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Posted to commits@lucene.apache.org by jb...@apache.org on 2021/03/01 19:40:21 UTC
[lucene-solr] branch branch_8x updated (a1d7758 -> 4bce143)
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jbernste pushed a change to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git.
from a1d7758 SOLR-15132: Update CHANGES.txt
new 29846a5 SOLR-15193: Add Graph to the Visual Guide to Streaming Expressions and Math Expressions
new c3aecab SOLR-15193: Fix typos
new 4340433 SOLR-15193: Fix typos
new 9bd300c SOLR-15193: Fix typos
new ca60c43 SOLR-15193: Fix wording
new 4bce143 SOLR-15193: Improve formatting
The 6 revisions listed above as "new" are entirely new to this
repository and will be described in separate emails. The revisions
listed as "add" were already present in the repository and have only
been added to this reference.
Summary of changes:
solr/solr-ref-guide/src/graph.adoc | 709 +++++++++++++++++++++
.../src/images/math-expressions/graph1.png | Bin 0 -> 23089 bytes
.../src/images/math-expressions/graph2.png | Bin 0 -> 27878 bytes
solr/solr-ref-guide/src/math-expressions.adoc | 4 +-
4 files changed, 712 insertions(+), 1 deletion(-)
create mode 100644 solr/solr-ref-guide/src/graph.adoc
create mode 100644 solr/solr-ref-guide/src/images/math-expressions/graph1.png
create mode 100644 solr/solr-ref-guide/src/images/math-expressions/graph2.png
[lucene-solr] 04/06: SOLR-15193: Fix typos
Posted by jb...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
jbernste pushed a commit to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git
commit 9bd300ccd3b09f2c3db9f313b50925f031be2591
Author: Joel Bernstein <jb...@apache.org>
AuthorDate: Wed Feb 24 17:39:02 2021 -0500
SOLR-15193: Fix typos
---
solr/solr-ref-guide/src/graph.adoc | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/solr/solr-ref-guide/src/graph.adoc b/solr/solr-ref-guide/src/graph.adoc
index 207dbe0..fdee70d 100644
--- a/solr/solr-ref-guide/src/graph.adoc
+++ b/solr/solr-ref-guide/src/graph.adoc
@@ -17,7 +17,7 @@
// under the License.
-This section of the user guide covers the syntax and theory behind *graph expressions*. Examples are presented for two key graph use cases: *bipartate graph recommenders* and *event correlation* with
+This section of the user guide covers the syntax and theory behind *graph expressions*. Examples are presented for two key graph use cases: *bipartite graph recommenders* and *event correlation* with
*temporal graph queries*.
== Graphs
[lucene-solr] 05/06: SOLR-15193: Fix wording
Posted by jb...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
jbernste pushed a commit to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git
commit ca60c43089ef963a8a796695d002b82e9387b361
Author: Joel Bernstein <jb...@apache.org>
AuthorDate: Thu Feb 25 08:38:57 2021 -0500
SOLR-15193: Fix wording
---
solr/solr-ref-guide/src/graph.adoc | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/solr/solr-ref-guide/src/graph.adoc b/solr/solr-ref-guide/src/graph.adoc
index fdee70d..4649d9e 100644
--- a/solr/solr-ref-guide/src/graph.adoc
+++ b/solr/solr-ref-guide/src/graph.adoc
@@ -362,10 +362,10 @@ to this subgraph, and a better recommendation to be paired with butter.
== Temporal Graph Expressions
-The examples above lay the groundwork for Solr's new temporal graph queries.
-Temporal graph queries allow Solr to walk the graph using *windows of time*.
-The initial release supports graph walks using ten second increments which is useful
-for *event correlation* and *root cause analysis* use cases in log analytics.
+The examples above lay the groundwork for temporal graph queries.
+Temporal graph queries allow the `nodes` function to walk the graph using *windows of time* to surface
+*cross-correlations* within the data. The nodes function currently supports graph walks using *ten second increments*
+which is useful for *event correlation* and *root cause analysis* in log analytics.
In order to support temporal graph queries a ten second truncated timestamp in *ISO 8601* format must
be added to the log records as a string field at indexing time. Here is a sample ten second
[lucene-solr] 03/06: SOLR-15193: Fix typos
Posted by jb...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
jbernste pushed a commit to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git
commit 4340433f6a02b332a995f64284be6f4fe69bf061
Author: Joel Bernstein <jb...@apache.org>
AuthorDate: Wed Feb 24 17:33:29 2021 -0500
SOLR-15193: Fix typos
---
solr/solr-ref-guide/src/math-expressions.adoc | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/solr/solr-ref-guide/src/math-expressions.adoc b/solr/solr-ref-guide/src/math-expressions.adoc
index 7d74f7b..9e2b0c1 100644
--- a/solr/solr-ref-guide/src/math-expressions.adoc
+++ b/solr/solr-ref-guide/src/math-expressions.adoc
@@ -63,7 +63,7 @@ image::images/math-expressions/searchiris.png[]
*<<machine-learning.adoc#,Machine Learning>>*: Distance, KNN, DBSCAN, K-means, fuzzy K-means and other ML functions.
-*<<graph.adoc#,Graph>>*: Bipartite graphs, in-degree centrality, graph recommenders, temporal graphs, event correlation.
