From 7229b1be92ad7adf681235c5e48032172e461853 Mon Sep 17 00:00:00 2001
From: Vasil Zlatanov <v@skozl.com>
Date: Thu, 13 Dec 2018 13:17:11 +0000
Subject: Fix inconsistencies

---
 report/paper.md | 35 ++++++++++++++++++++---------------
 1 file changed, 20 insertions(+), 15 deletions(-)

diff --git a/report/paper.md b/report/paper.md
index a961be0..9255920 100755
--- a/report/paper.md
+++ b/report/paper.md
@@ -1,4 +1,3 @@
-
 # Forulation of the Addresssed Machine Learning Problem
 
 ## Probelm Definition
@@ -55,7 +54,7 @@ Identification accuracies at top1, top5 and top10 are respectively 47%, 67% and
 \begin{figure}
 \begin{center}
 \includegraphics[width=20em]{fig/baseline.pdf}
-\caption{Recognition accuracy of baseline Nearest Neighbor @rank k}
+\caption{Top k identification accuracy of baseline Nearest Neighbor}
 \label{fig:baselineacc}
 \end{center}
 \end{figure}
@@ -67,7 +66,7 @@ identification is shown in red.
 \begin{figure}
 \begin{center}
 \includegraphics[width=22em]{fig/eucranklist.png}
-\caption{Ranklist @rank10 generated for 5 query images}
+\caption{Top 10 ranklist generated for 5 query images}
 \label{fig:eucrank}
 \end{center}
 \end{figure}
@@ -111,11 +110,17 @@ We find that for the query and gallery set clustering does not seem to improve i
 ## Comment on Mahalnobis Distance as a metric
 
 We were not able to achieve significant improvements using mahalanobis for 
-original distance ranking compared to square euclidiaen metrics. Results can 
-be observed using the `-m|--mahalanobis` when running evalution with the 
-repository complimenting this paper.
+original distance ranking compared to square euclidiaen metrics. 
+
+The mahalanobis distance metric was used to create the ranklist as an alternative to euclidean distance.
+When performing mahalanobis with the training set as the covariance matrix, reported accuracy is reduced to 
+**18%** .
+
+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.
 
-**COMMENT ON VARIANCE AND MAHALANOBIS RESULTS**
+These results are likely due to the **extremely** low covariance of features in the training set. This is evident when looking at the Covariance matrix of the training data, and is also visible in figure \ref{fig:subspace}. This is likely the result of the feature transformations performed the the ResNet-50 convolution model the features were extracted from.
 
 \begin{figure}
 \begin{center}
@@ -126,10 +131,10 @@ repository complimenting this paper.
 \end{center}
 \end{figure}
 
-## k-reciprocal Reranking Formulation
+## k-reciprocal Re-ranking Formulation
 
 The approach addressed to improve the identification performance is based on
-k-reciprocal reranking. The following section summarizes the idea behind
+k-reciprocal re-ranking. The following section summarizes the idea behind
 the method illustrated in reference @rerank-paper.
 
 We define $N(p,k)$ as the top k elements of the ranklist generated through NN,
@@ -197,15 +202,15 @@ training are close to the ones for the local maximum of gallery and query.
 \begin{center}
 \includegraphics[width=12em]{fig/lambda_acc.pdf}
 \includegraphics[width=12em]{fig/lambda_acc_tr.pdf}
-\caption{Top 1 Identification Accuracy with Rerank varying lambda(gallery-query left, train right) K1=9, K2=3}
+\caption{Top 1 Identification Accuracy with Re-rank varying lambda(gallery-query left, train right) K1=9, K2=3}
 \label{fig:lambda}
 \end{center}
 \end{figure}
 
 
-## k-reciprocal Reranking Evaluation 
+## k-reciprocal Re-ranking Evaluation 
 
-Reranking achieves better results than the other baseline methods analyzed both as $top k$
+Re-ranking achieves better results than the other baseline methods analyzed both as $top k$
 accuracy and mean average precision. 
 It is also necessary to estimate how precise the ranklist generated is.
 For this reason an additional method of evaluation is introduced: mAP. See reference @mAP.
@@ -216,20 +221,20 @@ has improved for the fifth query. The mAP improves from 47% to 61.7%.
 \begin{figure}
 \begin{center}
 \includegraphics[width=24em]{fig/ranklist.png}
-\caption{Ranklist (improved method) @rank10 generated for 5 query images}
+\caption{Top 10 Ranklist (improved method) generated for 5 query images}
 \label{fig:ranklist2}
 \end{center}
 \end{figure}
 
 Figure \ref{fig:compare} shows a comparison between $top k$ identification accuracies
-obtained with the two methods. It is noticeable that the k-reciprocal reranking method significantly
+obtained with the two methods. It is noticeable that the k-reciprocal re-ranking method significantly
 improves the results even for $top1$, boosting identification accuracy from 47% to 56.5%.
 The difference between the $top k$ accuracies of the two methods gets smaller as we increase k.
 
 \begin{figure}
 \begin{center}
 \includegraphics[width=20em]{fig/comparison.pdf}
-\caption{Comparison of recognition accuracy @rank k (KL=0.3,K1=9,K2=3)}
+\caption{Top K (@rank) Identification accuracy (KL=0.3,K1=9,K2=3)}
 \label{fig:compare}
 \end{center}
 \end{figure}
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