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Diffstat (limited to 'report')
| -rwxr-xr-x | report/paper.md | 17 |
1 files changed, 10 insertions, 7 deletions
diff --git a/report/paper.md b/report/paper.md index ecf1e3e..2789923 100755 --- a/report/paper.md +++ b/report/paper.md @@ -111,15 +111,16 @@ improve identification accuracy, and consider it an additional baseline. \end{center} \end{figure} -# Suggested Improvement - ## Mahalanobis Distance 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 rank-list as an alternative to euclidean distance. -When performing mahalanobis with the training set as the covariance matrix, reported accuracy is reduced to **38%** . +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%** . 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 @@ -139,7 +140,9 @@ 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 $k +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 ## $k$-reciprocal Re-ranking Formulation @@ -178,11 +181,11 @@ e\textsuperscript{\textit{-d(p,g\textsubscript{i})}}, & \text{if}\ \textit{g\tex Through this transformation it is possible to reformulate the distance obtained through Jaccardian metric as: -$$ d_J(p,g_i)=1-\frac{\sum\limits_{j=1}^N min(V_{p,g_j},V_{g_i,g_j})}{\sum\limits_{j=1}^N max(V_{p,g_j},V_{g_i,g_j})} $$ +$$ d_J(p,g_i)=1-\frac{\sum\limits_{j=1}^N min(V_{p,g_j},V_{g_i,g_j})}{\sum\limits_{j=1}^N max(V_{p,g_j},V_{g_i,g_j})}. $$ It is then possible to perform a local query expansion using the g\textsubscript{i} neighbors of defined as: -$$ V_p=\frac{1}{|N(p,k_2)|}\sum\limits_{g_i\in N(p,k_2)}V_{g_i} $$. +$$ V_p=\frac{1}{|N(p,k_2)|}\sum\limits_{g_i\in N(p,k_2)}V_{g_i}. $$ 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 $k_1$: $R^*(g_i,k_1)$. |