# CRIT

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# Cross Pattern Identification Technique (CRIT)

## Algorithm Overview

Label, Slice, Discriminate, Repeat.

## Core Functions and Their Parameters

### Initializer

Initializer: Only run the first time to obtain some set of labels for the rows of A. In all remaining steps, the discriminator generates the new label for propogation. Alternatively, this step can be skipped and a label can be supplied directly to the labeler function.

Required Arguments: Column of A, type of partitioning

Output: Vector assigning a label to every ROW of Column of A

```initializer<-function(A, type=c("median","mean")) {
#Create empty vector with the same number of rows of A
label<-matrix(0, length(A))
#Get value to threshold off of
t<-getThreshold(A, type=type)
#Create label
label<-labelSlicer(A ,t)
return (label)
}

```

### Labeler

In implementation both labeler and slicer (labelSlicer) are integrated as the label is a simple column vector. We show the breakdown to make the connection between the algorithm design and implementation more transparent.

Labeler: Transfers labels on columns of previous datasets (A) to rows of new dataset (B)

Required Arguments: Matrix (B), vector assigning a label to every ROW of A

Output: Vector assigning a label to every COLUMN of B

### Slicer

Slicer: Partition rows of N into "slices" based on labels from A

Required Arguments: Matrix (B), Vector assigning a label to every COLUMN of B

Output: Set of slices where slice is defined as a set of rows of B all containing the same label (in practice this is just the grouping variable as opposed to actual data slices)

```labelSlicer<-function(values, t){
#Set those strictly greater than threshold to 1
index<-which(values>=t)
label(index)<-1
return (label)
}
```

### Discriminator

Discriminator: Evaluates the discriminatory power of labels generated from B in the context of C. Set of slices where slice is defined as a set of rows of B all containing the same label. A random label would show no difference in the slices. (In practice this is implemented as an index instead of the literal data slice).

Required Arguments: Matrix (B), label

Optional Arguments: set to TRUE to compute the FDR

Output: Value of test for every column of B

```#In practice this is implemented as a index
#Additional discriminator functions that use KS test, hypergeometric
#distribution, etc are possible
discriminator<-function(mat=B, label=l, multCorrect=FALSE){

#Create empty list
ttest_struct<-list();

#Compute value of test for each row
for(i in 1:nrow(X)){
temp<-t.test(as.numeric(B[i,])~label)
ttest_struct[[i]]=temp;
}

#Extract pvalue from structure
all_pval<-getPvalfromStruct(ttest_struct);

#Test if we want to compute FDR
if (multCorrect) { all_pval<-p.adjust(all_pval, method="fdr") }

return  (all_pval)
}

```

## AUXILLIARY FUNCTIONS

### Checking against Threshold

```Returns a value to split on for the base case
getThreshold<-function(A, type=c("median","mean")) {
type <- match.arg(type)
threshold <- switch(type,
mean = mean(A),
median = median(A)
)
return (threshold)
}

```

### Return t-test Object

```Returns only the t-test from the ttest object
getTfromStruct<-function(struct){
p<-unlist(lapply(struct, "[",1));
return(p)
}
```

### Return p Value Object

```Returns only the pvalues from the ttest object
getPvalfromStruct<-function(struct){
p<-unlist(lapply(struct, "[",3));
return(p)
}
```