smile.math.distance.EditDistance Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see
* Given two strings x and y of length m and n (suppose {@code n >= m}), this
* implementation takes O(ne) time and O(mn) space by an extended Ukkonen's
* algorithm in case of unit cost, where e is the edit distance between x and y.
* Thus, this algorithm is output sensitive. The smaller the distance, the faster
* it runs.
*
* For weighted cost, this implements the regular dynamic programming algorithm,
* which takes O(mn) time and O(m) space.
*
* @author Haifeng Li
*/
public class EditDistance implements Metric {
@Serial
private static final long serialVersionUID = 1L;
/**
* Weight matrix for weighted Levenshtein distance.
*/
private IntArray2D weight;
/**
* Radius of Sakoe-Chiba band
*/
private double r = -1;
/**
* Calculate Damerau or basic Levenshitein distance.
*/
private boolean damerau = false;
/**
* Cost matrix. Because Java automatically initialize arrays, it
* takes O(mn) to declare this cost matrix every time before
* calculate edit distance. But the whole point of Berghel and Roach
* algorithm is to calculate fewer cells than O(mn). Therefore,
* we create this cost matrix here. Therefore, the methods using
* this cost matrix is not multi-thread safe.
*/
private IntArray2D FKP;
/**
* The lambda to calculate FKP array.
*/
private BRF brf;
/**
* Constructor. Multi-thread safe Levenshtein distance.
*/
public EditDistance() {
this(false);
}
/**
* Constructor. Multi-thread safe Damerau-Levenshtein distance.
* @param damerau if true, calculate Damerau-Levenshtein distance
* instead of plain Levenshtein distance.
*/
public EditDistance(boolean damerau) {
this.damerau = damerau;
}
/**
* Constructor. Highly efficient Levenshtein distance but not multi-thread safe.
* @param maxStringLength the maximum length of strings that will be
* feed to this algorithm.
*/
public EditDistance(int maxStringLength) {
this(maxStringLength, false);
}
/**
* Constructor. Highly efficient Damerau-Levenshtein distance but not multi-thread safe.
* @param maxStringLength the maximum length of strings that will be
* feed to this algorithm.
* @param damerau if true, calculate Damerau-Levenshtein distance
* instead of plain Levenshtein distance.
*/
public EditDistance(int maxStringLength, boolean damerau) {
this.damerau = damerau;
FKP = new IntArray2D(2*maxStringLength+1, maxStringLength+2);
brf = damerau ? new DamerauBRF() : new LevenshteinBRF();
}
/**
* Constructor. Weighted Levenshtein distance without path
* constraints. Only insertion, deletion, and substitution operations are
* supported.
* @param weight the weight matrix.
*/
public EditDistance(int[][] weight) {
this(weight, -1);
}
/**
* Constructor. Weighted Levenshtein distance with
* Sakoe-Chiba band, which improve computational cost. Only
* insertion, deletion, and substitution operations are supported.
* @param weight the weight matrix.
* @param radius the window width of Sakoe-Chiba band in terms of percentage of sequence length.
*/
public EditDistance(int[][] weight, double radius) {
this.weight = new IntArray2D(weight);
this.r = radius;
}
@Override
public String toString() {
if (damerau) {
if (weight != null)
return String.format("Damerau-Levenshtein Distance(radius = %f, weight = %s)", r, weight);
else
return "Damerau-Levenshtein Distance";
} else {
if (weight != null)
return String.format("Levenshtein Distance(radius = %f, weight = %s)", r, weight);
else
return "Levenshtein Distance";
}
}
/**
* Edit distance between two strings. O(mn) time and O(n) space for weighted
* edit distance. O(ne) time and O(mn) space for unit cost edit distance.
* For weighted edit distance, this method is multi-thread safe. However,
* it is NOT multi-thread safe for unit cost edit distance.
*/
@Override
public double d(String a, String b) {
if (weight != null)
return weightedEdit(a, b);
else if (FKP == null || a.length() == 1 || b.length() == 1)
return damerau ? damerau(a, b) : levenshtein(a, b);
else
return br(a, b);
}
/**
* Edit distance between two strings. O(mn) time and O(n) space for weighted
* edit distance. O(ne) time and O(mn) space for unit cost edit distance.
* For weighted edit distance, this method is multi-thread safe. However,
* it is NOT multi-thread safe for unit cost edit distance.
* @param a a string.
* @param b a string.
* @return the distance.
