Most frequent k chars distance
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In information theory, the MostFreqKDistance is a string metric for quickly estimating how similar two ordered sets or strings are. The scheme was invented by Sadi Evren SEKER,[1] and initially used in text mining applications like author recognition.[1] Method is originally based on a hashing function MaxFreqKChars [2] classical wp:author recognition problem and idea first came out while studying on wp:data stream mining.[3] The string distance
Definition
Method has two steps.
- Hash input strings str1 and str2 separately using MostFreqKHashing and output hstr1 and hstr2 respectively
- Calculate string distance (or string similarity coefficient) of two hash outputs, hstr1 and hstr2 and output an integer value
Most Frequent K Hashing
The first step of algorithm is calculating the hashing based on the most frequent k characters. The hashing algorithm has below steps:
string function MostFreqKHashing (string inputString, int K) def string outputString for each distinct characters count occurrence of each character for i from 0 to K char c = next most frequent ith character (if two chars have same frequency than get the first occurrence in inputString) int count = number of occurrence of the character append to outputString, c and count end for return outputString
Aim of 'Most Frequent K Hashing' function is calculating the most count of each character and returning the K most frequent character with the character and count. Rules of hash can be listed as below:
- Output will hold the character and count
- Most frequent character and count will appear before the least frequent at the output
- if two characters have equal frequency, the first appearing in input will appear before at the output
Similar to the most of hashing functions, Most Frequent K Hashing is also a wp:one way function.
Most Frequent K Distance
Distance calculation between two strings is based on the hash outputs of two strings.
int function MostFreqKSimilarity (string inputStr1, string inputStr2) def int similarity for each c = next character from inputStr1 lookup c in inputStr2 if c is not null similarity += frequency of c in inputStr1 + frequency of c in inputStr2 return similarity
Above function, simply gets two input strings, previously outputted from the MostFreqKHashing function. From the most frequent k hashing function, the characters and their frequencies are returned. So, the similarity function calculates the similarity based on characters and their frequencies by checking if the same character appears on both strings and if their frequencies are equal.
In some implementations, the distance metric is required instead of similarity coefficient. In order to convert the output of above similarity coefficient to distance metric, the output can be subtracted from any constant value (like the maximum possible output value). For the case, it is also possible to implement a wp:wrapper function over above two functions.
String Distance Wrapper Function
In order to calculate the distance between two strings, below function can be implemented
int function MostFreqKSDF (string inputStr1, string inputStr2, int K, int maxDistance) return maxDistance - MostFreqKSimilarity(MostFreqKHashing(inputStr1,K), MostFreqKHashing(inputStr2,K))
Any call to above string distance function will supply two input strings and a maximum distance value. The function will calculate the similarity and subtract that value from the maximum possible distance. It can be considered as a simple wp:additive inverse of similarity.
Examples
Let's consider maximum 2 frequent hashing over two strings ‘research’ and ‘seeking’. <lang javascript>MostFreqKHashing('research',2) = 'r2e2'</lang> because we have 2 'r' and 2 'e' characters with the highest frequency and we return in the order they appear in the string. <lang javascript>MostFreqKHashing('seeking',2) = 'e2s1'</lang> Again we have character 'e' with highest frequency and rest of the characters have same frequency of 1, so we return the first character of equal frequencies, which is 's'. Finally we make the comparison: <lang javascript>MostFreqKSimilarity('r2e2','e2s1') = 2</lang> We simply compared the outputs and only character occurring in both input is character 'e' and the occurrence in both input is 2. Instead running the sample step by step as above, we can simply run by using the string distance wrapper function as below: <lang javascript>MostFreqKSDF('research', 'seeking',2) = 2</lang>
Below table holds some sample runs between example inputs for K=2:
Inputs | Hash Outputs | SDF Output (max from 10) |
---|---|---|
