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new 16d9b4e Update Major Sketch Families.
16d9b4e is described below
commit 16d9b4eab6b209f6db2969b44fb536326ee521c2
Author: Lee Rhodes <[email protected]>
AuthorDate: Fri Jan 24 18:12:38 2020 -0800
Update Major Sketch Families.
---
docs/MajorSketchFamilies.md | 58 ++++++++++++++++++++++++++++++++++++++-------
1 file changed, 50 insertions(+), 8 deletions(-)
diff --git a/docs/MajorSketchFamilies.md b/docs/MajorSketchFamilies.md
index f3efac2..c4c0a58 100644
--- a/docs/MajorSketchFamilies.md
+++ b/docs/MajorSketchFamilies.md
@@ -19,6 +19,11 @@ layout: doc_page
specific language governing permissions and limitations
under the License.
-->
+# Cardinality Sketches
+
+## CPC Sketch: Estimating Stream Cardinalities more efficiently than the
famous HLL sketch!
+This sketch was developed by the late Keven Lang, our chief scientist at the
time, is an amazing *tour de force* of scientific design and engineering and
has substantially better accuracy / per stored size than the famous HLL sketch.
The theory and demonstration of its performance is detailed in Lang's paper
[Back to the Future: an Even More Nearly Optimal Cardinality Estimation
Algorithm](https://arxiv.org/abs/1708.06839). This sketch is available in
Java, C++ and Python.
+
## [Theta Sketches]({{site.docs_dir}}/Theta/ThetaSketchFramework.html):
Estimating Stream Expression Cardinalities
Internet content, search and media companies like Yahoo, Google, Facebook,
etc., collect many tens of billions of event records from the many millions of
users to their web sites each day. These events can be classified by many
different dimensions, such as the page visited and user location and profile
information. Each event also contains some unique identifiers associated with
the user, specific device (cell phone, tablet, or computer) and the web browser
used.
@@ -29,29 +34,66 @@ These same unique identifiers will appear on every page
that the user visits. I
Computing cardinalities with massive data requires lots of computer resources
and time.
However, if an approximate answer to these problems is acceptable, [Theta
Sketches]({{site.docs_dir}}/Theta/ThetaSketchFramework.html) can provide
reasonable estimates, in a single pass, orders of magnitude faster, even fast
enough for analysis in near-real time.
+The
[theta/Sketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/theta/Sketch.java)
can operate both on-heap and off-heap, has powerful Union, Intersection, AnotB
and Jaccard operators, has a high-performance concurrent form for
multi-threaded environments, has both immutable compact, and updatable
representations, and is quite fast. It is available in Java, C++ and Python.
Because of its flexibility, it is one of the most popular [...]
+
+## [Tuple Sketches]({{site.docs_dir}}/Tuple/TupleOverview.html): Extending
Theta Sketches to Perform Associative Analysis
+It is often not enough to perform stream expressions on sets of unique
identifiers, it is very valuable to be able to associate additive data with
these identifiers, such as impression counts, clicks or timestamps. Tuple
Sketches are a natural extension of the Theta sketch and have Java Genric
forms, that enable the user do define the sketch with arbitrary "summary" data.
The
[tuple/Sketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datas
[...]
+
+The Tuple sketch is effectively infinitely extendable and there are several
common variants of the Tuple Sketch, which also serve as examples on how to
extend the base classes, that are also in the library, including:
+
+-
[tuple/adouble/DoubleSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/tuple/adouble/DoubleSketch.java)
with a single column of *double* values as the *summary*.
+-
[tuple/aninteger/IntegerSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/tuple/aninteger/IntegerSketch.java)
with a single column of *int* values as the *summary*.
+-
[tuple/strings/ArrayOfStringsSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/tuple/strings/ArrayOfStringsSketch.java),
which is effectively a variable number of columns of strings as the *summary*.
+-
[tuple/ArrayOfDoublesSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/tuple/ArrayOfDoublesSketch.java),
which is effectively a variable number of columns of double values as the
*summary*. This variant also provides both on-heap and off-heap operation.