*/
public double d(char[] a, char[] b) {
if (weight != null) {
return weightedEdit(a, b);
} else if (FKP == null || a.length == 1 || b.length == 1) {
return damerau ? damerau(a, b) : levenshtein(a, b);
} else {
return br(a, b);
}
}
/**
* Weighted edit distance.
* @param a a string.
* @param b a string.
* @return the distance.
*/
private double weightedEdit(char[] a, char[] b) {
// switch parameters to use the shorter one as y to save space.
if (a.length < b.length) {
char[] swap = a;
a = b;
b = swap;
}
int radius = (int) Math.round(r * a.length);
double[][] d = new double[2][b.length + 1];
d[0][0] = 0.0;
for (int j = 1; j <= b.length; j++) {
d[0][j] = d[0][j - 1] + weight.get(0, b[j]);
}
for (int i = 1; i <= a.length; i++) {
d[1][0] = d[0][0] + weight.get(a[i], 0);
int start = 1;
int end = b.length;
if (radius > 0) {
start = i - radius;
if (start > 1)
d[1][start - 1] = Double.POSITIVE_INFINITY;
else
start = 1;
end = i + radius;
if (end < b.length)
d[1][end+1] = Double.POSITIVE_INFINITY;
else
end = b.length;
}
for (int j = start; j <= end; j++) {
double cost = weight.get(a[i - 1], b[j - 1]);
d[1][j] = MathEx.min(
d[0][j] + weight.get(a[i - 1], 0), // deletion
d[1][j - 1] + weight.get(0, b[j - 1]), // insertion
d[0][j - 1] + cost); // substitution
}
double[] swap = d[0];
d[0] = d[1];
d[1] = swap;
}
return d[0][b.length];
}
/**
* Weighted edit distance.
* @param a a string.
* @param b a string.
* @return the distance.
*/
private double weightedEdit(String a, String b) {
// switch parameters to use the shorter one as y to save space.
if (a.length() < b.length()) {
String swap = a;
a = b;
b = swap;
}
int radius = (int) Math.round(r * a.length());
double[][] d = new double[2][b.length() + 1];
d[0][0] = 0.0;
for (int j = 1; j <= b.length(); j++) {
d[0][j] = d[0][j - 1] + weight.get(0, b.charAt(j));
}
for (int i = 1; i <= a.length(); i++) {
d[1][0] = d[0][0] + weight.get(a.charAt(i), 0);
int start = 1;
int end = b.length();
if (radius > 0) {
start = i - radius;
if (start > 1)
d[1][start - 1] = Double.POSITIVE_INFINITY;
else
start = 1;
end = i + radius;
if (end < b.length())
d[1][end+1] = Double.POSITIVE_INFINITY;
else
end = b.length();
}
for (int j = start; j <= end; j++) {
double cost = weight.get(a.charAt(i - 1), b.charAt(j - 1));
d[1][j] = MathEx.min(
d[0][j] + weight.get(a.charAt(i - 1), 0), // deletion
d[1][j - 1] + weight.get(0, b.charAt(j - 1)), // insertion
d[0][j - 1] + cost); // substitution
}
double[] swap = d[0];
d[0] = d[1];
d[1] = swap;
}
return d[0][b.length()];
}
/**
* Berghel & Roach's extended Ukkonen's algorithm.
* @param a a string.
* @param b a string.
* @return the distance.
*/
private int br(char[] a, char[] b) {
if (a.length > b.length) {
char[] swap = a;
a = b;
b = swap;
}
final int m = a.length;
final int n = b.length;
int ZERO_K = n;
if (n+2 > FKP.ncol())
FKP = new IntArray2D(2*n+1, n+2);
for (int k = -ZERO_K; k < 0; k++) {
int p = -k - 1;
FKP.set(k + ZERO_K, p + 1, Math.abs(k) - 1);
FKP.set(k + ZERO_K, p, Integer.MIN_VALUE);
}
FKP.set(ZERO_K, 0, -1);
for (int k = 1; k <= ZERO_K; k++) {
int p = k - 1;
FKP.set(k + ZERO_K, p + 1, -1);
FKP.set(k + ZERO_K, p, Integer.MIN_VALUE);
}
int p = n - m - 1;
do {
p++;
for (int i = (p - (n-m))/2; i >= 1; i--) {
brf.f(a, b, FKP, ZERO_K, n-m+i, p-i);
}
for (int i = (n-m+p)/2; i >= 1; i--) {
brf.f(a, b, FKP, ZERO_K, n-m-i, p-i);
}
brf.f(a, b, FKP, ZERO_K, n - m, p);
} while (FKP.get((n - m) + ZERO_K, p) != m);
return p - 1;
}
/**
* Berghel & Roach's extended Ukkonen's algorithm.