+*<<graph.adoc#,Graph>>*: Bipartite graphs, in-degree centrality, graph recommenders, temporal graphs and event correlation.
*<<computational-geometry.adoc#,Computational Geometry>>*: Convex Hulls and Enclosing Disks.
[lucene-solr] 01/06: SOLR-15193: Add Graph to the Visual Guide to
Streaming Expressions and Math Expressions
Posted by jb...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
jbernste pushed a commit to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git
commit 29846a5f8070ab4f8069f45aeedf35ebdf751847
Author: Joel Bernstein <jb...@apache.org>
AuthorDate: Wed Feb 24 15:02:37 2021 -0500
SOLR-15193: Add Graph to the Visual Guide to Streaming Expressions and Math Expressions
---
solr/solr-ref-guide/src/graph.adoc | 703 +++++++++++++++++++++
.../src/images/math-expressions/graph1.png | Bin 0 -> 23089 bytes
.../src/images/math-expressions/graph2.png | Bin 0 -> 27878 bytes
solr/solr-ref-guide/src/math-expressions.adoc | 4 +-
4 files changed, 706 insertions(+), 1 deletion(-)
diff --git a/solr/solr-ref-guide/src/graph.adoc b/solr/solr-ref-guide/src/graph.adoc
new file mode 100644
index 0000000..887990d
--- /dev/null
+++ b/solr/solr-ref-guide/src/graph.adoc
@@ -0,0 +1,703 @@
+= Graph
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements. See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership. The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License. You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License 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.
+
+
+This section of user guide covers the syntax and theory behind *graph expressions*. Examples are presented for two key graph use cases: *bipartate graph recommenders* and *event correlation* with
+*temporal graph queries*.
+
+== Graphs
+
+Log records and other data indexed in Solr have connections between them that can be seen as a distributed graph.
+Graph expressions provide a mechanism for identifying root nodes in the graph and walking their connections.
+The general goal of the graph walk is to materialize a specific subgraph and perform link analysis to understand
+the connections between nodes.
+
+In the next few sections below we'll review the graph theory behind Solr's graph expressions.
+
+=== Subgraphs
+
+A subgraph is a smaller subset of the nodes and connections of the
+larger graph. Graph expressions allow you to flexibly define and materialize a subgraph from the larger graph stored in the distributed index.
+
+Subgraphs play two important roles:
+
+* They provide a local context for link analysis. The design of the subgraph defines the meaning of the link analysis.
+
+* They provide a foreground graph that can be compared to the background index for anomaly detection purposes.
+
+=== Bipartite Subgraphs
+
+Graph expressions can be used to materialize *bipartite subgraphs*.
+A bipartite graph is a graph where the nodes are split into two
+distinct categories. The links between those two categories can then
+be analyzed to study how they relate. Bipartite graphs are often discussed
+in the context of collaborative filter recommender systems.
+
+A bipartite graph between shopping baskets and products is a useful example.
+Through link analysis between the shopping baskets and products
+we can determine which products are most often purchased within the same shopping baskets.
+
+In the example below there is a Solr collection called baskets
+with three fields:
+
+*id*: Unique ID
+
+*basket_s*: Shopping basket ID
+
+*product_s*: Product
+
+Each record in the collection represents a product in a shopping basket.
+All products in the same basket share the same basket ID.
+
+Let's consider a simple example where we want to find a product
+that is often sold with *butter*. In order to do this we could create a
+bipartite subgraph of shopping baskets that contain butter.
+We won't include butter itself in the graph as it doesn't help with
+finding a complementary product for butter.
+
+Below is an example of this bipartite subgraph represented as a matrix:
+
+image::images/math-expressions/graph1.png[]
+
+In this example there are three shopping baskets shown by the rows: basket1, basket2, basket3.
+
+There are also three products shown by the columns: cheese, eggs, milk.
+
+Each cell has a 1 or 0 signifying if the product is in the basket.
+
+Let's look at how Solr graph expressions materializes this bipartite subgraph:
+
+The nodes function is used to materialize a subgraph from the larger graph. Below is an example nodes function which materializes the bipartite graph shown in the matrix above.
+
+[source,text]
+----
+nodes(baskets,
+ random(baskets, q="product_s:butter", fl="basket_s", rows="3"),
+ walk="basket_s->basket_s",
+ fq="-product_s:butter",
+ gather="product_s",
+ trackTraversal="true")
+----
+
+Let's break down this example starting with the random function:
+
+
+[source,text]
+----
+random(baskets, q="product_s:butter", fl="basket_s", rows="3")
+----
+
+The `random` function is searching the baskets collection with the query `product_s:butter`, and
+returning 3 random samples. Each sample contains the `basket_s` field which is the basket id.
+The three basket id's that are returned by the random sample are the root nodes of the graph query.
+
+The `nodes` function is the graph query. The nodes function is operating over the three root nodes returned
+by the random function.
+It "walks" the graph by searching the `basket_s` field of the root nodes against the `basket_s` field in the index.
+This finds all the product records for the root baskets.
+It will then "gather" the `product_s` field from the records it finds in the walk.
+A filter is applied so that records with butter in the product_s field will not be returned.
