# Streams and Vectorization

This section of the user guide explores techniques for retrieving streams of data from Solr and vectorizing the numeric fields.

See the section Text Analysis and Term Vectors which describes how to vectorize text fields.

## Streams

Streaming Expressions has a wide range of stream sources that can be used to retrieve data from SolrCloud collections. Math expressions can be used to vectorize and analyze the results sets.

Below are some of the key stream sources:

: Multi-dimensional aggregations are a powerful tool for generating co-occurrence counts for categorical data. The`facet`

`facet`

function uses the JSON facet API under the covers to provide fast, distributed, multi-dimension aggregations. With math expressions the aggregated results can be pivoted into a co-occurance matrix which can be mined for correlations and hidden similarities within the data.: Random sampling is widely used in statistics, probability and machine learning. The`random`

`random`

function returns a random sample of search results that match a query. The random samples can be vectorized and operated on by math expressions and the results can be used to describe and make inferences about the entire population.: The`timeseries`

`timeseries`

expression provides fast distributed time series aggregations, which can be vectorized and analyzed with math expressions.: K-nearest neighbor is a core machine learning algorithm. The`knnSearch`

`knnSearch`

function is a specialized knn algorithm optimized to find the k-nearest neighbors of a document in a distributed index. Once the nearest neighbors are retrieved they can be vectorized and operated on by machine learning and text mining algorithms.: SQL is the primary query language used by data scientists. The`sql`

`sql`

function supports data retrieval using a subset of SQL which includes both full text search and fast distributed aggregations. The result sets can then be vectorized and operated on by math expressions.: The`jdbc`

`jdbc`

function allows data from any JDBC compliant data source to be combined with streams originating from Solr. Result sets from outside data sources can be vectorized and operated on by math expressions in the same manner as result sets originating from Solr.: Messaging is an important foundational technology for large scale computing. The`topic`

`topic`

function provides publish/subscribe messaging capabilities by treating SolrCloud as a distributed message queue. Topics are extremely powerful because they allow subscription by query. Topics can be use to support a broad set of use cases including bulk text mining operations and AI alerting.: Graph queries are frequently used by recommendation engines and are an important machine learning tool. The`nodes`

`nodes`

function provides fast, distributed, breadth first graph traversal over documents in a SolrCloud collection. The node sets collected by the`nodes`

function can be operated on by statistical and machine learning expressions to gain more insight into the graph.: Ranked search results are a powerful tool for finding the most relevant documents from a large document corpus. The`search`

`search`

expression returns the top N ranked search results that match any Solr query, including geo-spatial queries. The smaller set of relevant documents can then be explored with statistical, machine learning and text mining expressions to gather insights about the data set.

## Assigning Streams to Variables

The output of any streaming expression can be set to a variable.
Below is a very simple example using the `random`

function to fetch
three random samples from collection1. The random samples are returned
as tuples which contain name/value pairs.

`let(a=random(collection1, q="*:*", rows="3", fl="price_f"))`

When this expression is sent to the `/stream`

handler it responds with:

```
{
"result-set": {
"docs": [
{
"a": [
{
"price_f": 0.7927976
},
{
"price_f": 0.060795486
},
{
"price_f": 0.55128294
}
]
},
{
"EOF": true,
"RESPONSE_TIME": 11
}
]
}
}
```

## Creating a Vector with the col Function

The `col`

function iterates over a list of tuples and copies the values
from a specific column into an array.

The output of the `col`

function is an numeric array that can be set to a
variable and operated on by math expressions.

Below is an example of the `col`

function:

```
let(a=random(collection1, q="*:*", rows="3", fl="price_f"),
b=col(a, price_f))
```

```
{
"result-set": {
"docs": [
{
"b": [
0.42105234,
0.85237443,
0.7566981
]
},
{
"EOF": true,
"RESPONSE_TIME": 9
}
]
}
}
```

## Applying Math Expressions to the Vector

Once a vector has been created any math expression that operates on vectors
can be applied. In the example below the `mean`

function is applied to
the vector assigned to variable ** b**.

```
let(a=random(collection1, q="*:*", rows="15000", fl="price_f"),
b=col(a, price_f),
c=mean(b))
```

When this expression is sent to the `/stream`

handler it responds with:

```
{
"result-set": {
"docs": [
{
"c": 0.5016035594638814
},
{
"EOF": true,
"RESPONSE_TIME": 306
}
]
}
}
```

## Creating Matrices

Matrices can be created by vectorizing multiple numeric fields and adding them to a matrix. The matrices can then be operated on by any math expression that operates on matrices.