+
## [HyperLogLog Sketches]({{site.docs_dir}}/HLL/HLL.html): Estimating Stream
Cardinalities
The HyperLogLog (HLL) is a cardinality sketch similar to the above Theta
sketches except they are anywhere from 2 to 16 times smaller in size. The HLL
sketches can be Unioned, but set intersection and difference operations are not
provided intrinsically, because the resulting error would be quite poor. If
your application only requires cardinality estimation and Unioning and space is
at a premium, the HLL sketch provided could be your best choice.
+The
[hll/HllSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/hll/HllSketch.java)
can operate both on-heap and off-heap, provides the Union operators, and has
both immutable compact, and updatable representations. It is available in Java,
C++ and Python.
+
## [HyperLogLog Map Sketch]({{site.docs_dir}}/HLL/HllMap.html): Estimating
Stream Cardinalities of Key-Value Pairs
-This is a specially designed sketch that addresses the problem of individually
tracking value cardinalities of Key-Value (K,V) pairs, where the number of keys
can be very large, such as IP addresses, or Geo identifiers, etc. Assigning
individual sketches to each key would create unnecessary overhead. This sketch
streamlines the process with much better space management.
+This is a specially designed sketch that addresses the problem of individually
tracking value cardinalities of Key-Value (K,V) pairs in real-time, where the
number of keys can be very large, such as IP addresses, or Geo identifiers,
etc. Assigning individual sketches to each key would create unnecessary
overhead. This sketch streamlines the process with much better space
management. This
[hllmap/UniqueCountMap](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/j
[...]
+# Quantiles Sketches
## [Quantiles Sketches]({{site.docs_dir}}/Quantiles/QuantilesOverview.html):
Estimating Distributions from a Stream of Values
There are many situations where is valuable to understand the distribution of
values in a stream. For example, from a stream of web-page time-spent values,
it would be useful to know arbitrary quantiles of the distribution, such as the
25th percentile value, the median value and the 75th percentile value. The
[Quantiles Sketches]({{site.docs_dir}}/Quantiles/QuantilesOverview.html) solve
this problem and enable the inverse functions such as the Probability Mass
Function (PMF) and the Cumu [...]
<img class="doc-img-full"
src="{{site.docs_img_dir}}/quantiles/TimeSpentHistogram.png"
alt="TimeSpentHistogram" />
-## [Frequent Items
Sketches]({{site.docs_dir}}/FrequentItems/FrequentItemsOverview.html): Finding
the Heavy Hitter Objects from a Stream
+There are two different families of quantiles sketches, the original
[quantiles/DoublesSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/quantiles/DoublesSketch.java),
which can be operated either on-heap or off-heap, and is also available in a
Java Generic form for arbitrary comparable objects. It is only available in
Java.
+
+Later we developed the
[kll/KllFloatsSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/kll/KllFloatsSketch.java)
(Named after its authors), which is also a quantiles sketch, that achieves
near optimal small size for a given accuracy. It is only available on-heap. It
is available in Java, C++ and Python.
+
+# Frequent Items / Heavy Hitters Sketches
+
+## [Frequent Items
Sketches]({{site.docs_dir}}/Frequency/FrequentItemsOverview.html): Finding the
Heavy Hitter Objects from a Stream
It is very useful to be able to scan a stream of objects, such as song titles,
and be able to quickly identify those items that occur most frequently. The
term <i>Heavy Hitter</i> is defined to be an item that occurs more frequently
than some fractional share of the overall count of items
in the stream including duplicates. Suppose you have a stream of 1M song
titles, but in that stream there are only 100K song titles that are unique. If
any single title consumes more than 10% of the stream elements it is a Heavy
Hitter, and the 10% is a threshold parameter we call epsilon.
-The accuracy of a Frequent Items Sketch is proportional to the configured size
of the sketch, the larger the sketch, the smaller is the epsilon threshold that
can detect Heavy Hitters.
+The accuracy of a Frequent Items Sketch is proportional to the configured size
of the sketch, the larger the sketch, the smaller is the epsilon threshold that
can detect Heavy Hitters. This sketch is available in two forms, as the
[frequencies/LongsSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/frequencies/LongsSketch.java)
used for processing a stream of tuples {*long*, weight}, and the
[frequencies/ItemsSketch](https://gi [...]