+
+The `trackTraversal` flag tells the nodes expression to track the links between the root baskets and products.
+
+=== Node Sets
+
+The output of the nodes function is a *node set* that represents the subgraph specified by the nodes function.
+The node set contains a unique set of nodes that are gathered during the graph walk.
+The `node` property in the result is the value of the gathered node.
+In the shopping basket example the `product_s` field is in the node property
+because that was what was specified to be gathered in the nodes expression.
+
+The output of the shopping basket graph expression is as follows:
+[source,json]
+----
+{
+ "result-set": {
+ "docs": [
+ {
+ "node": "eggs",
+ "collection": "baskets",
+ "field": "product_s",
+ "ancestors": [
+ "basket1",
+ "basket3"
+ ],
+ "level": 1
+ },
+ {
+ "node": "cheese",
+ "collection": "baskets",
+ "field": "product_s",
+ "ancestors": [
+ "basket2"
+ ],
+ "level": 1
+ },
+ {
+ "node": "milk",
+ "collection": "baskets",
+ "field": "product_s",
+ "ancestors": [
+ "basket1",
+ "basket2"
+ ],
+ "level": 1
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 12
+ }
+ ]
+ }
+}
+
+
+----
+
+The `ancestors` property in the result contains a unique, alphabetically sorted set of all the incoming links
+to the node in the subgraph. In this case it shows the basket IDs that are linked to each product.
+The ancestor links will only be tracked when the trackTraversal flag is turned on in the nodes expression.
+
+=== Link Analysis and Degree Centrality
+
+Link analysis is often performed to determine *node centrality*. When analyzing for centrality the
+goal is to assign a weight to each node based on how connected it is in the subgraph.
+There are different types of node centrality. Graph expressions very efficiently calculates
+*inbound degree centrality* (indegree).
+
+Inbound degree centrality is calculated by counting the number of inbound
+links to each node. For simplicity this document will sometimes refer
+to inbound degree simply as degree.
+
+Back to the shopping basket example:
+
+image::images/math-expressions/graph1.png[]
+
+We can calculate the degree of the products in the graph by summing the columns:
+[source,text]
+----
+cheese: 1
+eggs: 2
+milk: 2
+----
+
+From the degree calculation we know that *eggs* and *milk* appear more frequently in shopping baskets with
+butter than *cheese* does.
+
+The nodes function can calculate degree centrality by adding the `count(*)` aggregation as shown below:
+
+[source,text]
+----
+nodes(baskets,
+ random(baskets, q="product_s:butter", fl="basket_s", rows="3"),
+ walk="basket_s->basket_s",
+ fq="-product_s:butter",
+ gather="product_s",
+ trackTraversal="true",
+ count(*))
+----
+
+The output of this graph expression is as follows:
+
+[source,json]
+----
+{
+ "result-set": {
+ "docs": [
+ {
+ "node": "eggs",
+ "count(*)": 2,
+ "collection": "baskets",
+ "field": "product_s",
+ "ancestors": [
+ "basket1",
+ "basket3"
+ ],
+ "level": 1
+ },
+ {
+ "node": "cheese",
+ "count(*)": 1,
+ "collection": "baskets",
+ "field": "product_s",
+ "ancestors": [
+ "basket2"
+ ],
+ "level": 1
+ },
+ {
+ "node": "milk",
+ "count(*)": 2,
+ "collection": "baskets",
+ "field": "product_s",
+ "ancestors": [
+ "basket1",
+ "basket2"
+ ],
+ "level": 1
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 17
+ }
+ ]
+ }
+}
+----
+
+The `count(+++*+++)` aggregation counts the "gathered" nodes, in this case the values in the `product_s` field.
+Notice that the `count(+++*+++)` result is the same as the number of ancestors.
+This will always be the case because the nodes function first deduplicates the edges before
+counting the gathered nodes. Because of this the `count(+++*+++)` aggregation always calculates the degree centrality for the gathered nodes.
+
+=== Dot Product
+
+There is a direct relationship between the *inbound degree* with bipartite graph recommenders and the *dot product*.
+This relationship can be clearly seen in our working example once you include a column for butter:
+
+image::images/math-expressions/graph2.png[]
+
+If we compute the dot product between the butter column and the other product columns you will find that the dot product equals the inbound degree in each case. This tells us that a nearest neighbor search, using a maximum inner product similarity, would select the column with the highest inbound degree.
+
+=== Node Scoring
+
+The degree of the node describes how many nodes in the subgraph link to it.
+But this does not tell us if the node is particularly central to this subgraph or if it is just a
+very frequent node in the entire graph. Nodes that appear frequently in the subgraph but
+infrequently in the entire graph can be considered more relevant to the subgraph.
+
+The search index contains information about how frequently each node appears in the entire index.
+Using a technique similar to *tf-idf* document scoring, graph expressions can combine the
+degree of the node with its inverse document frequency in the index to determine a relevancy score.
+
+The `scoreNodes` function scores the nodes. Below is an example of the scoreNodes function applied to
+the shopping basket node set.
