Virtual Columns¶

Virtual columns are metrics derived from existing columns in the Dashboard, through applying some operation to one or more columns. Filtering and sorting on these virtual columns can give you deeper insights into your model and training set and help you find issues with your data, your model, or perhaps your entire approach to the problem at hand. The exact operations available will depend on the type of data in the selected columns. In general we can divide operations into two main categories: Global operations and Local operations. For a full list of operations, see Operations.

Creating a virtual column¶

To derive a virtual column, select one or more columns, RightClick on one of the selected columns, hover over Derive virtual column, and select an operation to derive the virtual column.

The virtual column will be next to the input column if there is only one input column or located at the far right of the table if there are multiple input columns. In the screenshot below, the virtual column Loss_rank is derived from a single column Loss and the virtual column RMSE/MAE is derived from a divide operation of two columns RMSE and MAE.

Properties of virtual columns¶

Virtual columns have following properties:

Virtual columns can be derived from one or more input columns.
Virtual columns can further be derived from input virtual columns.
The available operations depend on the type of data in the input columns. For instance, the False Positives (FP) operation is only available when the BBs and BBs_predicted columns are selected.
Some operations, e.g., divide and group, are order-dependent, i.e., they depend on the selection order of the input columns.
Global operations, e.g., rank and occurrence, calculate the results based on the context of all rows, whereas local operations, e.g., abs and sum, calculate the results on a single row basis.
Virtual columns are dynamic, that is, the values of virtual columns will be automatically re-calculated if the values of the input columns change.
Virtual columns are always calcuated on the basis of the full table and not affected by filters. If you want to create a virtual column on a portion of the data, you can create a subset table and derive the virtual column there.
Some operations can be chained together such that an intermediate virtual column does not need to be created. Chained operations are indicated by an arrow next to the operation’s name. For instance, the group operation can often be chained up with subsequent operations as shown in the figure below. An accumulative loss of all epochs for each sample can be calculated by selecting sum under group. The derived virtual column is named Loss_by(Example_id, Foreign table)_sum.

Use cases¶

Below are a few examples to illustrate how virtual columns can be used and beneficial for your data analysis.

Distribution of aspect ratios¶

If the images in your dataset have a wide range of aspect ratios, you can analyze the distribution of aspect ratios with following steps.

Steps:

Derive an aspect ratio column Height/Width: Select the Height and Width columns, then select the Divide operation
Derive a ranking column Heght/Width_rank: Select the Heght/Width column, then select the Rank operation
Create a 2D chart of Height/Width vs Heght/Width_rank: Select the two columns and press 2

Forgetting events¶

A forgetting event (FE) is defined as an correct prediction in an epoch followed by an incorrect one in the next epoch. FE-prone samples are often considered as hard ones to learn. We can find those FE-prone samples by following steps. Note: metrics of at least five epochs need to be collected to conduct this workflow.

Steps:

Derive an column of accuracy difference between an epoch and previous one: Select Accuracy, then select the From previous operation. This virtual column is named Accuracy_{from_prev}
Derive an chained Group|Min column: Select the Accuracy_{from_prev}, Example_id, and Foreign table in this order, then select the chained Group|Min operation. This derived column is named (Accuracy_from_prev_by-(Example_id, Foreign table))_min
Filter (Accuracy_from_prev_by-(Example_id, Foreign table))_min to -1. The resulted samples are those with forgetting events.

Embeddings travel distances¶

We can use this workflow to explore the samples that travel long distances in the embeddings space. Embeddings travel distances are the sum of Euclid lengths from one epoch to the next for a given sample. Long travel distances can be used as an indication of hard samples. This workflow requires embeddings collection for multiple epochs. Note that this workflow is also available in how to use workflows.

Steps:

Derive a chained From previous|Length column on the embeddings: select the Embeddings column, then select the chained From previous|Length operation. This virtual column is named Embeddings_from_prev_length.
Derive a chained Group|Sum column on the the Length virtual column: select Embeddings_from_prev_length, Example_id, and Foreign table in this order, then select the chained Group|Sum operation. The derived column is named (Embeddings_from_prev_length_by-(Example_id, Foreign table))_sum.
Filter (Embeddings_from_prev_length_by-(Example_id, Foreign table))_sum to mid to high value range. The resulted samples are those with long embeddings travel distances.

