Update vignette.

vignettes/smartid_Demo.Rmd

@@ -104,7 +104,7 @@ data_sim
 
 ## Score Samples
 
-The first step is to score all samples/cells by using specified approach. The score can be composed of 3 terms: TF (term/feature frequency), IDF (inverse document/cell frequency) and IAE (inverse average expression of features). Each term has a couple of available choices with different formats to suit labeled or un-labeled data. Users can use function `idf_iae_methods()` to see available methods for IDF/IAE term. More details of each term can be seen in help page of each function, e.g. `?smartid:::idf`.
+The first step is to score all samples/cells by using specified approach. The score can be composed of 3 terms: TF (term/feature frequency), IDF (inverse document/cell frequency) and IAE (inverse average expression of features). Each term has a couple of available choices with different formats to suit labeled or un-labeled data. Users can use function `idf_iae_methods()` to see available methods for IDF/IAE term. More details of each term can be seen in help page of each function, e.g. `?idf`.
 
 ```{r}
 ## show available methods
@@ -117,17 +117,17 @@ $\mathbf{TF_{i,j}}=\frac{N_{i,j}}{\sum_j{N_{i,j}}},$
 $\mathbf{IDF_i} = \log(1+\frac{n}{n_i+1}),$
 $\mathbf{IAE_i} = \log(1+\frac{n}{\sum_j^n\hat N_{i,j}+1})$
 
-Where $N_{i,j}$ is the counts of feature $i$ in cell $j$; $\hat N_{i,j}$ is $max(0,N_{i,j}-threshold)$;
-$n$ is the total number of documents(cells); $n_i$ is $\sum_{j = 1}^{n} sign(N_{i,j} > threshold)$.
+Where $N_{i,j}$ is the counts of feature $i$ in cell $j$; $\hat N_{i,j}$ is $\max(0,N_{i,j}-threshold)$;
+$n$ is the total number of documents(cells); $n_i$ is $\sum_{j = 1}^{n} \mathrm{sign}(N_{i,j} > \mathrm{threshold})$.
 
 Here for labeled data, we can choose logTF * IDF_prob * IAE_prob for marker identification:
 $$\mathbf{score}=\log \mathbf{TF}*\mathbf{IDF}_{prob}*\mathbf{IAE}_{prob}$$
 
 The probability version of IDF can be termed as:
-$$\mathbf{IDF_{i,j}} = \log(1+\frac{\frac{n_{i,j\in D}}{n_{j\in D}}}{max(\frac{n_{i,j\in \hat D}}{n_{j\in \hat D}})+ e^{-8}}\frac{n_{i,j\in D}}{n_{j\in D}})$$
+$$\mathbf{IDF_{i,j}} = \log(1+\frac{\frac{n_{i,j\in D}}{n_{j\in D}}}{\max(\frac{n_{i,j\in \hat D}}{n_{j\in \hat D}})+ e^{-8}}\frac{n_{i,j\in D}}{n_{j\in D}})$$
 
 And the probability version of IAE can be termed as:
-$$\mathbf{IAE_{i,j}} = \log(1+\frac{mean(\hat N_{i,j\in D})}{max(mean(\hat N_{i,j\in \hat D}))+ e^{-8}}*mean(\hat N_{i,j\in D}))$$
+$$\mathbf{IAE_{i,j}} = \log(1+\frac{\mathrm{mean}(\hat N_{i,j\in D})}{\max(\mathrm{mean}(\hat N_{i,j\in \hat D}))+ e^{-8}}*\mathrm{mean}(\hat N_{i,j\in D}))$$
 
 Where $D$ is the category of cell $j$; $\hat D$ is the category other than $D$.
 
@@ -263,8 +263,8 @@ Here we choose logTF * IDF_sd * IAE_sd for for gene-set scoring as a use case:
 $$\mathbf{score}=\log \mathbf{TF}*\mathbf{IDF}_{sd}*\mathbf{IAE}_{sd}$$
 
 Where IDF and IAE can be termed as:
-$$\mathbf{IDF_i} = \log(1+SD(\mathbf{TF}_{i})*\frac{n}{n_i+1})$$
-$$\mathbf{IAE_i} = \log(1+SD(\mathbf{TF}_{i})*\frac{n}{\sum_{j=1}^{n}\hat N_{i,j}+1})$$
+$$\mathbf{IDF_i} = \log(1+\mathrm{SD}(\mathbf{TF}_{i})*\frac{n}{n_i+1})$$
+$$\mathbf{IAE_i} = \log(1+\mathrm{SD}(\mathbf{TF}_{i})*\frac{n}{\sum_{j=1}^{n}\hat N_{i,j}+1})$$
 
 ## Score Samples