of all items in the dataset. + Using a technique such as \textbf{Singular Value Decomposition (SVD)}, the data space can be reduced, and due to this reduction a correlation may be found between similar users who do not have overlapping ratings in the original matrix of ratings. + + \item \textbf{Size of Matrix:} in general, the matrix is very large, which can affect computational efficiency. + SVD has been used to improve scalability by dimensionality reduction. + + \item \textbf{Noise in Matrix:} we need to consider how would a user's ratings change for items and how to model time dependencies; are all ratings honest \& reliable? + + \item \textbf{Size of Neighbourhood:} while the size of the neighbourhood affects predictions, there is no way to know the ``right'' size. + Need to consider whether visualisation of the would neighbourhood help, whether summarisation of the main themes/feature of neighbourhoods help. + + \item \textbf{How to Gather Ratings:} new users, new items: perhaps use weighted average of global mean \& users or items. + What if the user is not similar to others? +\end{itemize} + +\subsection{Combining Content \& Collaborative Filtering} +For most items rated in a collaborative filtering domain, content information is also available: +\begin{itemize} + \item Books: author, genre, plot summary, language, etc. + \item Music: artist, genre, sound samples, etc. + \item Films: director, genre, actors, year, country, etc. +\end{itemize} + +Traditionally, content is not used in collaborative filtering, although it could be. +\\\\ +Different approaches may suffer from different problems, so can consider combining multiple approaches. +We can also view collaborative filtering as a machine learning classification problem: for an item, do we classify it as relevant to a user or not? +\\\\ +Much recent work has been focused on not only giving a recommendation, but also attempting to explain the recommendation to the user. +Questions arise in how best to ``explain'' or visualise the recommendation. + \end{document} diff --git a/year4/semester1/CT4100: Information Retrieval/notes/images/userbyitemmatrix.png b/year4/semester1/CT4100: Information Retrieval/notes/images/userbyitemmatrix.png new file mode 100644 index 0000000000000000000000000000000000000000..2e388e6e4dac0658b41c0af03ffb794964e988fd GIT binary patch literal 73657 zcmeFZXH=Ehnk{T7%Zz0y1{5%$C{YANlBkG^B$b?1k`g6LuF_Hz35t@Fie%VG+9UxJ 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