Operations¶

The following sections describe all the available operations for creating virtual columns.

Global operations¶

Global operations need the full context of every row of its input columns to produce a result for any individual row. The Occurrences operation, which counts the number of times each value(s) occur in one or more columns, is an example of a global operation. A complete list of the available global operations, along with their input requirements, can be seen below.

Operation	Input Type	Output type	Description
Traversal index	Any	Number	Traversal index maximizing the walk within the input column coordinate space
Bin	Number	Number	The input value, discretized to a set number of bins
Cluster by threshold	Any	Number	Groups data points by specified distance threshold.
Rank	Any	Number	The rank of each row, as sorted by the input value(s)
Group	Any	Same as input	Group index shared by all rows with the same value(s) in the input column(s)
Nearest neighbor	Numbers	Number	Distance to closest neighbor within the input column coordinate space
Nearest neighbors	Numbers	Numbers	Links to closest neighbors within the input column coordinate space
Group-neighbor links	Any	Numbers	Links to Table rows within same group
Zip	Number	Number	Joins (‘zips’) multiple columns into a single, component column.
Link distance	Numbers	Numbers	The ‘jump’ distance of each link.
Category	Any	Number	The category of each input value (i.e. their index within a combined value map.
Derivative	Numbers	Numbers	For a numeric input column evolving over time, this operation returns the difference between the next value and the previous one, divided by two (and handling first and last values appropriately).
Deviation	Numbers	Numbers	For a numeric input column evolving over time, this operation returns the difference between a value and the average between the next and previous one.
From previous	Numbers	Numbers	For a numeric input column evolving over time, this operation returns the difference between this value and the previous one.
To next	Numbers	Numbers	For a numeric input column evolving over time, this operation returns the difference between the next value and the current one.
Aggregate	Numbers	Numbers	For a numeric input column evolving over time, this operation reports the aggregated sum at each epoch/iteration.
Occurrence	Any	Number	Number of columns with the same value(s) in the input column(s)
Primary element	Any	Boolean	Whether an element is first in a group or not
Normalize	Number	Number	Normalizes the column so that its sum is 1.
Semantic matches (before)	String	Number	How many candidates were originally matched between the wide- and the narrow-search scenarios.
Semantic matches (after)	String	Number	How many candidates are finally matched between the wide- and the narrow-search scenarios.
Chunk-to-question links	String	Number	Links to Questions referring to this Article chunk.
Question-to-chunk links	String	Number	Links to article chunks referenced by this question.
Chunk relation	String	Number	Relation between this Table row and the current selection
Embedding distances (before)	String	Number	The original distances from the question to the top-K candidates (in ND-embedding space).
Embedding distances (after)	String	Number	The final distances from the question to the top-K candidates (in ND-embedding space).
Semantic similarities (before)	String	Number	The original semantic similarities between the question and the top-K candidates from embedding space.
Semantic similarities (after)	String	Number	The final semantic similarities between the question and the top-K candidates from embedding space.
In foreign table	Number	Boolean	Whether the row is present in a foreign table
Run constants	Number	Any	The entire ‘constants’ structure of the referenced Run
Foreign table row	Number	Any	The entire row of a foreign table, as referenced by a foreign key in the input table row
Foreign table row edited	Number	Boolean	Whether the foreign table row has any pending edits
Index	None	Number	Row index within table
Filtered index	None	Number	Row index within filtered table
Random	None	Number	Random value [0..1]

Local operations¶

Local operations only need the context of a single row to produce a result. We can further subdivide local operations into three categories: Unary operations, Order-independent operations, and Order-dependent operations.

Unary operations¶

Unary operations take a single column as input, and produce a result for each row in that column. The Character count operation, which returns the length of a string, is an example of a unary operation. A complete list of the available unary operations, along with their input requirements, can be seen below.