+
+[source,text]
+----
+scoreNodes(nodes(baskets,
+ random(baskets, q="product_s:butter", fl="basket_s", rows="3"),
+ walk="basket_s->basket_s",
+ fq="-product_s:butter",
+ gather="product_s",
+ trackTraversal="true",
+ count(*)))
+----
+
+The output now includes a `nodeScore` property. In the output below notice how eggs has a higher
+nodeScore than milk even though they have the same `count(+++*+++)`. This is because milk appears more
+frequently in the entire index than eggs does. The `docFreq` property added by the `nodeScore` function
+shows the term frequency in the index. Because of the lower `docFreq` eggs is considered more relevant
+to this subgraph, and a better recommendation to be paired with butter.
+
+[source,json]
+----
+{
+ "result-set": {
+ "docs": [
+ {
+ "node": "eggs",
+ "nodeScore": 3.8930247,
+ "field": "product_s",
+ "numDocs": 10,
+ "level": 1,
+ "count(*)": 2,
+ "collection": "baskets",
+ "ancestors": [
+ "basket1",
+ "basket3"
+ ],
+ "docFreq": 2
+ },
+ {
+ "node": "milk",
+ "nodeScore": 3.0281217,
+ "field": "product_s",
+ "numDocs": 10,
+ "level": 1,
+ "count(*)": 2,
+ "collection": "baskets",
+ "ancestors": [
+ "basket1",
+ "basket2"
+ ],
+ "docFreq": 4
+ },
+ {
+ "node": "cheese",
+ "nodeScore": 2.7047482,
+ "field": "product_s",
+ "numDocs": 10,
+ "level": 1,
+ "count(*)": 1,
+ "collection": "baskets",
+ "ancestors": [
+ "basket2"
+ ],
+ "docFreq": 1
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 26
+ }
+ ]
+ }
+}
+----
+
+== Temporal Graph Expressions
+
+The examples above lay the groundwork for Solr's new temporal graph queries.
+Temporal graph queries allow Solr to walk the graph using *windows of time*.
+The initial release supports graph walks using ten second increments which is useful
+for *event correlation* and *root cause analysis* use cases in log analytics.
+
+In order to support temporal graph queries a ten second truncated timestamp in *ISO 8601* format must
+be added to the log records as a string field at indexing time. Here is a sample ten second
+truncated timestamp: `2021-02-10T20:51:30Z`. This small data change enables some very important
+use cases so it's well worth the effort.
+
+Solr's indexing tool for Solr logs, described <<logs.adoc#,here>>, already adds the ten second truncated timestamps.
+So those using Solr to analyze Solr logs get temporal graph expressions for free.
+
+=== Root Events
+
+Once the ten second windows have been indexed with the log records we can devise a query that creates a set of root events. We can demonstrate this with an example using Solr log records.
+
+In this example we'll perform a Streaming Expression facet aggregation that finds the top 25, ten second windows with the highest average query time. These time windows can be used to represent slow query events in a temporal graph query.
+
+Here is the facet function:
+
+[source,text]
+----
+facet(solr_logs, q="+type_s:query +distrib_s:false", buckets="time_ten_second_s", avg(qtime_i))
+----
+
+Below is a snippet of the results with the 25 windows with the highest average query times:
+
+[source,text]
+----
+{
+ "result-set": {
+ "docs": [
+ {
+ "avg(qtime_i)": 105961.38461538461,
+ "time_ten_second_s": "2020-08-25T21:05:00Z"
+ },
+ {
+ "avg(qtime_i)": 93150.16666666667,
+ "time_ten_second_s": "2020-08-25T21:04:50Z"
+ },
+ {
+ "avg(qtime_i)": 87742,
+ "time_ten_second_s": "2020-08-25T21:04:40Z"
+ },
+ {
+ "avg(qtime_i)": 72081.71929824562,
+ "time_ten_second_s": "2020-08-25T21:05:20Z"
+ },
+ {
+ "avg(qtime_i)": 62741.666666666664,
+ "time_ten_second_s": "2020-08-25T12:30:20Z"
+ },
+ {
+ "avg(qtime_i)": 56526,
+ "time_ten_second_s": "2020-08-25T12:41:20Z"
+ },
+ ...
+
+ {
+ "avg(qtime_i)": 12893,
+ "time_ten_second_s": "2020-08-25T17:28:10Z"
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 34
+ }
+ ]
+ }
+}
+----
+=== Temporal Bipartite Subgraphs
+
+Once we've identified a set of root event windows it's easy to perform a graph query that creates a
+bipartite graph of the log events that occurred within the same ten second windows.
+With Solr logs there is a field called `type_s` which is the type of log event.
+
+In order to see what log events happened in the same ten second window of our root events we can "walk" the ten second windows and gather the type_s field.
+
+[source,text]
+----
+nodes(solr_logs,
+ facet(solr_logs,
+ q="+type_s:query +distrib_s:false",
+ buckets="time_ten_second_s",
+ avg(qtime_i)),
+ walk="time_ten_second_s->time_ten_second_s",
+ gather="type_s",
+ count(*))
+----
+
+Below is the resulting node set:
+
+[source,json]
+----
+{
+
+ "result-set": {
+ "docs": [
+ {
+ "node": "query",
+ "count(*)": 10,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "admin",
+ "count(*)": 2,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "other",
+ "count(*)": 3,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "update",
+ "count(*)": 2,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "error",
+ "count(*)": 1,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 50
+ }
+ ]
+ }
+}
+----
+
+In this result set the node field holds the type of log events that occurred within the
+same ten second windows as the root events. Notice that the event types include:
+query, admin, update and error. The `count(+++*+++)` shows the degree centrality of the different
+log event types.
