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| -rwxr-xr-x | report2/paper.md | 19 |
1 files changed, 17 insertions, 2 deletions
diff --git a/report2/paper.md b/report2/paper.md index 05f0ac1..8e76142 100755 --- a/report2/paper.md +++ b/report2/paper.md @@ -108,7 +108,7 @@ We find that for the query and gallery set clustering does not seem to improve i # Suggested Improvement -## k-reciprocal Reranking +## k-reciprocal Reranking Formulation The approach addressed to improve the identification performance is based on k-reciprocal reranking. The following section summarizes the idea behind @@ -120,7 +120,7 @@ intersection $R(p,k)=\{g_i|(g_i \in N(p,k))\land(p \in N(g_i,k))\}$. Adding $\frac{1}{2}k$ reciprocal nearest neighbors of each element in the ranklist $R(p,k)$, it is possible to form a more reliable set $R^*(p,k) \longleftarrow R(p,k) \cup R(q,\frac{1}{2}k)$ that aims to overcome -the problem query and gallery images being affected by factors such +the problem of query and gallery images being affected by factors such as position, illumination and foreign objects. $R^*(p,k)$ is used to recalculate the distance between query and gallery images. @@ -147,6 +147,21 @@ through Jaccardian metric as: $$ d_J(p,g_i)=1-\frac{\sum\limits_{j=1}^N min(V_{p,g_j},V_{g_i,g_j})}{\sum\limits_{j=1}^N max(V_{p,g_j},V_{g_i,g_j})} $$ +It is then possible to perform a local query expansion using the g\textsubscript{i} neighbors of +defined as $V_p=\frac{1}{|N(p,k_2)|}\sum\limits_{g_i\in N(p,k_2)}V_{g_i}$. We refer to $k_2$ since +we limit the size of the nighbors to prevent noise from the $k_2$ neighbors. The dimension k of the *$R^*$* +set will instead be defined as $k_1$:$R^*(g_i,k_1)$. + +The distances obtained are then mixed, obtaining a final distance $d^*(p,g_i)$ that is used to obtain the +improved ranklist: $d^*(p,g_i)=(1-\lambda)d_J(p,g_i)+\lambda d(p,g_i)$. + +The aim is to learn optimal values for $k_1,k_2$ and $\lambda$ in the training set that improve top1 identification accuracy. +This is done through a simple **GRADIENT DESCENT** algorithm followed by exhaustive search to estimate +$k_{1_{opt}}$ and $k_{2_{opt}}$ for eleven values of $\lambda$ from zero(only Jaccard distance) to one(only original distance) +in steps of 0.1. The results obtained through this approach suggest: $k_{1_{opt}}=9, k_{2_{opt}}=3, 0.1\leq\lambda_{opt}\leq 0.3$. + +## k-reciprocal Reranking Formulation + \begin{figure} \begin{center} \includegraphics[width=24em]{fig/ranklist.png} |