Rewrite some paper

1 files changed, 7 insertions, 5 deletions

diff --git a/report2/paper.md b/report2/paper.md
index 7099df8..6358445 100755
--- a/report2/paper.md
+++ b/report2/paper.md
@@ -115,7 +115,7 @@ 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.
 
-COMMENT ON VARIANCE AND MAHALANOBIS RESULTS
+**COMMENT ON VARIANCE AND MAHALANOBIS RESULTS**
 
 \begin{figure}
 \begin{center}
@@ -166,15 +166,17 @@ 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 $k_1$:$R^*(g_i,k_1)$.
+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 
+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: $k_{1_{opt}}=9, k_{2_{opt}}=3, 0.1\leq\lambda_{opt}\leq 0.3$.