Arrange tables

Why arrange?

• Design options for the spatial organization cover all aspects related to the use of spatial channels for visual encoding.

• It is the visual encoding option most important because the use of space affects the mental model of the dataset that the user forms.

Why arrange?

• The three most effective channels to represent ordered attributes are related to the spatial position:

• 2D spatial positions along an aligned scale.• 2D spatial positions along a common scale.• Length.

• The most effective channel to represent categorical attributes is also the use of space:

• Grouping of items within the same region.

Design options

• Express values• Separate regions• Order regions• Align regions• Orient the spatial axes• Define densities

Design options: express values

• Quantitative attributes can be transformed into spatial positions along an axis of reference.

• Encoding each item with one mark on any axis position is the simplest case of coding an attribute with a unique value.

• Additional attributes can be encoded in the same mark with other non-spatial channels, such as the color or size.

• For more complex cases, you can resort to the use of glyphs: object whose internal structure is generated from various marks.

Express values: scatterplots

• Scatterplots encode two quantitative variables using horizontal and vertical spatial position channels, and the mark is necessarily a point.

• Scatterplots are effective for the abstract tasks of overviewing the dataset and to characterize the distributions, but more specifically to find outliers and extreme values.

• They are also very effective to correlate two attributes because if the attributes are correlated, points compose diagonal patterns (positive or negative).

Express values: scatterplots

• Often, scatterplots are extended with the use of color and size in point marks to display two additional attributes. They are called bubble plots.

• The scalability of scatter plots is limited by the need to distinguish the points, making them suitable to represent tens or hundreds of items (resolution 1000x1000).

Express values: scatterplots [Gapminder]

Design options: separate, order, align regions

• The semantics of categorical attributes fits with the use of spatial regions: adjacent bounded areas that are distinguished from each other.

• All items with the same values of a categorical attribute will be assigned to a region using spatial proximity to encode their similarity according to any particular visual encoding.

• However, it remains unresolved how regions are distributed by the different spatial positions of the plane.

• The problem is simplified by decomposing the distribution of regions into three operations: separation, ordering and alignment.

Design options: separate, order, align regions

• The separation and ordering are always necessary, but alignment is optional.

• The separation must be made according to a categorical attribute, while the alignment and ordering could be performed with another ordered attribute.

• If alignment is used, often, the attribute chosen for region alignment is the same used for encoding the spatial positions of the items within a region.

List alignment

• With a single key, separation into regions with that key leads to one region per item.

• The regions are aligned in a one-dimensional list, either horizontally or vertically.

• The view covers a two-dimensional area: the list of items aligned with respect to one dimension and the region in which the values are displayed is stretched in the other dimension.

List alignment: bar charts• Bar charts use a line mark and encode a quantitative attribute with a

spatial position channel.• Each mark is an independent spatial area, and there is one for each value

of the categorical attribute.• The usual practice is to align all marks on a common reference.• This type of diagrams requires that we leave enough space to areas that

separate the marks so that they can be clearly distinguished.• The scalability of these diagrams can represent several, tens, or hundreds

of items, but not thousands if the screen resolution is limited to 1 K.• La escalabilidad de este tipo de diagramas permite representar desde

varios, decenas o cientos de ítems, pero no miles si la resolución de la pantalla se limita a 1 K.

• They are suitable to lookup specific values or to find trends.

List alignment: bar charts

050

100150200250300

Cat Cheetah Lion Panther

Felines

Average weight

050

100150200250300

Cat Cheetah Panther Lion

Felines

Average weight

List alignment: stacked bar charts• The stacked bar charts use a more complex glyph for each component (bar):

multiple subcomponents (bars) are stacked in one dimension.• The total length of the entire glyph encodes a value, just like the lengths of each

subcomponent do.• This type of diagrams allow to display information of multidimensional tables.

Specifically, tables with two keys.• The glyphs are organized as a list according to the primary key. The secondary key is

used to build the one-dimensional structure of the glyph.• They are also suitable for consulting values accessing with the two keys.• They use both the length and color as visual channels.• Each component is visually encoded in function of the same key value that defines

the ordering within the structure of the glyph.• This representation is less scalable than bar charts because the components that

must form the glyph.

List alignment: stacked bar charts

0

2

4

6

8

10

12

14

CPU0 CPU1 CPU2 CPU3

Cache miss statistics

Graphics Arithmetic Recursive

List alignment: normalized stacked bar charts• The normalized stacked bar charts stretch each component of the glyph to the

maximum possible length, representing percentages instead of absolute values.

