diff --git a/README.md b/README.md
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+++ b/README.md
@@ -282,6 +282,14 @@ p│  └── FACS_metadata.csv
With the files in these locations, everything is set up to run the code as
presented in the RMarkdown files in the workshop.
+##### Case study dataset
+
+The dataset we used in the case study is from (O’Koren et al), you can download
+all the relevant files via [this link](https://www.svi.edu.au/MIG_2019_scRNAseq-workshop/case_study_data.tar.gz)
+
+It includes the raw fastqs and processed count matrix data and is of size 2.1GB.
+If you would like to start with the count matrix data, please follow the instruction in the [RMarkdown](https://gitlab.svi.edu.au/biocellgen-public/mig_2019_scrnaseq-workshop/blob/master/case_study_data/case_study.Rmd)
+to download the processed count matrix data from GEO.
### RStudio
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diff --git a/course_files/latent-spaces.Rmd b/course_files/latent-spaces.Rmd
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--- a/course_files/latent-spaces.Rmd
+++ b/course_files/latent-spaces.Rmd
@@ -3,7 +3,7 @@ output: html_document
---
```{r setup, echo=FALSE}
-knitr::opts_chunk$set(fig.align = "center")
+knitr::opts_chunk$set(fig.align = "center", eval = TRUE)
knitr::opts_knit$set(root.dir = normalizePath(".."))
```
@@ -433,22 +433,66 @@ ggplot(dt, aes(x=PHATE1, y=PHATE2, color=clust)) +
## Matrix factorization and factor analysis
-Factor Analysis is similar to PCA in that,
-they both aim to obtain a new set of distinct summary variables,
-which are fewer in number than the original number of variables.
-
-The key concept of factor analysis is that the original, observed variables are
+__The key concept of factor analysis__: The original, observed variables are
correlated because they are all associated with some unobservable variables,
-called latent factors.
+the __latent factors__.
+
+It looks similar to PCA, but instead of dimensionality reduction, factor analysis
+focuses on studying the latent factors.
-The variance of a variable can be splitted into two parts: \
+The variance of an observed variable can be splitted into two parts: \
- Common variance: the part of variance that is explained by latent factors; \
-- Unique variance: the part that is specific to only one variable, usually considered as an error component or residual.
+- Unique variance: the part that is specific to only one variable, usually considered as an error component or __residual__.
+
+The __factor loadings__ or weights indicate how much each latent factor is affecting the observed features.
-<center> {width=80%} </center>
+<center> {width=60%} </center>
### [Slalom](https://bioconductor.org/packages/release/bioc/html/slalom.html): Interpretable latent spaces
+Highlight of Slalom:
+
+- It incorporates prior information to help the model estimation;
+
+- It learns whatever not provided by prior knowledge in the model training process;
+
+- It enforces sparsity in the weight matrix.
+
+#### Methodology
+
+__Matrix expression of factor analysis:__
+
+<center>{width=80%} </center>
+
+__How prior knowledge affects the model:__
+
+<center> </center>
+
+- $I_{g, k}$: (observed) Indicator of whether a gene $g$ is annotated to a given pathway or factor $k$;\
+- $z_{g, k}$: (latent) Indicator of whether factor $k$ has a regulatory effect on gene $g$;\
+- $w_{g, k}$: (estimated) weights.
+
+__grey arrow__:
+$$ P(I_{g, k}\vert z_{g, k}) = \begin{cases}
+\text{Bernoulli}(p_1), \text{if } z_{g, k} = 1\\
+\text{Bernoulli}(p_2), \text{if } z_{g, k} = 0\\
+\end{cases}$$
+
+__green arrow__:
+$$ P(w_{g, k}\vert z_{g, k}) = \begin{cases}
+N(w_{g, k}, 1/\alpha), \text{ if } z_{g, k} = 1\\
+\delta_0(w_{g, k}), \text{ if } z_{g, k} = 0\\
+\end{cases}$$
+
+<center></center>
+
+We only look at the part of the __likelihood__ that is relavant to this part:
+$\prod_{g} \prod_{k}P(I_{g, k}, w_{g, k}, z_{g, k})$, \
+where $P(I_{g, k}, w_{g, k}, z_{g, k}) = P(I_{g, k}, w_{g, k}| z_{g, k})P(z_{g,k})
+= P( I_{g, k}| z_{g, k})P( w_{g, k}| z_{g, k})P(z_{g,k})$.
+Since we do not know anything about $z_{g,k}$, it is assumed as Bernoulli(1/2).
+
+#### Example
First, get a geneset in a `GeneSetCollection` object.
```{r}
gmtfile <- system.file("extdata", "reactome_subset.gmt", package = "slalom")