Semantic Search API (#12105)

* initial event search api implementation

* fix lint

* fix tests

* move chromadb imports and pysqlite hotswap to fix tests

* remove unused import

* switch default limit to 50

* fix events accidently pulling inside chroma results loop

frigate/embeddings/util.py

@@ -0,0 +1,47 @@
+"""Z-score normalization for search distance."""
+
+import math
+
+
+class ZScoreNormalization:
+    """Running Z-score normalization for search distance."""
+
+    def __init__(self):
+        self.n = 0
+        self.mean = 0
+        self.m2 = 0
+
+    @property
+    def variance(self):
+        return self.m2 / (self.n - 1) if self.n > 1 else 0.0
+
+    @property
+    def stddev(self):
+        return math.sqrt(self.variance)
+
+    def normalize(self, distances: list[float]):
+        self._update(distances)
+        if self.stddev == 0:
+            return distances
+        return [(x - self.mean) / self.stddev for x in distances]
+
+    def _update(self, distances: list[float]):
+        for x in distances:
+            self.n += 1
+            delta = x - self.mean
+            self.mean += delta / self.n
+            delta2 = x - self.mean
+            self.m2 += delta * delta2
+
+    def to_dict(self):
+        return {
+            "n": self.n,
+            "mean": self.mean,
+            "m2": self.m2,
+        }
+
+    def from_dict(self, data: dict):
+        self.n = data["n"]
+        self.mean = data["mean"]
+        self.m2 = data["m2"]
+        return self