+
+Notice that there is one error event within the same ten second windows of the slow query events.
+
+=== Window Parameter
+
+For event correlation and root cause analysis it's not enough to find events that occur
+within the same ten second root event windows. What's needed is to find events that occur
+within a window of time *prior to each root event window*. The window parameter allows you to
+specify this prior window of time as part of the query. The window parameter is an integer
+which specifies the number of ten second time windows, prior to each root event window,
+to include in the graph walk.
+
+[source,text]
+----
+nodes(solr_logs,
+ facet(solr_logs,
+ q="+type_s:query +distrib_s:false",
+ buckets="time_ten_second_s",
+ avg(qtime_i)),
+ walk="time_ten_second_s->time_ten_second_s",
+ gather="type_s",
+ window="3",
+ count(*))
+----
+
+Below is the node set returned when the window parameter is added.
+Notice that there are 29 error events within the 3 ten second windows prior to the slow query events.
+
+[source,json]
+----
+{
+ "result-set": {
+ "docs": [
+ {
+ "node": "query",
+ "count(*)": 62,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "admin",
+ "count(*)": 41,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "other",
+ "count(*)": 48,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "update",
+ "count(*)": 11,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "node": "error",
+ "count(*)": 29,
+ "collection": "solr_logs",
+ "field": "type_s",
+ "level": 1
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 117
+ }
+ ]
+ }
+}
+----
+
+=== Degree as a Representation of Correlation
+
+By performing link analysis on the temporal bipartite graph we can calculate the
+degree of each event type that occurs in the specified time windows.
+We established in the bipartite graph recommender example the direct relationship between
+*inbound degree* and the *dot product*. In the field of digital signal processing the
+dot product is used to represent *correlation*.
+In our temporal graph queries we can then view the inbound degree as a
+representation of correlation between the root events and the events that
+occur within the specified time windows.
+
+=== Lag Parameter
+
+Understanding the *lag* in the correlation is important for certain use cases.
+In a lagged correlation an event occurs and following a *delay* another event occurs.
+The window parameter doesn't capture the delay as we only know that an event
+occurred somewhere within a prior window.
+
+The `lag` parameter can be used to start calculating the window parameter a
+number of ten second windows in the past. For example we could walk the graph in 20 seconds
+windows starting from 30 seconds prior to a set of root events.
+By adjusting the lag and re-running the query we can determine which lagged
+window has the highest degree. From this we can determine the delay.
+
+=== Node Scoring and Temporal Anomaly Detection
+
+The concept of node scoring can be applied to temporal graph queries to find events that are
+both correlated with a set of root events and *anomalous* to the root events.
+The degree calculation establishes the correlation between events
+but it does not establish if the event is a very common occurrence in
+the entire graph or specific to the subgraph.
+
+The `scoreNodes` functions can be applied to score the nodes based on the degree and the
+commonality of the node's term in the index. This will establish whether the event is anomalous to
+the root events.
+
+[source,text]
+----
+scoreNodes(nodes(solr_logs,
+ facet(solr_logs,
+ q="+type_s:query +distrib_s:false",
+ buckets="time_ten_second_s",
+ avg(qtime_i)),
+ walk="time_ten_second_s->time_ten_second_s",
+ gather="type_s",
+ window="3",
+ count(*)))
+----
+
+Below is the node set once the `scoreNodes` function is applied. Now we see that the highest scoring node is the `error` event. This score give us a good indication of where to begin our *root cause analysis*.
