# Algorithm of Text Separators Extraction

## Definitions

### Functions definitions

To explain the algorithm some functions have to be defined. The implementation of the functions is out of this scope; the given article only defines the functions used.

P1(ch: Character, tokens: List<String>): Double - Function that returns probability that character ch occurs in the end (or beginning) of the tokens.

For example, for the tokens input “hello, my name is” P1 is going to look like this:

• P1(‘,’, “hello, my name is”) == 1.0
• P1(‘e’, “hello, my name is”) == 0.5
• P1(‘l’, “hello, my name is”) == 0.0
• P1(‘s’, “hello, my name is”) == 1.0
• P1(‘a’, “hello, my name is”) == 0.0
• P1(‘m’, “hello, my name is”) == 0.5
• P1(‘o’, “hello, my name is”) == 0.0
• P1(‘h’, “hello, my name is”) == 0.0

P2(ch: Character, tokens: List<String>): Double - Function that returns average P1 probability of all characters from the tokens that occur before character ch.

For example, for the tokens input “hello, my name is” P2 is going to look like this (P1 values can be seen in example for P1):

• P2(‘,’, “hello, my name is”) == (P1(‘o’, “…”) * 1.0) / 1.0 == 0.0 / 1.0 == 0.0
• P2(‘y’, “hello, my name is”) == (P1(‘m’, “…”) * 1.0) / 1.0 == 0.5 / 1.0 == 0.5
• P2(‘e’, “hello, my name is”) == (P1(‘m’, “…”) * 1.0 + P1(‘h’, “…”) * 1.0) / 2.0 == (0.5 + 0.0) / 2.0 == 0.25

## Algorithm

The algorithm contains 2 steps:

1. Initial search
2. Search result filter.

The first step finds all text separators plus some “noise” (non-separators/alphabetic characters). The second step filters out all non-separators found in the first step.

The probability of being a separator must be calculated for each unique character in tokens. This can be done according to the following formula:

P(ch: Character, tokens: List<String>): Double = P1(ch, tokens) * (P2(ch, tokens) ^ 2)


The result should contain 30% of characters that have the highest probability (calculated by formula P above).

### Search result filter

Search result may contain characters that are not separators. They must be filtered out. Here is a filter that can be applied for each character in search result:

P1(ch, tokens) > 0.65


## Research problems for the given steps

• How to determine the number of characters that should be used as a result during initial search (why is 30% is chosen and how to choose this value?);
• What value should be used as probability threshold in search result filter (why 0.65?).