Add data variance info, correct grammar

1 files changed, 7 insertions, 6 deletions

diff --git a/report/paper.md b/report/paper.md
index b9aa477..73c49de 100755
--- a/report/paper.md
+++ b/report/paper.md
@@ -38,7 +38,7 @@ of its nearest neighbor(s). The distance between images can be calculated throug
 different distance metrics, however one of the most commonly used is euclidean
 distance:
 
-$$ \textrm{NN}(x) = \operatorname*{argmin}_{i\in[m]} \|x-x_i\| $$
+$$ \textrm{NN}(x) = \operatorname*{argmin}_{i\in[m]} \|x-x_i\|. $$
 
 # Baseline Evaluation
 
@@ -73,7 +73,7 @@ Applying magnitude normalization (scaling feature vectors to unit length) had a
 effect re-identification. Furthemore standartization by removing feature mean and deviation 
 also had negative effect on performance as seen on figure \ref{fig:baselineacc}. This may 
 be due to the fact that we are removing feature scaling that was introduced by the Neural network, 
-such that some of the features are more significant than the others. By standartizing our 
+such that some of the features are more significant than others. By standartizing our 
 features at this point, we remove such scaling and may be losing using useful metrics.
 
 ## kMeans Clustering
@@ -122,7 +122,8 @@ $$ d_M(p,g_i) = (p-g_i)^TM(p-g_i). $$
 
 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 
+We also attempted to perform the same Mahalanobis metric on a reduced PCA featureset. PCA performed with the top 100 eigenvectors
+reduces the feature space while keeping 94% of the data variance. 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.
 
@@ -161,7 +162,7 @@ as position, illumination and foreign objects. $R^*(p,k)$ is used to
 recalculate the distance between query and gallery images.
 
 Jaccard metric of the $k$-reciprocal sets is used to calculate the distance 
-between $p$ and $g_i$ as: $$d_J(p,g_i)=1-\frac{|R^*(p,k)\cap R^*(g_i,k)|}{|R^*(p,k)\cup R^*(g_i,k)|}$$.
+between $p$ and $g_i$ as: $$d_J(p,g_i)=1-\frac{|R^*(p,k)\cap R^*(g_i,k)|}{|R^*(p,k)\cup R^*(g_i,k)|}.$$
 
 However, since the neighbors of the query $p$ are close to $g_i$ as well, 
 they would be more likely to be identified as true positive. This implies
@@ -255,8 +256,8 @@ The difference between the top $k$ accuracies of the two methods gets smaller as
 The improved results due to $k$-reciprocal re-ranking may be explained by considering that re-ranks based on second order neighbours,
 that is, the neighbours of the neighbours. For neighbours which display identifiable features, such as a backpack or binder that is
 not visible in the query but visible in a close neighbour, the reranking algorithm is able to infer that the strong relationship based on this newly introduced
-feature such as a backpack or folder by the neighbour, uniuqly identify other identities in the gallery with the same feature, and moving them up the rankinlist 
-as a result despite the identifiable feature being hidden in the query. EXAMPLE BACKPACK HERE
+feature such as a backpack or folder by the neighbour, uniquely identify other identities in the gallery with the same feature, and moving them up the rankinlist 
+as a result despite the identifiable feature being hidden in the query. An example of this can be seen in figure \ref{fig:rerank}.
 
 \begin{figure}
 \begin{center}