+
+[source,json]
+----
+{
+ "result-set": {
+ "docs": [
+ {
+ "node": "other",
+ "nodeScore": 23.441727,
+ "field": "type_s",
+ "numDocs": 4513625,
+ "level": 1,
+ "count(*)": 48,
+ "collection": "solr_logs",
+ "docFreq": 99737
+ },
+ {
+ "node": "query",
+ "nodeScore": 16.957537,
+ "field": "type_s",
+ "numDocs": 4513625,
+ "level": 1,
+ "count(*)": 62,
+ "collection": "solr_logs",
+ "docFreq": 449189
+ },
+ {
+ "node": "admin",
+ "nodeScore": 22.829023,
+ "field": "type_s",
+ "numDocs": 4513625,
+ "level": 1,
+ "count(*)": 41,
+ "collection": "solr_logs",
+ "docFreq": 96698
+ },
+ {
+ "node": "update",
+ "nodeScore": 3.9480786,
+ "field": "type_s",
+ "numDocs": 4513625,
+ "level": 1,
+ "count(*)": 11,
+ "collection": "solr_logs",
+ "docFreq": 3838884
+ },
+ {
+ "node": "error",
+ "nodeScore": 26.62394,
+ "field": "type_s",
+ "numDocs": 4513625,
+ "level": 1,
+ "count(*)": 29,
+ "collection": "solr_logs",
+ "docFreq": 27622
+ },
+ {
+ "EOF": true,
+ "RESPONSE_TIME": 124
+ }
+ ]
+ }
+}
+----
+
diff --git a/solr/solr-ref-guide/src/images/math-expressions/graph1.png b/solr/solr-ref-guide/src/images/math-expressions/graph1.png
new file mode 100644
index 0000000..8cb3887
Binary files /dev/null and b/solr/solr-ref-guide/src/images/math-expressions/graph1.png differ
diff --git a/solr/solr-ref-guide/src/images/math-expressions/graph2.png b/solr/solr-ref-guide/src/images/math-expressions/graph2.png
new file mode 100644
index 0000000..cc3e8c8
Binary files /dev/null and b/solr/solr-ref-guide/src/images/math-expressions/graph2.png differ
diff --git a/solr/solr-ref-guide/src/math-expressions.adoc b/solr/solr-ref-guide/src/math-expressions.adoc
index 1edb713..23b90e9 100644
--- a/solr/solr-ref-guide/src/math-expressions.adoc
+++ b/solr/solr-ref-guide/src/math-expressions.adoc
@@ -1,5 +1,5 @@
= Streaming Expressions and Math Expressions
-:page-children: visualization, math-start, loading, search-sample, transform, scalar-math, vector-math, variables, matrix-math, term-vectors, probability-distributions, statistics, regression, curve-fitting, time-series, numerical-analysis, dsp, simulations, machine-learning, computational-geometry, logs
+:page-children: visualization, math-start, loading, search-sample, transform, scalar-math, vector-math, variables, matrix-math, term-vectors, probability-distributions, statistics, regression, curve-fitting, time-series, numerical-analysis, dsp, simulations, machine-learning, graph, computational-geometry, logs
:page-show-toc: false
// Licensed to the Apache Software Foundation (ASF) under one
@@ -63,6 +63,8 @@ image::images/math-expressions/searchiris.png[]
*<<machine-learning.adoc#,Machine Learning>>*: Distance, KNN, DBSCAN, K-means, fuzzy K-means and other ML functions.
+*<<graph.adoc#,Graph>>*: Bipartite graphs, in-degree centrality, graph recommenders, temporal graphs, event correlation
+
*<<computational-geometry.adoc#,Computational Geometry>>*: Convex Hulls and Enclosing Disks.
*<<logs.adoc#,Appendix A>>*: Solr log analytics and visualization.
[lucene-solr] 06/06: SOLR-15193: Improve formatting
Posted by jb...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
jbernste pushed a commit to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git
commit 4bce14386459b07a4279ff16ca95581caa7c7d38
Author: Joel Bernstein <jb...@apache.org>
AuthorDate: Mon Mar 1 14:19:17 2021 -0500
SOLR-15193: Improve formatting
---
solr/solr-ref-guide/src/graph.adoc | 70 +++++++++++++++++++++-----------------
1 file changed, 38 insertions(+), 32 deletions(-)
diff --git a/solr/solr-ref-guide/src/graph.adoc b/solr/solr-ref-guide/src/graph.adoc
index 4649d9e..2896724 100644
--- a/solr/solr-ref-guide/src/graph.adoc
+++ b/solr/solr-ref-guide/src/graph.adoc
@@ -24,7 +24,7 @@ This section of the user guide covers the syntax and theory behind *graph expres
Log records and other data indexed in Solr have connections between them that can be seen as a distributed graph.
Graph expressions provide a mechanism for identifying root nodes in the graph and walking their connections.
-The general goal of the graph walk is to materialize a specific subgraph and perform link analysis to understand
+The general goal of the graph walk is to materialize a specific *subgraph* and perform *link analysis* to understand
the connections between nodes.
In the next few sections below we'll review the graph theory behind Solr's graph expressions.
@@ -32,7 +32,8 @@ In the next few sections below we'll review the graph theory behind Solr's graph
=== Subgraphs
A subgraph is a smaller subset of the nodes and connections of the
-larger graph. Graph expressions allow you to flexibly define and materialize a subgraph from the larger graph stored in the distributed index.
+larger graph. Graph expressions allow you to flexibly define and materialize a subgraph from the larger graph
+stored in the distributed index.
Subgraphs play two important roles:
@@ -48,7 +49,7 @@ distinct categories. The links between those two categories can then
be analyzed to study how they relate. Bipartite graphs are often discussed
in the context of collaborative filter recommender systems.
-A bipartite graph between shopping baskets and products is a useful example.
+A bipartite graph between *shopping baskets* and *products* is a useful example.
Through link analysis between the shopping baskets and products
we can determine which products are most often purchased within the same shopping baskets.
@@ -66,7 +67,7 @@ All products in the same basket share the same basket ID.
Let's consider a simple example where we want to find a product
that is often sold with *butter*. In order to do this we could create a
-bipartite subgraph of shopping baskets that contain butter.
+*bipartite subgraph* of shopping baskets that contain *butter*.
We won't include butter itself in the graph as it doesn't help with
finding a complementary product for butter.
@@ -82,7 +83,7 @@ Each cell has a 1 or 0 signifying if the product is in the basket.
Let's look at how Solr graph expressions materializes this bipartite subgraph:
-The nodes function is used to materialize a subgraph from the larger graph. Below is an example nodes function which materializes the bipartite graph shown in the matrix above.