• The lower component of the glyph is the only one aligned with the rest, so that this component is where most accuracy is obtained.

• Although the rest channel use the non-aligned position channel, it is more accurate than an angular comparison (i.e. used in pie charts).

• The most outstanding feature of these representations is that they show the relative contribution of each part to the whole.

List alignment: normalized stacked bar charts

0%10%20%30%40%50%60%70%80%90%

100%

CPU0 CPU1 CPU2 CPU3

Cache miss statistics

Graphics Arithmetic Recursive

List alignment: stream graph• The stream graphs are a more complex generalization of stacked bar charts,

where the main axis (horizontal or vertical) represents an ordered attribute (time) and the complementary spatial dimension represents a categorical key attribute together with a quantitative attribute.

• They can represent the continuity of a dataset over time.• The shape of the stream graph can be optimized according to different factors

that affect the readability and aesthetic of the glyph, such as the overall silhouette, the deviation of each layer from the base line, the layer wiggle or the color mapping and the labeling of the layers.

• The representation generates a derived attribute with the layer ordering. • They scale better than stacked bar charts because most layers do not cover

the entire period of time collected.

List alignment: stream graph

[Byr08]

List alignment: stream graph

[Byr08]

List alignment: dot charts• The dot charts allow to visually encode a quantitative attribute along with a

qualitative attribute using the spatial position of the marks, which in this case are points.

• They are also called dot plots.• It is a representation equivalent to bar charts.

List alignment: line charts• The line charts are dot diagrams with lines as connecting marks between

points.• These diagrams emphasize the ordering of items according to the key attribute

by links between an item and the next, allowing to detect trends in the data.• These diagrams should be used with ordered keys, but not with categorical

keys because they would not respect the principle of expressiveness.

List alignment: dot and line charts

0

2

4

6

2011 2012 2013 2014

Stock market price (€)

Company1 Company2 Company3

Dot chart

0

2

4

6

2011 2012 2013 2014

Stock market price (€)

Company1 Company2 Company3

Line chart

Matrix alignment

• Datasets with two categorical keys are most often arranged into a two dimensional array, where one of the keys is shown in the rows and the other key in the columns.

• Thus, a rectangular area is generated in the matrix to represent the values of the items in each cell.

Matrix alignment: heatmaps• In heatmaps each attribute value in a cell is represented by a two-

dimensional mark that has been assigned a color.• This type of representations are very compact, and this is the reason

they are typically used to provide an overview of data sets that have a high information density.

• Scalability of categorical attributes can reach hundreds on each axis, but in the quantitative attribute (color cell) is much lower due to the limitations of the human visual system (recommended between 3 and 11 levels).

Matrix alignment: heatmaps

Matrix alignment: cluster heatmaps• Cluster heatmaps combine the basic allocation of color with the

rearranged matrix, where the two attributes are reordered together to detect trends in the combination of both attributes.

• A dendrogram is a visual encoding of a tree.• This representation is formed by combining one heatmap and two

dendrograms, one for each axis, which collect data derived from the hierarchical clustering applied for the rearrangement.

• Each leaf of the hierarchical cluster represents one item, and the internal nodes gather the order in which the groupings have been made, based on some similarity measure.

Matrix alignment: cluster heatmaps

[Seo02]

Matrix alignment: scatter plot matrix• The scatterplot matrices (SPLOM) are matrices where each cell

contains a scatterplot chart.• SPLOM shows all possible combinations of the values of the attributes

that are represented in rows and columns.• If the same attribute is represented in the two dimensions, usually

only a triangular matrix is presented removing the main diagonal because it would show the degenerate case of an attribute plotted against itself.

• SPLOM is mainly used to find correlations, trends and outliers.• The scalability of this representation is limited to a dozen of attributes

and hundreds of items.

Matrix alignment: scatterplot matrices

Volumetric alignment• Just like the data can be arranged 1D lists and 2D matrices, it would

also be possible a 3D arrangement in a volumetric grid.• However, this design choice is not recommended for non-spatial data

because it introduces problems in perception, such as occlusions or perspective distortion.

• An alternative for the representation of multidimensional tables with three keys using a spatial solution would be the recursive subdivision of each cell in a list or a matrix.

• The recursive subdivision is still using ordering and alignment, but container elements are added to perform the spatial partition.