Operation	Input Type	Output type	Description
Parse string	String	Number	The input string parsed as a number. In the case of multiple numeric values being present, the last one is reported.
PickInner[…]	Any	Any	A single element picked from dimension 0 of an array.
Pick[…]	Any	Any	A single element picked from the outermost dimension of an array.
PickProperty[…]	Any	Any	A child property picked from a composite property.
PickUnrolledProperty[…]	Any	Any	A child property picked by unrulling a composite property.
Count	String	Number	The number of elements within the input array.
Element index	Numbers	Numbers	The index of each array element.
Reverse element index	Numbers	Numbers	The reverse index of each array element (i.e. 0 refers to last element in array).
Pick random	Any	Any	A random element picked from the input array (if any)
Normalize	Numbers	Numbers	The input vector in normalized form
Abs	Number	Number	The absolute value of the numeric input value
Character count	String	Number	The number of characters in the input string (including whitespace).
Log	Number	Number	The log value of the numeric input value
Non-zero	Numbers	Boolean	Whether the numeric input value is non-zero
Not	Any	Boolean	The boolean ‘not’ of the input value(s)
Sign	Number	Number	The sign (i.e. -1, 0, or 1) of the input value(s).
Inverse	Number	Number	The inverse (i.e. 1/x) of the input value(s).
Raw	Any	Same as input	The raw value of the input property, i.e. with value maps and/or string roles removed from the schema (recursive when required)
Word count	String	Number	The number of words in the input string
Filename	String	String	The file name from the input URL
Zero	Number	Boolean	Whether the numeric input value is zero
Positive	Number	Boolean	Whether the numeric input value is above zero
Negative	Number	Boolean	Whether the numeric input value is below zero
In range	Number	Boolean	Whether the numeric input values are within a user specified range
In set	Number	Boolean	Whether the categorical input values are part of the user specified set
Value selected	Any	Boolean	Whether the value is shared with one or more selected Table rows
Url	Number	Number	The URL defined by each input value
Angle	Number	Number	The angle of th input 2D vector
* A	Numbers	Numbers	An input value multiplied by a constant number.
+ A	Numbers	Numbers	An input value with an added constant value.
^ A	Numbers	Numbers	An input value raised to a constant power.
Exp	Numbers	Numbers	A constant value raised to a power defined by the input value.
==	Numbers	Boolean	Whether an input value equals a constant number.
>	Numbers	Boolean	Whether an input value is greater than a constant number.
>=	Numbers	Boolean	Whether an input value is greater than or equal to a constant number.
<	Numbers	Boolean	Whether an input value is less than a constant number.
<=	Numbers	Boolean	Whether an input value is less than or equal to a constant number.
Token length	String	Number	The number of characters in each input token.
Overlap ratio	List elements	Numbers	Quotient stating how much one bounding box is overlapped by others within an image
Unique overlap ratio	List elements	Numbers	Quotient stating how much one bounding box is uniquely overlapped by others within an image
Rectangles (absolute)	List elements	Rectangles	The rectangle geometry of the bounding box list (in absolute min/max pixel coordinates)
Rectangles (relative)	List elements	Rectangles	The rectangle geometry of the bounding box list (in min/max coordinates relative to the reference image size)
Area	Rectangles	Numbers	The area of each rectangle within the input list
Aspect	Rectangles	Numbers	The aspect (i.e. width divided by height) of each rectangle within the input list
Width	Rectangles	Numbers	The width of each rectangle within the input list
Height	Rectangles	Numbers	The height of each rectangle within the input list
Non-maximum suppression (NMS)	List elements	List elements	A bounding box list where non-maximum-suppression has been performed (with a user-specified IoU threshold)
Angle	Geo	Number	The rotation angle of each bounding box.
Distance to origin	Geo	Number	The distance to the origin (0, 0) from each bounding box.
Area	Geo	Number	The area of each bounding box.
Aspect	Geo	Number	The aspect ration (width divided by height) of each bounding box.
Width	Geo	Number	The width of each bounding box.
Height	Geo	Number	The height of each bounding box.
Center (X)	Geo	Number	The center x-position of each bounding box.
Center (Y)	Geo	Number	The center y-position of each bounding box.
Volume	Geo	Number	The volume of each 3D bounding box.
Aspect	Geo	Number	The aspect ratio of each 3D bounding box (i.e. longest edge / shortest edge).
Week since epoch	Datetime string	Number	For input datetime string, returns the week since epoch.
Hour of day	Datetime string	Number	For input datetime string, returns the hour [0..23].
Day of week	Datetime string	Number	For input datetime string, returns the day of week.
Milliseconds since epoch	Datetime string	Number	For an input datetime string, returns the number of milliseconds since epoch.
ConstantBool	None	Boolean	A constant boolean value
ConstantInt	None	Number	A constant integer value
ConstantFloat	None	Number	A constant floating point value
ConstantString	None	String	A constant string value
Line length	Geo	Numbers	The length of each line within the input geometry
Triangle area	Geo	Numbers	The area of each triangle within the input geometry

