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diff --git a/report/paper.md b/report/paper.md index a20e943..89e260c 100755 --- a/report/paper.md +++ b/report/paper.md @@ -113,16 +113,16 @@ improve identification accuracy, and consider it an additional baseline. ## Mahalanobis Distance -We were not able to achieve significant improvements using mahalanobis for +We were not able to achieve significant improvements using Mahalanobis for original distance ranking compared to square euclidiaen metrics. -The mahalanobis distance metric was used to create the ranklist as an alternative to euclidean distance: +The Mahalanobis distance metric was used to create the ranklist as an alternative to euclidean distance: $$ d_M(p,g_i) = (p-g_i)^TM(p-g_i). $$ -When performing mahalanobis with the covariance matrix $M$ generated from the training set, reported accuracy is reduced to **38%** . +When performing Mahalanobis with the covariance matrix $M$ generated from the training set, reported accuracy is reduced to **38%** . -We also attempted to perform the same mahalanobis metric on a reduced PCA featureset. This allowed for significant execution +We also attempted to perform the same Mahalanobis metric on a reduced PCA featureset. This allowed for significant execution time improvements due to the greatly reduced computation requierments for smaller featurespace, but nevertheless demonstrated no improvements over an euclidean metric. @@ -140,7 +140,7 @@ transformations performed the the ResNet-50 convolution model the features were \end{center} \end{figure} -While we did not use mahalanobis as a primary distance metric, it is possible to use the Mahalanobis metric, together with the next investigated solution involving $k$-reciprocal re-ranking. +While we did not use Mahalanobis as a primary distance metric, it is possible to use the Mahalanobis metric, together with the next investigated solution involving $k$-reciprocal re-ranking. # Suggested Improvement @@ -193,12 +193,13 @@ 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 rank-list: $d^*(p,g_i)=(1-\lambda)d_J(p,g_i)+\lambda d(p,g_i)$. +## Optimisation 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 multi-direction search 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: $k_{1_{opt}}=9, k_{2_{opt}}=3, 0.1\leq\lambda_{opt}\leq 0.3$. -It is possible to verify that the optimization of $k_{1_{opt}}$, $k_{2_{opt}}$ and $\lambda$ +It is possible to verify that the optimisation of $k_{1_{opt}}$, $k_{2_{opt}}$ and $\lambda$ has been successful. Figures \ref{fig:pqvals} and \ref{fig:lambda} show that the optimal values obtained from training are close to the ones for the local maximum of gallery and query. @@ -220,7 +221,6 @@ training are close to the ones for the local maximum of gallery and query. \end{center} \end{figure} - ## $k$-reciprocal Re-ranking Evaluation Re-ranking achieves better results than the other baseline methods analyzed both as top $k$ @@ -252,6 +252,9 @@ The difference between the top $k$ accuracies of the two methods gets smaller as \end{center} \end{figure} +The improved results due to $k$-reciprocal re-ranking can be explained by considering...re-ranking can be explained by considering... + + # Conclusion # References |