* @param a a string.
* @param b a string.
* @return the distance.
*/
private int br(String a, String b) {
if (a.length() > b.length()) {
String swap = a;
a = b;
b = swap;
}
final int m = a.length();
final int n = b.length();
int ZERO_K = n;
if (n+3 > FKP.ncol())
FKP = new IntArray2D(2*n+1, n+3);
for (int k = -ZERO_K; k < 0; k++) {
int p = -k - 1;
FKP.set(k + ZERO_K, p + 1, Math.abs(k) - 1);
FKP.set(k + ZERO_K, p, Integer.MIN_VALUE);
}
FKP.set(ZERO_K, 0, -1);
for (int k = 1; k <= ZERO_K; k++) {
int p = k - 1;
FKP.set(k + ZERO_K, p + 1, -1);
FKP.set(k + ZERO_K, p, Integer.MIN_VALUE);
}
int p = n - m - 1;
do {
p++;
for (int i = (p - (n-m))/2; i >= 1; i--) {
brf.f(a, b, FKP, ZERO_K, n-m+i, p-i);
}
for (int i = (n-m+p)/2; i >= 1; i--) {
brf.f(a, b, FKP, ZERO_K, n-m-i, p-i);
}
brf.f(a, b, FKP, ZERO_K, n - m, p);
} while (FKP.get((n - m) + ZERO_K, p) != m);
return p - 1;
}
private interface BRF {
/**
* Calculate FKP arrays in BR's algorithm.
*/
void f(char[] x, char[] y, IntArray2D FKP, int ZERO_K, int k, int p);
/**
* Calculate FKP arrays in BR's algorithm.
*/
void f(String x, String y, IntArray2D FKP, int ZERO_K, int k, int p);
}
private static class LevenshteinBRF implements BRF {
@Override
public void f(char[] x, char[] y, IntArray2D FKP, int ZERO_K, int k, int p) {
int t = MathEx.max(FKP.get(k + ZERO_K, p) + 1, FKP.get(k - 1 + ZERO_K, p), FKP.get(k + 1 + ZERO_K, p) + 1);
int mnk = Math.min(x.length, y.length - k);
while (t < mnk && x[t] == y[t + k]) {
t++;
}
FKP.set(k + ZERO_K, p + 1, t);
}
@Override
public void f(String x, String y, IntArray2D FKP, int ZERO_K, int k, int p) {
int t = MathEx.max(FKP.get(k + ZERO_K, p) + 1, FKP.get(k - 1 + ZERO_K, p), FKP.get(k + 1 + ZERO_K, p) + 1);
int mnk = Math.min(x.length(), y.length() - k);
while (t < mnk && x.charAt(t) == y.charAt(t + k)) {
t++;
}
FKP.set(k + ZERO_K, p + 1, t);
}
}
/**
* Calculate FKP arrays in BR's algorithm with support of transposition operation.
*/
private static class DamerauBRF implements BRF {
@Override
public void f(char[] x, char[] y, IntArray2D FKP, int ZERO_K, int k, int p) {
int t = FKP.get(k + ZERO_K, p) + 1;
int mnk = Math.min(x.length, y.length - k);
if (t >= 1 && k + t >= 1 && t < mnk) {
if (x[t - 1] == y[k + t] && x[t] == y[k + t - 1]) {
t++;
}
}
t = MathEx.max(FKP.get(k - 1 + ZERO_K, p), FKP.get(k + 1 + ZERO_K, p) + 1, t);
while (t < mnk && x[t] == y[t + k]) {
t++;
}
FKP.set(k + ZERO_K, p + 1, t);
}
@Override
public void f(String x, String y, IntArray2D FKP, int ZERO_K, int k, int p) {
int t = FKP.get(k + ZERO_K, p) + 1;
int mnk = Math.min(x.length(), y.length() - k);
if (t >= 1 && k + t >= 1 && t < mnk) {
if (x.charAt(t - 1) == y.charAt(k + t) && x.charAt(t) == y.charAt(k + t - 1)) {
t++;
}
}
t = MathEx.max(FKP.get(k - 1 + ZERO_K, p), FKP.get(k + 1 + ZERO_K, p) + 1, t);
while (t < mnk && x.charAt(t) == y.charAt(t + k)) {
t++;
}
FKP.set(k + ZERO_K, p + 1, t);
}
}
/**
* Levenshtein distance between two strings allows insertion, deletion,
* or substitution of characters. O(mn) time and O(n) space.
