---
title: "Step 2: The Scone Workflow"
author: "Tyler J Burns"
date: "9/30/2017"
output: html_document
vignette: >
  %\VignetteIndexEntry{General Scone Analysis}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, 
                      results = "markup", 
                      message = FALSE, 
                      warning = FALSE)
```

### K-nearest neighbors:
We read in input.scone.csv, which is our file modified (and renamed) from the 
get.marker.names() function. The K-nearest neighbor generation is derived from 
the Fast Nearest Neighbors (FNN) R package, within our function Fnn(), which 
takes as input the “input markers” to be used, along with the concatenated data
previously generated, and the desired k. We advise the default selection to the 
total number of cells in the dataset divided by 100, as has been optimized on 
existing mass cytometry datasets. The output of this function is a matrix of 
each cell and the identity of its k-nearest neighbors, in terms of its row 
number in the dataset used here as input. 

```{r}
library(Sconify)
# Markers from the user-generated excel file
marker.file <- system.file('extdata', 'markers.csv', package = "Sconify")
markers <- ParseMarkers(marker.file)

# How to convert your excel sheet into vector of static and functional markers
markers
# Get the particular markers to be used as knn and knn statistics input
input.markers <- markers[[1]]
funct.markers <- markers[[2]]

# Selection of the k. See "Finding Ideal K" vignette
k <- 30

# The built-in scone functions
wand.nn <- Fnn(cell.df = wand.combined, input.markers = input.markers, k = k)
# Cell identity is in rows, k-nearest neighbors are columns
# List of 2 includes the cell identity of each nn, 
#   and the euclidean distance between
#   itself and the cell of interest

# Indices
str(wand.nn[[1]])
wand.nn[[1]][1:20, 1:10]

# Distance
str(wand.nn[[2]])
wand.nn[[2]][1:20, 1:10]
```

### Finding scone values:

This function iterates through each KNN, and performs a series of calculations. 
The first is fold change values for each maker per KNN, where the user chooses 
whether this will be based on medians or means. The second is a statistical 
test, where the user chooses t test or Mann-Whitney U test. I prefer the 
latter, because it does not assume any properties of the distributions. Of 
note, the p values are adjusted for false discovery rate, and therefore are 
called q values in the output of this function. The user also inputs a 
threshold parameter (default 0.05), where the fold change values will only be 
shown if the corresponding statistical test returns a q value below said 
threshold. Finally, the "multiple.donor.compare" option, if set to TRUE will 
perform a t test based on the mean per-marker values of each donor. This is to 
allow the user to make comparisons across replicates or multiple donors if that 
is relevant to the user's biological questions. This function returns a matrix 
of cells by computed values (change and statistical test results, labeled 
either marker.change or marker.qvalue). This matrix is intermediate, as it gets 
concatenated with the original input matrix in the post-processing step (see 
the relevant vignette). We show the code and the output below. See the 
post-processing vignette, where we show how this gets combined with the input 
data, and additional analysis is performed. 


```{r}
wand.scone <- SconeValues(nn.matrix = wand.nn, 
                      cell.data = wand.combined, 
                      scone.markers = funct.markers, 
                      unstim = "basal")

wand.scone
```

### For programmers: performing additional per-KNN statistics
If one wants to export KNN data to perform other statistics not available in 
this package, then I provide a function that produces a list of each cell 
identity in the original input data matrix, and a matrix of all cells x 
features of its KNN. 

I also provide a function to find the KNN density estimation independently of 
the rest of the "scone.values" analysis, to save time if density is all the 
user wants. With this density estimation, one can perform interesting analysis, 
ranging from understanding phenotypic density changes along a developmental 
progression (see post-processing vignette for an example), to trying out 
density-based binning methods (eg. X-shift). Of note, this density is 
specifically one divided by the aveage distance to k-nearest neighbors. This 
specific measure is related to the Shannon Entropy estimate of that point on 
the manifold (https://hal.archives-ouvertes.fr/hal-01068081/document). 

I use this metric to avoid the unusual properties of the volume of a sphere as 
it increases in dimensions (https://en.wikipedia.org/wiki/Volume_of_an_n-ball). 
This being said, one can modify this vector to be such a density estimation 
(example http://www.cs.haifa.ac.il/~rita/ml_course/lectures_old/KNN.pdf), by 
treating the distance to knn as the radius of a n-dimensional sphere and 
incoroprating said volume accordingly. 

An individual with basic programming skills can iterate through these elements 
to perform the statistics of one's choosing. Examples would include per-KNN 
regression and classification, or feature imputation. The additional 
functionality is shown below, with the example knn.list in the package being 
the first ten instances: 

```{r}
# Constructs KNN list, computes KNN density estimation
wand.knn.list <- MakeKnnList(cell.data = wand.combined, nn.matrix = wand.nn)
wand.knn.list[[8]]

# Finds the KNN density estimation for each cell, ordered by column, in the 
# original data matrix
wand.knn.density <- GetKnnDe(nn.matrix = wand.nn)
str(wand.knn.density)
```