Order-independent operations¶

Order-independent operations take two or more columns as input, and produce a result for each row in those columns. The order of the input columns does not matter. The Sum operation, which adds two or more columns together, is an example of an order-independent operation. A complete list of the available order-independent operations, along with their input requirements, can be seen below.

Operation	Input Type	Output type	Description
Sum	Numbers	Number	The sum of all numeric input values
Average	Numbers	Number	The arithmetic average of the numeric input values.
Common	Any	Any	The common value within the input array (if any)
Length	Numbers	Number	The length of the input vector (i.e. the square root of the sum of squared values).
Equal	Any	Boolean	Whether all input values are equal.
Not equal	Any	Boolean	Whether some of the input values differ.
Max	Numbers	Number	The largest numeric value of all input values
Min	Numbers	Number	The smallest numeric value of all input values
Multiply	Numbers	Number	The product of all numeric input values.
Range	Numbers	Number	The absolute range (i.e. ‘max value - min value’) across all numeric input values.
Unique	Any	Any	A list of all unique input values (i.e. with duplicates removed)
Sorted	Numbers	Numbers	The input vector, sorted in ascending order
Median	Numbers	Number	The median of the input vector

Order-dependent operations¶

Order-dependent operations take two or more columns as input, and produce a result for each row in those columns. The order of the input columns affects the results of these operations. The “Subtract” operation, which subtracts one or more columns from another, is an example of an order-dependent operation. A complete list of the available order-dependent operations, along with their input requirements, can be seen below.

