Added: Streaming median content from webinar

Author: djarpin

README.md

@@ -36,6 +36,7 @@ These examples provide quick walkthroughs to get you up and running with Amazon
 
 These examples provide more thorough mathematical treatment on a select group of algorithms.
 
+- [Streaming Median](scientific_details_of_algorithms/streaming_median) sequentially introduces concepts used in streaming algorithms, which many SageMaker algorithms rely on to deliver speed and scalability.
 - [Latent Dirichlet Allocation (LDA)](scientific_details_of_algorithms/lda_topic_modeling) dives into Amazon SageMaker's spectral decomposition approach to LDA.
 
 ### Advanced Amazon SageMaker Functionality

scientific_details_of_algorithms/README.md

@@ -4,4 +4,5 @@
 
 These examples provide more thorough mathematical treatment on a select group of algorithms.
 
+- [Streaming Median](streaming_median) sequentially introduces concepts used in streaming algorithms, which many SageMaker algorithms rely on to deliver speed and scalability.
 - [Latent Dirichlet Allocation (LDA)](lda_topic_modeling) dives into Amazon SageMaker's spectral decomposition approach to LDA.

scientific_details_of_algorithms/streaming_median/kll300.py

@@ -0,0 +1,55 @@
+#!/usr/bin/python
+
+# Copyright 2017 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+# 
+# Licensed under the Apache License, Version 2.0 (the "License"). You may not use this file except in compliance with the License. A copy of the License is located at
+#
+#     http://aws.amazon.com/apache2.0/
+#
+# or in the "license" file accompanying this file. This file is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
+
+import sys
+from random import randint
+
+class  KLL300:
+    def __init__(self):
+        self.maxSize = 300
+        self.size = 0
+        self.capacities = [2, 2, 4, 6, 10, 18, 28, 44, 70, 112]
+        self.H = len(self.capacities)
+        self.compactors = [Compactor() for _ in range(self.H)]
+
+    def sizef(self):
+        return sum([len(c) for c in self.compactors])
+
+    def update(self, item):
+        self.compactors[0].append(item)
+        self.size += 1
+        if self.size >= self.maxSize:
+            for h in range(self.H - 1):
+                if len(self.compactors[h]) >= self.capacities[h]:
+                    newItems = self.compactors[h].compact()
+                    self.compactors[h+1].extend(newItems)
+                    break
+        self.size = self.sizef()
+        assert(self.size < self.maxSize)
+
+    def cdf(self):
+        itemsAndWeights = []
+        for (h, items) in enumerate(self.compactors):
+             itemsAndWeights.extend( (item, 2**h) for item in items )
+        itemsAndWeights.sort()
+        items = [t[0] for t in itemsAndWeights]
+        weights = [t[1] for t in itemsAndWeights]
+        for i in range(len(weights)-1):
+            weights[i+1]+=weights[i]
+        totWeight = weights[-1]
+        return items, [w/totWeight for w in weights]
+
+class Compactor(list):
+    def compact(self):
+        self.sort()
+        offset = randint(0,1)
+        for item in self[offset::2]:
+            yield item
+        self.clear()