+The `nodes` function is used to materialize a subgraph from the larger graph. Below is an example nodes function which materializes the bipartite graph shown in the matrix above.
[source,text]
----
@@ -94,8 +95,7 @@ nodes(baskets,
trackTraversal="true")
----
-Let's break down this example starting with the random function:
-
+Let's break down this example starting with the `random` function:
[source,text]
----
@@ -104,7 +104,7 @@ random(baskets, q="product_s:butter", fl="basket_s", rows="3")
The `random` function is searching the baskets collection with the query `product_s:butter`, and
returning 3 random samples. Each sample contains the `basket_s` field which is the basket id.
-The three basket id's that are returned by the random sample are the root nodes of the graph query.
+The three basket id's that are returned by the random sample are the *root nodes* of the graph query.
The `nodes` function is the graph query. The nodes function is operating over the three root nodes returned
by the random function.
@@ -165,12 +165,10 @@ The output of the shopping basket graph expression is as follows:
]
}
}
-
-
----
-The `ancestors` property in the result contains a unique, alphabetically sorted set of all the incoming links
-to the node in the subgraph. In this case it shows the basket IDs that are linked to each product.
+The `ancestors` property in the result contains a unique, alphabetically sorted set of all the *inbound links*
+to the node in the subgraph. In this case it shows the baskets that are linked to each product.
The ancestor links will only be tracked when the trackTraversal flag is turned on in the nodes expression.
=== Link Analysis and Degree Centrality
@@ -263,23 +261,25 @@ The output of this graph expression is as follows:
The `count(+++*+++)` aggregation counts the "gathered" nodes, in this case the values in the `product_s` field.
Notice that the `count(+++*+++)` result is the same as the number of ancestors.
This will always be the case because the nodes function first deduplicates the edges before
-counting the gathered nodes. Because of this the `count(+++*+++)` aggregation always calculates the degree centrality for the gathered nodes.
+counting the gathered nodes. Because of this the `count(+++*+++)` aggregation always calculates the
+inbound degree centrality for the gathered nodes.
=== Dot Product
There is a direct relationship between the *inbound degree* with bipartite graph recommenders and the *dot product*.
-This relationship can be clearly seen in our working example once you include a column for butter:
+This relationship can be clearly seen in our working example once we include a column for butter:
image::images/math-expressions/graph2.png[]
-If we compute the dot product between the butter column and the other product columns you will find that the dot product equals the inbound degree in each case. This tells us that a nearest neighbor search, using a maximum inner product similarity, would select the column with the highest inbound degree.
+If we compute the dot product between the butter column and the other product columns you will find that the dot product equals the inbound degree in each case.
+This tells us that a nearest neighbor search, using a maximum inner product similarity, would select the column with the highest inbound degree.
=== Node Scoring
The degree of the node describes how many nodes in the subgraph link to it.
But this does not tell us if the node is particularly central to this subgraph or if it is just a
very frequent node in the entire graph. Nodes that appear frequently in the subgraph but
-infrequently in the entire graph can be considered more relevant to the subgraph.
+infrequently in the entire graph can be considered more *relevant* to the subgraph.
The search index contains information about how frequently each node appears in the entire index.
Using a technique similar to *tf-idf* document scoring, graph expressions can combine the
@@ -299,10 +299,10 @@ scoreNodes(nodes(baskets,
count(*)))
----
-The output now includes a `nodeScore` property. In the output below notice how eggs has a higher
-nodeScore than milk even though they have the same `count(+++*+++)`. This is because milk appears more
+The output now includes a `nodeScore` property. In the output below notice how *eggs* has a higher
+nodeScore than *milk* even though they have the same `count(+++*+++)`. This is because milk appears more
frequently in the entire index than eggs does. The `docFreq` property added by the `nodeScore` function
-shows the term frequency in the index. Because of the lower `docFreq` eggs is considered more relevant
+shows the document frequency in the index. Because of the lower `docFreq` eggs is considered more relevant
to this subgraph, and a better recommendation to be paired with butter.
[source,json]
@@ -377,9 +377,12 @@ So those using Solr to analyze Solr logs get temporal graph expressions for free
=== Root Events
-Once the ten second windows have been indexed with the log records we can devise a query that creates a set of root events. We can demonstrate this with an example using Solr log records.
+Once the ten second windows have been indexed with the log records we can devise a query that
+creates a set of *root events*. We can demonstrate this with an example using Solr log records.
-In this example we'll perform a Streaming Expression facet aggregation that finds the top 25, ten second windows with the highest average query time. These time windows can be used to represent slow query events in a temporal graph query.
+In this example we'll perform a Streaming Expression `facet` aggregation that finds the top 10, ten second windows
+with the highest average query time. These time windows can be used to represent *slow query events* in a temporal
+graph query.
Here is the facet function:
@@ -435,11 +438,12 @@ Below is a snippet of the results with the 25 windows with the highest average q
----
=== Temporal Bipartite Subgraphs
-Once we've identified a set of root event windows it's easy to perform a graph query that creates a
-bipartite graph of the log events that occurred within the same ten second windows.
+Once we've identified a set of root events it's easy to perform a graph query that creates a
+bipartite graph of the log events types that occurred within the same ten second windows.
With Solr logs there is a field called `type_s` which is the type of log event.