Operation	Input Type	Output type	Description
Divide	Numbers	Number	The first value divided by the second.
To string	Any	String	The input value(s) converted to a string. In the case of multiple input columns, values are comma separated. In the case of nested input columns, the values are represented as JSON.
Hash	Any	Number	A numeric hash value calculated from all input values (including scalars, nested inputs and arrays
Subtract	Numbers	Number	The first numeric input value minus all following ones.
Delta	Numbers	Number	The difference between one column and the next (i.e. ‘next value - this value’
Delta angle	Numbers	Number	The difference between the two input angles, full-circle symmetry taken into account.
Delta angle (two-way)	Numbers	Number	The difference between the two input angles, half-circle symmetry taken into account.
Delta angle (four-way)	Numbers	Number	The difference between the two input angles, quad-circle symmetry taken into account.
Matched prediction (TP)	List elements	Boolean	Whether each predicted element is a True Positive, i.e. has a matching ground truth instance
Unmatched prediction (FP)	List elements	Boolean	Whether each prediction is a False Positive, i.e. lacks a matching ground truth instance.
Unmatched ground truth (FN)	List elements	Boolean	Whether each ground truth instance is a False Negative, i.e. has no matching prediction
Matched ground truth (TP)	List elements	Boolean	Whether each ground truth instance is a True Positive, i.e. has a matching prediction
_matched_prediction	List elements	Numbers	The for all matched predictions (or 0.0 for unmatched ones).
_matched_ground_truth	List elements	Numbers	The for all matched ground truth instances (or 0.0 for unmatched ones).
Per-point OKS_matched_ground_truth	List elements	Numbers	The OKS for all points within matched ground truth instances (or NaN for unmatched ones).
Per-point OKS_matched_prediction	List elements	Numbers	The OKS for all points within matched predictions (or NaN for unmatched ones).
Precision	List elements	Numbers	The Precision score calculated between the predicted and ground truth instances (considering the and confidence thresholds).
Recall	List elements	Numbers	The Recall score calculated between the predicted and ground truth instances (considering the and confidence thresholds).
F1	List elements	Numbers	The F1 score calculated between the predicted and ground truth instances (considering the and confidence thresholds).
Matched value	List elements	Any	The matched value for each ground truth or predicted instance (considering the and confidence thresholds).
Greater than or equal	Numbers	Boolean	Whether each value is greater than or equal to the next.
Greater than	Numbers	Boolean	Whether each value is greater than the next.
Less than or equal	Numbers	Boolean	Whether each value is less than or equal to than the next.
Less than	Numbers	Boolean	Whether each value is less than the next.
Divide (element-wise)	Numbers	Number	The first value divided by the second. (element-wise)
Subtract (element-wise)	Numbers	Number	The first numeric input value minus all following ones. (element-wise)
Delta angle (element-wise)	Numbers	Number	The difference between the two input angles, full-circle symmetry taken into account. (element-wise)
Delta angle (two-way) (element-wise)	Numbers	Number	The difference between the two input angles, half-circle symmetry taken into account. (element-wise)
Delta angle (four-way) (element-wise)	Numbers	Number	The difference between the two input angles, quad-circle symmetry taken into account. (element-wise)
Sum (element-wise)	Numbers	Number	The sum of all numeric input values (element-wise)
Average (element-wise)	Numbers	Number	The arithmetic average of the numeric input values. (element-wise)
Length (element-wise)	Numbers	Number	The length of the input vector (i.e. the square root of the sum of squared values). (element-wise)
Equal (element-wise)	Any	Boolean	Whether all input values are equal. (element-wise)
Not equal (element-wise)	Any	Boolean	Whether some of the input values differ. (element-wise)
Greater than or equal (element-wise)	Numbers	Boolean	Whether each value is greater than or equal to the next. (element-wise)
Greater than (element-wise)	Numbers	Boolean	Whether each value is greater than the next. (element-wise)
Less than or equal (element-wise)	Numbers	Boolean	Whether each value is less than or equal to than the next. (element-wise)
Less than (element-wise)	Numbers	Boolean	Whether each value is less than the next. (element-wise)
Max (element-wise)	Numbers	Number	The largest numeric value of all input values (element-wise)
Min (element-wise)	Numbers	Number	The smallest numeric value of all input values (element-wise)
Multiply (element-wise)	Numbers	Number	The product of all numeric input values. (element-wise)
Normalize (element-wise)	Numbers	Numbers	The input vector in normalized form (element-wise)
Abs (element-wise)	Number	Number	The absolute value of the numeric input value (element-wise)
Character count (element-wise)	String	Number	The number of characters in the input string (including whitespace). (element-wise)
Log (element-wise)	Number	Number	The log value of the numeric input value (element-wise)
Non-zero (element-wise)	Numbers	Boolean	Whether the numeric input value is non-zero (element-wise)
Not (element-wise)	Any	Boolean	The boolean ‘not’ of the input value(s) (element-wise)
Sign (element-wise)	Number	Number	The sign (i.e. -1, 0, or 1) of the input value(s). (element-wise)
Inverse (element-wise)	Number	Number	The inverse (i.e. 1/x) of the input value(s). (element-wise)
Zero (element-wise)	Number	Boolean	Whether the numeric input value is zero (element-wise)
Url (element-wise)	Number	Number	The URL defined by each input value (element-wise)
Angle (element-wise)	Number	Number	The angle of th input 2D vector (element-wise)