* Multi-thread safe.
* @param a a string.
* @param b a string.
* @return the distance.
*/
public static int levenshtein(String a, String b) {
// switch parameters to use the shorter one as b to save space.
if (a.length() < b.length()) {
String swap = a;
a = b;
b = swap;
}
int[][] d = new int[2][b.length() + 1];
for (int j = 0; j <= b.length(); j++) {
d[0][j] = j;
}
for (int i = 1; i <= a.length(); i++) {
d[1][0] = i;
for (int j = 1; j <= b.length(); j++) {
int cost = a.charAt(i - 1) == b.charAt(j - 1) ? 0 : 1;
d[1][j] = MathEx.min(
d[0][j] + 1, // deletion
d[1][j - 1] + 1, // insertion
d[0][j - 1] + cost); // substitution
}
int[] swap = d[0];
d[0] = d[1];
d[1] = swap;
}
return d[0][b.length()];
}
/**
* Levenshtein distance between two strings allows insertion, deletion,
* or substitution of characters. O(mn) time and O(n) space.
* Multi-thread safe.
* @param a a string.
* @param b a string.
* @return the distance.
*/
public static int levenshtein(char[] a, char[] b) {
// switch parameters to use the shorter one as b to save space.
if (a.length < b.length) {
char[] swap = a;
a = b;
b = swap;
}
int[][] d = new int[2][b.length + 1];
for (int j = 0; j <= b.length; j++) {
d[0][j] = j;
}
for (int i = 1; i <= a.length; i++) {
d[1][0] = i;
for (int j = 1; j <= b.length; j++) {
int cost = a[i - 1] == b[j - 1] ? 0 : 1;
d[1][j] = MathEx.min(
d[0][j] + 1, // deletion
d[1][j - 1] + 1, // insertion
d[0][j - 1] + cost); // substitution
}
int[] swap = d[0];
d[0] = d[1];
d[1] = swap;
}
return d[0][b.length];
}
/**
* Damerau-Levenshtein distance between two strings allows insertion,
* deletion, substitution, or transposition of characters.
* O(mn) time and O(n) space. Multi-thread safe.
* @param a a string.
* @param b a string.
* @return the distance.
*/
public static int damerau(String a, String b) {
// switch parameters to use the shorter one as b to save space.
if (a.length() < b.length()) {
String swap = a;
a = b;
b = swap;
}
int[][] d = new int[3][b.length() + 1];
for (int j = 0; j <= b.length(); j++) {
d[1][j] = j;
}
for (int i = 1; i <= a.length(); i++) {
d[2][0] = i;
for (int j = 1; j <= b.length(); j++) {
int cost = a.charAt(i-1) == b.charAt(j-1) ? 0 : 1;
d[2][j] = MathEx.min(
d[1][j] + 1, // deletion
d[2][j-1] + 1, // insertion
d[1][j-1] + cost); // substitution
if (i > 1 && j > 1) {
if (a.charAt(i-1) == b.charAt(j-2) && a.charAt(i-2) == b.charAt(j-1))
d[2][j] = Math.min(d[2][j], d[0][j-2] + cost); // damerau
}
}
int[] swap = d[0];
d[0] = d[1];
d[1] = d[2];
d[2] = swap;
}
return d[1][b.length()];
}
/**
* Damerau-Levenshtein distance between two strings allows insertion,
* deletion, substitution, or transposition of characters.
* O(mn) time and O(n) space. Multi-thread safe.
* @param a a string.
* @param b a string.
* @return the distance.
*/
public static int damerau(char[] a, char[] b) {
// switch parameters to use the shorter one as b to save space.
if (a.length < b.length) {
char[] swap = a;
a = b;
b = swap;
}
int[][] d = new int[3][b.length + 1];
for (int j = 0; j <= b.length; j++) {
d[1][j] = j;
}
for (int i = 1; i <= a.length; i++) {
d[2][0] = i;
for (int j = 1; j <= b.length; j++) {
int cost = a[i-1] == b[j-1] ? 0 : 1;
d[2][j] = MathEx.min(
d[1][j] + 1, // deletion
d[2][j-1] + 1, // insertion
d[1][j-1] + cost); // substitution
if (i > 1 && j > 1) {
if (a[i-1] == b[j-2] && a[i-2] == b[j-1])
d[2][j] = Math.min(d[2][j], d[0][j-2] + cost); // damerau
}
}
int[] swap = d[0];
d[0] = d[1];
d[1] = d[2];
d[2] = swap;
}
return d[1][b.length];
}
}