feat(vectors): add new distance metrics

- add distBrayCurtis()
- add distCanberra()
- add distHamming()
- add distJaccard()
- add distMinkowski()
- add distSorensenDice()

packages/vectors/src/dist-braycurtis.ts

@@ -0,0 +1,26 @@
+import type { DistanceFn } from "./api";
+
+/**
+ * Bray-Curtis **dissimilarity** metric. Result always in [0..1] interval.
+ *
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Bray%E2%80%93Curtis_dissimilarity
+ *
+ * @example
+ * ```ts
+ * distBrayCurtis([6, 7, 4], [10, 0, 6])
+ * // 0.393939...
+ * ```
+ *
+ * @param a
+ * @param b
+ */
+export const distBrayCurtis: DistanceFn = (a, b) => {
+    let c = 0;
+    let s = 0;
+    for (let i = a.length; i-- > 0; ) {
+        c += Math.abs(a[i] - b[i]);
+        s += Math.abs(a[i] + b[i]);
+    }
+    return s > 0 ? c / s : 0;
+};

packages/vectors/src/dist-canberra.ts

@@ -0,0 +1,19 @@
+import type { DistanceFn } from "./api";
+
+/**
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Canberra_distance
+ *
+ * @param a
+ * @param b
+ */
+export const distCanberra: DistanceFn = (a, b) => {
+    let delta = 0;
+    for (let i = a.length; --i >= 0; ) {
+        const aa = a[i];
+        const bb = b[i];
+        const d = Math.abs(aa) + Math.abs(bb);
+        d > 0 && (delta += Math.abs(aa - bb) / d);
+    }
+    return delta;
+};

packages/vectors/src/dist-chebyshev.ts

@@ -17,6 +17,10 @@ const $ = (dim: number) =>
         )
     );
 
+/**
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Chebyshev_distance
+ */
 export const distChebyshev: MultiVecOpRoVV<number> = vop();
 
 distChebyshev.default((a, b) => {

packages/vectors/src/dist-hamming.ts

@@ -0,0 +1,19 @@
+import type { DistanceFn } from "./api";
+
+/**
+ * Normalized Hamming distance between `a` and `b`, i.e. number of differing
+ * components divided by vector size.
+ *
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Hamming_distance
+ *
+ * @param a
+ * @param b
+ */
+export const distHamming: DistanceFn = (a, b) => {
+    let delta = 0;
+    for (let i = a.length; --i >= 0; ) {
+        a[i] !== b[i] && delta++;
+    }
+    return delta / a.length;
+};

packages/vectors/src/dist-jaccard.ts

@@ -0,0 +1,20 @@
+import type { DistanceFn } from "./api";
+
+/**
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Jaccard_index
+ *
+ * @param a
+ * @param b
+ */
+export const distJaccard: DistanceFn = (a, b) => {
+    let numNZ = 0;
+    let numEQ = 0;
+    for (let i = a.length; --i >= 0; ) {
+        const aa = a[i] !== 0;
+        const bb = b[i] !== 0;
+        numNZ += ~~(aa || bb);
+        numEQ += ~~(aa && bb);
+    }
+    return numNZ ? (numNZ - numEQ) / numNZ : 0;
+};

packages/vectors/src/dist-manhattan.ts

@@ -17,6 +17,10 @@ const $ = (dim: number) =>
         )
     );
 
+/**
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Taxicab_geometry
+ */
 export const distManhattan: MultiVecOpRoVV<number> = vop();
 
 distManhattan.default(

packages/vectors/src/dist-minkowski.ts

@@ -0,0 +1,19 @@
+import type { ReadonlyVec } from "./api";
+
+/**
+ * @remarks
+ * The Minkowski power `p` MUST be > 0.
+ *
+ * Reference: https://en.wikipedia.org/wiki/Minkowski_distance
+ *
+ * @param a
+ * @param b
+ * @param p
+ */
+export const distMinkowski = (a: ReadonlyVec, b: ReadonlyVec, p: number) => {
+    let delta = 0;
+    for (let i = a.length; --i >= 0; ) {
+        delta += Math.abs(a[i] - b[i]) ** p;
+    }
+    return delta ** (1 / p);
+};

packages/vectors/src/dist-sorensendice.ts

@@ -0,0 +1,20 @@
+import type { DistanceFn } from "./api";
+
+/**
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient
+ *
+ * @param a
+ * @param b
+ */
+export const distSorensenDice: DistanceFn = (a, b) => {
+    let numTP = 0;
+    let numFP = 0;
+    for (let i = a.length; i-- > 0; ) {
+        const aa = a[i] !== 0;
+        const bb = b[i] !== 0;
+        numTP += ~~(aa && bb);
+        numFP += ~~(aa !== bb);
+    }
+    return numFP ? numFP / (2 * numTP + numFP) : 0;
+};

packages/vectors/src/index.ts

@@ -49,9 +49,15 @@ export * from "./crosss";
 export * from "./degrees";
 export * from "./direction";
 export * from "./dist";
+export * from "./dist-braycurtis";
+export * from "./dist-canberra";
 export * from "./dist-chebyshev";
+export * from "./dist-hamming";
 export * from "./dist-haversine";
+export * from "./dist-jaccard";
 export * from "./dist-manhattan";
+export * from "./dist-minkowski";
+export * from "./dist-sorensendice";
 export * from "./dist-weighted";
 export * from "./distsq";
 export * from "./div";