From c62071cae4f4adc688a330c35e2c601c3610d823 Mon Sep 17 00:00:00 2001 From: Andrew Date: Thu, 17 Oct 2024 08:20:49 +0100 Subject: [PATCH] [CT4100]: Add Week 5 lecture materials & notes --- .../Lecture_5_Relevance_Feedback_slides.pdf | Bin 0 -> 143682 bytes .../notes/CT4100-Notes.pdf | Bin 300812 -> 307347 bytes .../notes/CT4100-Notes.tex | 113 +++++++++++++++++- 3 files changed, 112 insertions(+), 1 deletion(-) create mode 100644 year4/semester1/CT4100: Information Retrieval/materials/05. Feedback Mechanisms/Lecture_5_Relevance_Feedback_slides.pdf diff --git a/year4/semester1/CT4100: Information Retrieval/materials/05. Feedback Mechanisms/Lecture_5_Relevance_Feedback_slides.pdf b/year4/semester1/CT4100: Information Retrieval/materials/05. 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Retrieval/notes/CT4100-Notes.tex index c6ae0971..4895642f 100644 --- a/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.tex +++ b/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.tex @@ -679,7 +679,7 @@ where The \textbf{Okapi BM25} weighting scheme is a standard benchmark weighting scheme with relatively good performance, although it needs to be tuned per collection: \begin{align*} - \text{BM25}(Q,D) = \sum_{t \in Q \cap D} \left( \frac{\textit{tf}_{t,D} \cdot \log \left( \frac{N - \textit{df}_t _ 0.5}{\textit{df} + 0.5} \right) \cdot \textit{tf}_{t, Q}}{\textit{tf}_{t,D} + k_1 \cdot \left( (1-b) + b \cdot \frac{\textit{dl}}{\textit{dl}_\text{avg}} \right)} \right) + \text{BM25}(Q,D) = \sum_{t \in Q \cap D} \left( \frac{\textit{tf}_{t,D} \cdot \log \left( \frac{N - \textit{df}_t + 0.5}{\textit{df} + 0.5} \right) \cdot \textit{tf}_{t, Q}}{\textit{tf}_{t,D} + k_1 \cdot \left( (1-b) + b \cdot \frac{\textit{dl}}{\textit{dl}_\text{avg}} \right)} \right) \end{align*} The \textbf{Pivoted Normalisation} weighting scheme is also as standard benchmark which needs to be tuned for collection, although it has its issues with normalisation: @@ -700,4 +700,115 @@ The \textbf{Axiomatic Approach} to weighting consists of the following constrain New weighting schemes that adhere to all these constraints outperform the best known benchmarks. +\section{Relevance Feedback} +We often attempt to improve the performance of an IR system by modifying the user query; +the new modified query is then re-submitted to the system. +Typically, the user examines the returned list of documents and marks those which are relevant. +The new query is usually created via incorporating new terms and re-weighting existing terms. +The feedback from the user is used to re-calculate the term weights. +Analysis of the document set can either be \textbf{local analysis} (on the returned set) or \textbf{global analysis} (on the whole document set). +This feedback allows for the re-formulation of the query, which has the advantage of shielding the user from the task of query reformulation and from the inner details of the comparison algorithm. + +\subsection{Feedback in the Vector Space Model} +We assume that relevant documents have similarly weighted term vectors. +$D_r$ is the set of relevant documents returned, $D_n$ is the set of the non-relevant documents returned, and $C_r$ is the set of relevant documents in the entire collection. +If we assume that $C_r$ is known for a query $q$, then the best vector for a query to distinguish relevant documents from non-relevant documents is +\[ + \vec{q} = \left( \frac{1}{\left|C_r\right|} \sum_{d_j \in C_r}d_j \right) - \left( \frac{1}{N - \left|C_r\right|} \sum_{d_j \notin C_r} d_j \right) +\] + +However, it is impossible to generate this query as we do not know $C_r$. +We can however estimate $C_r$ as we know $D_r$ which is a subset of $C_r$: the main approach for doing this is the \textbf{Rocchio Algorithm:} +\[ + \overrightarrow{q_{\text{new}}} = \alpha \overrightarrow{q_\text{orginal}} + \frac{\beta}{\left| D_r \right|} \sum_{d_j \in D_r} d_j - \frac{\gamma}{\left| D_n \right|} \sum_{d_j \in D_n}d_j +\] + +where $\alpha$, $\beta$, \& $\gamma$ are constants which determine the importance of feedback and the relative importance of positive feedback over negative feedback. +Variants on this algorithm include: +\begin{itemize} + \item \textbf{IDE Regular:} + \[ + \overrightarrow{q_\text{new}} = \alpha \overrightarrow{q_\text{old}} + \beta \sum_{d_j \in D_r} d_j - \gamma \sum_{d_j \in D_n} d_j + \] + + \item \textbf{IDE Dec Hi:} (based on the assumption that positive feedback is more useful than negative feedback) + \[ + \overrightarrow{q_\text{new}} = \alpha \overrightarrow{q_\text{old}} + \beta \sum_{d_j \in D_r} d_j - \gamma \text{MAXNR}(d_j) + \] + where $\text{MAXNR}(d_j)$ is the highest ranked non-relevant document. +\end{itemize} + +The use of these feedback mechanisms have shown marked improvement in the precision \& recall of IR systems. +Salton indicated in early work on the vector space model that these feedback mechanisms result in an average precision of at least 10\%. +\\\\ +The precision-recall is re-calculated for the new returned set, often with respect to the returned document set less the set marked by the user. + +\subsection{Pseudo-Feedback / Blind Feedback} +In \textbf{local analysis}, the retrieved documents are examined at query time to determine terms for query expansion. +We typically develop some form of term-term correlation matrix. +To quantify connection between two terms, we expand the query to include terms correlated to the query terms. + +\subsubsection{Association Clusters} +To create an \textbf{association cluster}, first create a matrix $M$; +We can create term $\times$ term matrix to represent the level of association between terms. +This is usually weighted according to +\[ + M_{i,j} = \frac{\text{freq}_{i,j}}{\text{freq}_{i} + \text{freq}_{j} - \text{freq}_{i,j}} +\] + +To perform query expansion with local analysis, we can develop an association cluster for each term $t_i$ in the query. +For each term $t_i \in q$ choose the $i^\text{th}$ query term and select the top $N$ values from its row in the term matrix. +For a query $q$, select a cluster for each query term so that $\left| q \right|$ clusters are formed. +$N$ is usually small to prevent generation of very large queries. +We may then either take all terms or just those with the highest summed correlation. + +\subsubsection{Metric Clusters} +Association clusters do not take into account the position of terms within documents: \textbf{metric clusters} attempt to overcome this limitation. +Let $\text{dis}(t_i, t_j)$ be the distance between two terms $t_i$ \& $t_j$ in the same document. +If $t_i$ \& $t_j$ are in different documents, then $\text{dis}(t_i, t_j) = \inf$. +We can define the term-term correlation matrix by the following equation, and we can define clusters as before: +\[ + M_{i,j} = \sum_{t_i, t_j \in D_i} \frac{1}{\text{dis}(t_i, t_j)} +\] + +\subsubsection{Scalar Clusters} +\textbf{Scalar clusters} are based on comparing sets of words: +if two terms have similar neighbourhoods then there is a high correlation between terms. +Similarity can be based on comparing the two vectors representing the neighbourhoods. +This measure can be used to define term-term correlation matrices and the procedure can continue as before. + +\subsection{Global Analysis} +\textbf{Global analysis} is based on analysis of the whole document collection and not just the returned set. +A similarity matrix is created with a similar technique to the method used in the vector space comparison. +We then index each term by the documents in which the term is contained. +It is then possible to calculate the similarity between two terms by taking some measure of the two vectors, e.g. the dot product. +To use this to expand a query, we then: +\begin{enumerate} + \item Map the query to the document-term space. + \item Calculate the similarity between the query vector and vectors associated with query terms. + \item Rank the vectors $\vec{t_i}$ based on similarity. + \item Choose the top-ranked terms to add to the query. +\end{enumerate} + +\subsection{Issues with Feedback} +The Rocchio \& IDE methods can be used in all vector-based approaches. +Feedback is an implicit component of many other IR models (e.g., neural networks \& probabilistic models). +The same approaches with some modifications are used in information filtering. +Problems that exist in obtaining user feedback include: +\begin{itemize} + \item Users tend not to give a high degree of feedback. + \item Users are typically inconsistent with their feedback. + \item Explicit user feedback does not have to be strictly binary, we can allow a range of values. + \item Implicit feedback can also be used, we can make assumptions that a user found an article useful if: + \begin{itemize} + \item The user reads the article. + \item The user spends a certain amount of time reading the article. + \item The user saves or prints the article. + \end{itemize} + + However, these metrics are rarely as trustworthy as explicit feedback. +\end{itemize} + + + \end{document}