-## [Tuple Sketches]({{site.docs_dir}}/Tuple/TupleOverview.html): Extending
Theta Sketches to Perform Associative Analysis
-It is often not enough to perform stream expressions on sets of unique
identifiers, it is very valuable to be able to associate additive data with
these identifiers, such as impression counts or clicks. Tuple Sketches are a
recent addition to the library and can be extended with arbitrary "summary"
data.
+## [Frequent Distinct Tuples
Sketch]({{site.docs_dir}}/Frequency/FrequentDistinctTuplesSketch.html): Finding
the Heavy Hitter tuples from a Stream.
+Suppose our data is a stream of pairs {IP address, User ID} and we want to
identify the IP addresses that have the most distinct User IDs. Or conversely,
we would like to identify the User IDs that have the most distinct IP
addresses. This is a common challenge in the analysis of big data and the FDT
sketch helps solve this problem using probabilistic techniques.
-## [Sampling Sketches]({{site.docs_dir}}/Sampling/ReservoirSampling.html):
Uniform Sampling of a Stream into a fixed size space
-This implements the famous Reservoir sampling algorithm and extends it with
the capabilities that large-scale distributed systems really need: mergability
(even with different sized sketches), uses Java Generics so that the base
classes can be trivially extended for any input type (even polymorphic types),
and an extensible means of performing serialization and deserialization. VarOpt
sampling extends the family to weighted sampling, additionally providing subset
sum estimates from the s [...]
+More generally, given a multiset of tuples with *N* dimensions *{d1,d2, d3, …,
dN}*, and a primary subset of dimensions *M < N*, our task is to identify the
combinations of *M* subset dimensions that have the most frequent number of
distinct combinations of the *N - M* non-primary dimensions.
+
+The
[fdt/FdtSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/fdt/FdtSketch.java)
is currently only available in Java, but because it is an extension of the
Tuple Sketch family, it inherits many of the same properties: it can operate
both on-heap and off-heap, includes both Union and Intersection operators, has
both immutable compact, and updatable representations.
## Frequent Directions: Distributed, mergeable Singular Value Decomposition
-Part of a new separate sketches-vector package, Frequent Directions is in many
ways a generalization of the Frequent Items sketch to handle vector data. This
sketch computes an approximate singular value decomposition (SVD) of a matrix,
providing a projection matrix that can be used for dimensionality reduction.
SVD is a key technique in many recommender systems, providing shopping
suggestions based on a customer's past purchases compared with other similar
customers.
+Part of a new separate sketches-vector package, Frequent Directions is in many
ways a generalization of the Frequent Items sketch to handle vector data. This
sketch computes an approximate singular value decomposition (SVD) of a matrix,
providing a projection matrix that can be used for dimensionality reduction.
SVD is a key technique in many recommender systems, providing shopping
suggestions based on a customer's past purchases compared with other similar
customers. This sketch is stil [...]
+
+# Sampling Sketches
+
+## [Sampling Sketches]({{site.docs_dir}}/Sampling/ReservoirSampling.html):
Uniform Sampling of a Stream into a fixed size space
+This family of sketches implements an enhanced version of the famous Reservoir
sampling algorithm and extends it with the capabilities that large-scale
distributed systems really need: mergability (even with different sized
sketches), uses Java Generics so that the base classes can be trivially
extended for any input type (even polymorphic types), and an extensible means
of performing serialization and deserialization.
+
+The
[sampling/ReservoirLongsSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/sampling/ReservoirLongsSketch.java)
accepts a stream of *long* values as identifiers with a weight of one, and
produces a result Reservoir of a pre-determined size that represents a uniform
random sample of the stream.
+
+The
[sampling/ReservoirItemsSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/sampling/ReservoirItemsSketch.java)
accepts a stream of type *T* as identifiers with a weight of one, and produces
a result Reservoir of a pre-determined size that represents a uniform random
sample of the stream.
+
+The
[sampling/VarOptItemsSketch](https://github.com/apache/incubator-datasketches-java/blob/master/src/main/java/org/apache/datasketches/sampling/VarOptItemsSketch.java)
extends the Reservoir family to weighted sampling, additionally providing
subset sum estimates from the sample with provably optimal variance.
+
+This family is currently only available in Java.
+
+
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