-In order to see what log events happened in the same ten second window of our root events we can "walk" the ten second windows and gather the type_s field.
+In order to see what log events happened in the same ten second window of our root events we can "walk" the
+ten second windows and gather the `type_s` field.
[source,text]
----
@@ -505,18 +509,18 @@ Below is the resulting node set:
}
----
-In this result set the node field holds the type of log events that occurred within the
+In this result set the `node` field holds the type of log events that occurred within the
same ten second windows as the root events. Notice that the event types include:
query, admin, update and error. The `count(+++*+++)` shows the degree centrality of the different
log event types.
-Notice that there is one error event within the same ten second windows of the slow query events.
+Notice that there is only one *error* event within the same ten second windows of the slow query events.
=== Window Parameter
For event correlation and root cause analysis it's not enough to find events that occur
-within the same ten second root event windows. What's needed is to find events that occur
-within a window of time *prior to each root event window*. The window parameter allows you to
+within the *same* ten second root event windows. What's needed is to find events that occur
+within a window of time *prior to each root event*. The `window` parameter allows you to
specify this prior window of time as part of the query. The window parameter is an integer
which specifies the number of ten second time windows, prior to each root event window,
to include in the graph walk.
@@ -535,7 +539,7 @@ nodes(solr_logs,
----
Below is the node set returned when the window parameter is added.
-Notice that there are 29 error events within the 3 ten second windows prior to the slow query events.
+Notice that there are *now 29 error* events within the 3 ten second windows prior to the slow query events.
[source,json]
----
@@ -605,7 +609,7 @@ The window parameter doesn't capture the delay as we only know that an event
occurred somewhere within a prior window.
The `lag` parameter can be used to start calculating the window parameter a
-number of ten second windows in the past. For example we could walk the graph in 20 seconds
+number of ten second windows in the past. For example we could walk the graph in 20 second
windows starting from 30 seconds prior to a set of root events.
By adjusting the lag and re-running the query we can determine which lagged
window has the highest degree. From this we can determine the delay.
@@ -613,7 +617,7 @@ window has the highest degree. From this we can determine the delay.
=== Node Scoring and Temporal Anomaly Detection
The concept of node scoring can be applied to temporal graph queries to find events that are
-both correlated with a set of root events and *anomalous* to the root events.
+both *correlated* with a set of root events and *anomalous* to the root events.
The degree calculation establishes the correlation between events
but it does not establish if the event is a very common occurrence in
the entire graph or specific to the subgraph.
@@ -635,7 +639,9 @@ scoreNodes(nodes(solr_logs,
count(*)))
----
-Below is the node set once the `scoreNodes` function is applied. Now we see that the highest scoring node is the `error` event. This score give us a good indication of where to begin our *root cause analysis*.
+Below is the node set once the `scoreNodes` function is applied.
+Now we see that the *highest scoring node* is the *error* event.
+This score give us a good indication of where to begin our *root cause analysis*.
[source,json]
----
[lucene-solr] 02/06: SOLR-15193: Fix typos
Posted by jb...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
jbernste pushed a commit to branch branch_8x
in repository https://gitbox.apache.org/repos/asf/lucene-solr.git
commit c3aecab8b22c1baa426c903703d6613f8479176b
Author: Joel Bernstein <jb...@apache.org>
AuthorDate: Wed Feb 24 15:19:35 2021 -0500
SOLR-15193: Fix typos
---
solr/solr-ref-guide/src/graph.adoc | 2 +-
solr/solr-ref-guide/src/math-expressions.adoc | 2 +-
2 files changed, 2 insertions(+), 2 deletions(-)
diff --git a/solr/solr-ref-guide/src/graph.adoc b/solr/solr-ref-guide/src/graph.adoc
index 887990d..207dbe0 100644
--- a/solr/solr-ref-guide/src/graph.adoc
+++ b/solr/solr-ref-guide/src/graph.adoc
@@ -17,7 +17,7 @@
// under the License.
-This section of user guide covers the syntax and theory behind *graph expressions*. Examples are presented for two key graph use cases: *bipartate graph recommenders* and *event correlation* with
+This section of the user guide covers the syntax and theory behind *graph expressions*. Examples are presented for two key graph use cases: *bipartate graph recommenders* and *event correlation* with
*temporal graph queries*.
== Graphs
diff --git a/solr/solr-ref-guide/src/math-expressions.adoc b/solr/solr-ref-guide/src/math-expressions.adoc
index 23b90e9..7d74f7b 100644
--- a/solr/solr-ref-guide/src/math-expressions.adoc
+++ b/solr/solr-ref-guide/src/math-expressions.adoc
@@ -63,7 +63,7 @@ image::images/math-expressions/searchiris.png[]
*<<machine-learning.adoc#,Machine Learning>>*: Distance, KNN, DBSCAN, K-means, fuzzy K-means and other ML functions.
-*<<graph.adoc#,Graph>>*: Bipartite graphs, in-degree centrality, graph recommenders, temporal graphs, event correlation
+*<<graph.adoc#,Graph>>*: Bipartite graphs, in-degree centrality, graph recommenders, temporal graphs, event correlation.
*<<computational-geometry.adoc#,Computational Geometry>>*: Convex Hulls and Enclosing Disks.