'night'
'nacht' |
n1i1
n1a1 |
9 |
'my'
'a' |
m1y1
a1NULL0 |
10 |
‘research’
‘research’ |
r2e2
r2e2 |
8 |
‘aaaaabbbb’
‘ababababa’ |
a5b4
a5b4 |
1 |
‘significant’
‘capabilities’ |
i3n2
i3a2 |
5 |
Method is also suitable for bioinformatics to compare the genetic strings like in wp:fasta format
Str1= LCLYTHIGRNIYYGSYLYSETWNTGIMLLLITMATAFMGYVLPWGQMSFWGATVITNLFSAIPYIGTNLV Str2 = EWIWGGFSVDKATLNRFFAFHFILPFTMVALAGVHLTFLHETGSNNPLGLTSDSDKIPFHPYYTIKDFLG MostFreqKHashing(str1,2) = L9T8 MostFreqKHashing(str2,2) = F9L8 MostFreqKSDF(str1,str2,2,100) = 83
Implementations
Java
Translation of the pseudo-code of the Wikipedia article wp:Most frequent k characters to wp:java implementation of three functions given in the definition section are given below with wp:JavaDoc comments:
<lang java>import java.util.Collections; import java.util.Comparator; import java.util.HashMap; import java.util.LinkedHashMap; import java.util.ArrayList; import java.util.List; import java.util.Map;
public class SDF {
/** Counting the number of occurrences of each character * @param character array * @return hashmap : Key = char, Value = num of occurrence */ public static HashMap<Character, Integer> countElementOcurrences(char[] array) {
HashMap<Character, Integer> countMap = new HashMap<Character, Integer>();
for (char element : array) { Integer count = countMap.get(element); count = (count == null) ? 1 : count + 1; countMap.put(element, count); }
return countMap; } /** * Sorts the counted numbers of characters (keys, values) by java Collection List * @param HashMap (with key as character, value as number of occurrences) * @return sorted HashMap */ private static <K, V extends Comparable<? super V>> HashMap<K, V> descendingSortByValues(HashMap<K, V> map) {
List<Map.Entry<K, V>> list = new ArrayList<Map.Entry<K, V>>(map.entrySet()); // Defined Custom Comparator here Collections.sort(list, new Comparator<Map.Entry<K, V>>() { public int compare(Map.Entry<K, V> o1, Map.Entry<K, V> o2) { return o2.getValue().compareTo(o1.getValue()); } });
// Here I am copying the sorted list in HashMap // using LinkedHashMap to preserve the insertion order HashMap<K, V> sortedHashMap = new LinkedHashMap<K, V>(); for (Map.Entry<K, V> entry : list) { sortedHashMap.put(entry.getKey(), entry.getValue()); } return sortedHashMap;
} /** * get most frequent k characters * @param array of characters * @param limit of k * @return hashed String */ public static String mostOcurrencesElement(char[] array, int k) { HashMap<Character, Integer> countMap = countElementOcurrences(array); System.out.println(countMap); Map<Character, Integer> map = descendingSortByValues(countMap); System.out.println(map); int i = 0; String output = ""; for (Map.Entry<Character, Integer> pairs : map.entrySet()) {
if (i++ >= k) break;
output += "" + pairs.getKey() + pairs.getValue(); } return output; } /** * Calculates the similarity between two input strings * @param input string 1 * @param input string 2 * @param maximum possible limit value * @return distance as integer */ public static int getDiff(String str1, String str2, int limit) { int similarity = 0; for (int i = 0; i < str1.length(); i += 2) { System.out.println(i); int pos = str2.indexOf(str1.charAt(i)); System.out.println(str2.charAt(i) + " - " + pos); if (pos >= 0) { similarity += Integer.parseInt(str2.substring(pos+1, pos+2)) + Character.getNumericValue(str1.charAt(i+1)); } } return limit-similarity; } /** * Wrapper function * @param input string 1 * @param input string 2 * @param maximum possible limit value * @return distance as integer */ public static int SDFfunc(String str1, String str2, int limit) { return getDiff(mostOcurrencesElement(str1.toCharArray(), 2), mostOcurrencesElement(str2.toCharArray(), 2), limit); }
public static void main(String[] args) { String input1 = "LCLYTHIGRNIYYGSYLYSETWNTGIMLLLITMATAFMGYVLPWGQMSFWGATVITNLFSAIPYIGTNLV"; String input2 = "EWIWGGFSVDKATLNRFFAFHFILPFTMVALAGVHLTFLHETGSNNPLGLTSDSDKIPFHPYYTIKDFLG"; System.out.println(SDF.SDFfunc(input1,input2,100));
}
}</lang>
References
- ↑ 1.0 1.1 SEKER, Sadi E.; Altun, Oguz; Ayan, Ugur; Mert, Cihan (2014), "A Novel String Distance Function based on Most Frequent K Characters", wp:International Journal of Machine Learning and Computing (IJMLC), 4, wp:International Association of Computer Science and Information Technology Press (IACSIT Press), pp. 177-183, http://arxiv.org/abs/1401.6596.
- ↑ Seker, Sadi E.; Mert, Cihan (2013), "A Novel Feature Hashing For Text Mining", Journal of Technical Science and Technologies, 2, wp:International Black Sea University, pp. 37 -41, Template:Citation/identifier, http://journal.ibsu.edu.ge/index.php/jtst/article/view/428.