Note that this section deals with the creation of matrices from numeric data. The section Text Analysis and Term Vectors describes how to build TF-IDF term vector matrices from text fields. |

Below is a simple example where four random samples are taken
from different sub-populations in the data. The `price_f`

field of
each random sample is
vectorized and the vectors are added as rows to a matrix.
Then the `sumRows`

function is applied to the matrix to return a vector containing
the sum of each row.

```
let(a=random(collection1, q="market:A", rows="5000", fl="price_f"),
b=random(collection1, q="market:B", rows="5000", fl="price_f"),
c=random(collection1, q="market:C", rows="5000", fl="price_f"),
d=random(collection1, q="market:D", rows="5000", fl="price_f"),
e=col(a, price_f),
f=col(b, price_f),
g=col(c, price_f),
h=col(d, price_f),
i=matrix(e, f, g, h),
j=sumRows(i))
```

When this expression is sent to the `/stream`

handler it responds with:

```
{
"result-set": {
"docs": [
{
"j": [
154390.1293375,
167434.89453,
159293.258493,
149773.42769,
]
},
{
"EOF": true,
"RESPONSE_TIME": 9
}
]
}
}
```

## Facet Co-occurrence Matrices

The `facet`

function can be used to quickly perform multi-dimension aggregations of categorical data from
records stored in a SolrCloud collection. These multi-dimension aggregations can represent co-occurrence
counts for the values in the dimensions. The `pivot`

function can be used to move two dimensional
aggregations into a co-occurrence matrix. The co-occurrence matrix can then be clustered or analyzed for
correlations to learn about the hidden connections within the data.

In the example below the `facet`

expression is used to generate a two dimensional faceted aggregation.
The first dimension is the US State that a car was purchased in and the second dimension is the car model.
This two dimensional facet generates the co-occurrence counts for the number of times a particular car model
was purchased in a particular state.

`facet(collection1, q="*:*", buckets="state, model", bucketSorts="count(*) desc", rows=5, count(*))`

When this expression is sent to the `/stream`

handler it responds with:

```
{
"result-set": {
"docs": [
{
"state": "NY",
"model": "camry",
"count(*)": 13342
},
{
"state": "NJ",
"model": "accord",
"count(*)": 13002
},
{
"state": "NY",
"model": "civic",
"count(*)": 12901
},
{
"state": "CA",
"model": "focus",
"count(*)": 12892
},
{
"state": "TX",
"model": "f150",
"count(*)": 12871
},
{
"EOF": true,
"RESPONSE_TIME": 171
}
]
}
}
```

The `pivot`

function can be used to move the facet results into a co-occurrence matrix. In the example below
The `pivot`

function is used to create a matrix where the rows of the matrix are the US States (state) and the
columns of the matrix are the car models (model). The values in the matrix are the co-occurrence counts (count(*))
from the facet results. Once the co-occurrence matrix has been created the US States can be clustered
by car model, or the matrix can be transposed and car models can be clustered by the US States
where they were bought.

```
let(a=facet(collection1, q="*:*", buckets="state, model", bucketSorts="count(*) desc", rows="-1", count(*)),
b=pivot(a, state, model, count(*)),
c=kmeans(b, 7))
```

## Latitude / Longitude Vectors

The `latlonVectors`

function wraps a list of tuples and parses a lat/lon location field into
a matrix of lat/long vectors. Each row in the matrix is a vector that contains the lat/long
pair for the corresponding tuple in the list. The row labels for the matrix are
automatically set to the `id`

field in the tuples. The lat/lon matrix can then be operated
on by distance-based machine learning functions using the `haversineMeters`

distance measure.

The `latlonVectors`

function takes two parameters: a list of tuples and a named parameter called
`field`

, which tells the `latlonVectors`

function which field to parse the lat/lon
vectors from.

Below is an example of the `latlonVectors`

.

```
let(a=random(collection1, q="*:*", fl="id, loc_p", rows="5"),
b=latlonVectors(a, field="loc_p"))
```

When this expression is sent to the `/stream`

handler it responds with:

```
{
"result-set": {
"docs": [
{
"b": [
[
42.87183530723629,
76.74102353397778
],
[
42.91372904094898,
76.72874889228416
],
[
42.911528804897564,
76.70537292977619
],
[
42.91143870500213,
76.74749913047408
],
[
42.904666267479705,
76.73933236046092
]
]
},
{
"EOF": true,
"RESPONSE_TIME": 21
}
]
}
}
```