assignment-1.tex

% This version of CVPR template is provided by Ming-Ming Cheng.
% Please leave an issue if you found a bug:
% https://github.com/MCG-NKU/CVPR_Template.

\documentclass[final]{cvpr}

\usepackage{times}
\usepackage{epsfig}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amssymb}

% Include other packages here, before hyperref.
\usepackage{csquotes}

% If you comment hyperref and then uncomment it, you should delete
% egpaper.aux before re-running latex.  (Or just hit 'q' on the first latex
% run, let it finish, and you should be clear).
\usepackage[pagebackref=true,breaklinks=true,colorlinks,bookmarks=false]{hyperref}


\def\cvprPaperID{****} % *** Enter the CVPR Paper ID here
\def\confYear{2021}
%\setcounter{page}{4321} % For final version only

\newcommand{\q}[1]{\enquote{#1}}

\begin{document}

%%%%%%%%% TITLE
\title{
	Project proposal \\~\\
	\large{Team name: M2 Robo}
}

\author{
	Lee Chun Yin\\
	3035469140\\
	\and
	Chiu Yu Ying\\
	3035477630
	\and
	Chan Kwan Yin\\
	3035466978 \\
	Team leader
}

\maketitle

\clearpage

\section{Data set to analyze}

We will analyze the \q{Netflix Prize} dataset.

\section{Proposed methodology}
We are going to construct the following three models to analzye the data set
and compare their performance.

\subsection{KNN}
We will include item-based $k$-nearest neighbours (KNN) as the first model.
It is a kind of neighbourhood-based approaches, which are popular collaborative filtering methods in previous competitions (Progress Prize 2008's KNNMovie).
The item-item correlation $\rho_{ij}$ between item $i, j$ will be calculated based on the ratings of users who rated both movies
using different statistics such as Pearson and Spearman correlation.
It is a robust classifier with a simple implementation and involves few parameters to tune (e.g. distance metric and $k$).
However, it is sensitive to outliers during the choice of neighbour process based on distance criteria.
Furthermore, KNN does not output rating values,
reducing the interpretability of the recommendation results
and hinders the potential to compare with other data directly.

\subsection{Simple SVD}
Our second model will use the \q{SVD} model,
proposed by Yehuda Koren~\cite{CollabFiltering}.
The model predicts the rating for movie $i$ by user $u$ in the form
$$ \hat r_{ui} = \mu + b_u + b_i + \mathbf q_i \cdot \mathbf p_u $$
where the parameters to train are \begin{itemize}
	\item $\mu$ is the mean rating
	\item $b_u(t)$ is a time-sensitive user-specific bias predicted by parameter binning
	\item $b_i(t)$ is a time-sensitive item-specific bias predicted by parameter binning
	\item $\mathbf q_i$ and $\mathbf p_u$ are latent factors
		produced from matrix factorization with simple stochastic gradient descent
		after the ratings are offset by the bias.
\end{itemize}

Compared to KNN, SVD provides better serendipity
since it computes all movies globally and provides a single objective metric,
unlike KNN, which largely depends on the user's similarity to other users.
However, this method requires more training time
since it involves a collection of different parameters to tune.

\subsection{SVD++}
The third model is a modification to the SVD model
by introducing time effects.
We will bin the training data over time intervals
and train the parameters $b_u, b_i, \mathbf p_u$ as functions in terms of rating date $t$,
where each user-bin is considered as a separate $u$ in the factorization.
This idea is a simplification based on the \q{SVD++} model
proposed by BellKor in Progress Prize 2008~\cite{BellKor2008}.

Since this model additionally considers time effect,
it is speculated that it performs no worse than the simple SVD model.
The temporal effects of item bias, user bias and user-preference bias
are thoroughly explained in BellKor's paper~\cite{BellKor2008}.
However, since recommendation systems are often only useful for predicting future events,
the time-dependent functions may be somehow extrapolated to the future,
while extrapolation is known to be unreliable.
Nevertheless, this is helpful in offseting rating bias during training.

{\small
	\bibliographystyle{ieee_fullname}
	\bibliography{egbib}
}

\end{document}