help js

R/cosineTopics.R

@@ -5,9 +5,12 @@
 #' Cosine Similarity.
 #'
 #' @details
-#' The Cosine Similarity for two topics \eqn{\bm z_{i}} and \eqn{\bm z_{j}} is calculated by
-#' \deqn{ \cos(\theta,\bm z_{i}, \bm z_{j}) = \frac{ \sum_{v=1}^{V}{n_{i}^{(v)} \cdot n_{j}^{(v)}} }{ \sqrt{\sum_{v=1}^{V}{\left(n_{i}^{(v)}\right)^2}} \cdot \sqrt{\sum_{v=1}^{V}{\left(n_{j}^{(v)}\right)^2}} }}
-#' with \eqn{V} is the vocabulary size, and \eqn{n_k^{(v)}} is the count of
+#' The Cosine Similarity for two topics \eqn{\bm z_{i}} and \eqn{\bm z_{j}}
+#' is calculated by
+#' \deqn{ \cos(\theta | \bm z_{i}, \bm z_{j}) = \frac{ \sum_{v=1}^{V}{n_{i}^{(v)} \cdot n_{j}^{(v)}} }{ \sqrt{\sum_{v=1}^{V}{\left(n_{i}^{(v)}\right)^2}} \cdot \sqrt{\sum_{v=1}^{V}{\left(n_{j}^{(v)}\right)^2}} }}
+#' with \eqn{\theta} determining the angle between the corresponding
+#' count vectors \eqn{\bm z_{i}} and \eqn{\bm z_{j}},
+#' \eqn{V} is the vocabulary size and \eqn{n_k^{(v)}} is the count of
 #' assignments of the \eqn{v}-th word to the \eqn{k}-th topic.
 #'
 #' @family TopicSimilarity functions

R/jaccardTopics.R

@@ -5,9 +5,10 @@
 #' Jaccard Coefficient.
 #'
 #' @details
-#' The modified Jaccard Coefficient for two topics \eqn{\bm z_{i}} and \eqn{\bm z_{j}} is calculated by
+#' The modified Jaccard Coefficient for two topics \eqn{\bm z_{i}} and
+#' \eqn{\bm z_{j}} is calculated by
 #' \deqn{J_m(\bm z_{i}, \bm z_{j} \mid \bm c) = \frac{\sum_{v = 1}^{V} 1_{\left\{n_{i}^{(v)} > c_i ~\wedge~ n_{j}^{(v)} > c_j\right\}}\left(n_{i}^{(v)}, n_{j}^{(v)}\right)}{\sum_{v = 1}^{V} 1_{\left\{n_{i}^{(v)} > c_i ~\vee~ n_{j}^{(v)} > c_j\right\}}\left(n_{i}^{(v)}, n_{j}^{(v)}\right)}}
-#' with \eqn{V} is the vocabulary size, and \eqn{n_k^{(v)}} is the count of
+#' with \eqn{V} is the vocabulary size and \eqn{n_k^{(v)}} is the count of
 #' assignments of the \eqn{v}-th word to the \eqn{k}-th topic. The threshold vector \eqn{\bm c}
 #' is determined by the maximum threshold of the user given lower bounds \code{limit.rel}
 #' and \code{limit.abs}. In addition, at least \code{atLeast} words per topic are

R/jsTopics.R

@@ -5,18 +5,12 @@
 #' Jensen-Shannon Divergence.
 #'
 #' @details
-#' The Jensen-Shannon Similarity for two topics \eqn{\bm z_{i}} and \eqn{\bm z_{j}} ...
+#' The Jensen-Shannon Similarity for two topics \eqn{\bm z_{i}} and
+#' \eqn{\bm z_{j}} is calculated by
+#' \deqn{\text{JS}(\bm z_{i}, \bm z_{j}) = 1 - \left( \text{KLD}(p_i, (p_i+p_j)/2) + \text{KLD}((p_j, (p_i+p_j)/2)) \right)/2 }
 #'
-#' \eqn{J_m} is calculated by
-#' \deqn{J_m(\bm z_{i}, \bm z_{j} \mid \bm c) = \frac{\sum_{v = 1}^{V} 1_{\left\{n_{i}^{(v)} > c_i ~\wedge~ n_{j}^{(v)} > c_j\right\}}\left(n_{i}^{(v)}, n_{j}^{(v)}\right)}{\sum_{v = 1}^{V} 1_{\left\{n_{i}^{(v)} > c_i ~\vee~ n_{j}^{(v)} > c_j\right\}}\left(n_{i}^{(v)}, n_{j}^{(v)}\right)}}
-#' with \eqn{V} is the vocabulary size, and \eqn{n_k^{(v)}} is the count of
-#' assignments of the \eqn{v}-th word to the \eqn{k}-th topic. The threshold vector \eqn{\bm c}
-#' is determined by the maximum threshold of the user given lower bounds \code{limit.rel}
-#' and \code{limit.abs}. In addition, at least \code{atLeast} words per topic are
-#' considered for calculation. According to this, if there are less than
-#' \code{atLeast} words considered as relevant after applying \code{limit.rel}
-#' and \code{limit.abs} the \code{atLeast} most common words per topic are taken
-#' to determine topic similarities.
+#' with \eqn{V} is the vocabulary size and \eqn{n_k^{(v)}} is the count of
+#' assignments of the \eqn{v}-th word to the \eqn{k}-th topic.
 #'
 #' @family TopicSimilarity functions
 #'