Design options: spatial axis orientation

• Another design option is to define the axis orientation: rectilinear, parallel or radial.

• In the rectilinear, regions or items are distributed along two perpendicular axes, horizontal and vertical, ranging from a minimum value located at one end of the axis to a maximum located at the other extreme.

• The design examples seen so far respond to this scheme.

Spatial axis orientation: parallel coordinates

• The rectilinear arrangement of the axes used with scatterplots is only feasible only for two attributes when the spatial positioning accuracy of the items is high.

• When you have datasets with more than three quantitative attributes, the problem of non-separability of the channels limits the number of channels that can be effectively combined in a view.

• By means of the parallel coordinates multiple quantitative attributes can be simultaneously displayed using spatial positioning.

Spatial axis orientation: parallel coordinates

• An item is represented by a polyline that runs crossing all parallel axes at one point that represents the value of that item in the corresponding attribute represented by the axis.

• It is a very adequate representation to search for correlations between attributes because we can easily find different patterns:

• If two neighbor attributes are positively correlated, almost all segments of polylines are parallel.

• If they have negative correlation, the segments intersect at a point between the two axes.

• If they have no correlation, a mixture of different crosses are shown.

Spatial axis orientation: parallel coordinates

• They are also often used to get an overview of all the attributes, determine the range of values of the different attributes, select a set of items or for the detection of outliers.

• The parallel coordinates require two dimensions for the spatial arrangement of the dataset.

• Most implementations using parallel coordinates allow an interactive reordering of the axes.

• Typically, they require a longer training than other representations for users who previously did not know.

• Scalability is high regarding the number of values of quantitative attributes that can be presented (hundreds), but moderate compared to the number of attributes that can be represented (dozens), as a given space is needed to visually discriminate crossings polylines between axes.

Parallel coordinates

Spatial axis orientation: radial axis

• For radial representations, items are distributed around a circle using the angular channel (orientation) plus one or more linear spatial channels.

Radial axis: polar coordinates• The most natural form of representation are the polar coordinates, where

one of the dimensions is measured angularly with respect to a reference line and the other is measured as a distance from the center point.

• Representations by rectangular and polar coordinates are equivalent from a mathematical point of view: one of the axes of the rectangular coordinates collapses into a single point from which emanate the values represented in the other rectangular axis.

• But they are not from the perceptual point of view:• The angular channel is perceived with less precision than a rectilinear spatial

positioning channel• The angular channel is cyclic.

• Radial representations may be more appropriate than rectilinear for representing periodic patterns in the angular channel.

• But they are inadequate to represent attributes of the same importance, because the two channels used are clearly asymmetric.

050

100150200250300

Cat Cheetah Lion Panther

Felines

Average weight

Radial axis: polar coordinates

0

100

200

300Cat

Cheetah

Lion

Panther

Average weight

Cat

Cheetah

Lion

Panther

Radial axis: radial bar diagrams

Cheetah

Cat

Lion

Panther

0

50

100

150

200

250

300

Cat Cheetah Lion Panther

Felines

Average weight

Radial axis: pie charts• The pie chart is the radial representation more used in the field of statistics• They encode a single attribute-based on area marks in combination with the

angular channel.• Estimations based on this combination are less accurate than those based on the

length of the line marks.• The width of the portions varies radially from the center outward, so that the

perception of the area actually covered is complicated.• The most outstanding feature of these representations is that they show the

relative contribution of each part to the whole, but this too was achieved with normalized stacked bar charts.

• The pie charts require more surface for representation than normalized stacked bar charts because the angular channel has less accuracy than the length channel.

• Each pie chart would become one of the standard stacked bars.• Both representations are limited to show a limited number of categories (ten).

Radial axis: pie charts

1%16%

61%

22%

Felines

CatCheetahLionPanther

Comparison between rectilinear and radial arrangements• [Wickam et al 12] have conducted a study comparing the efficacy of using

maps glyphs designed with linear channels (lines) and radial (stars).• The radials are a transformation from linear to polar coordinates.• They verified that linear are more effective to show differences between

linear and nonlinear trends, while the radial are more effective to show cyclic patterns.

• [Diehl et al 10] have conducted a study oriented to memorize the positions of the objects presented for a few seconds, concluding that the rectilinear representations achieve better results for perceptual speed and accuracy. Also they conclude that the radial can be used when one attribute is more important than the other. Furthermore, the encoding based on the position of the sectors has more relevance than the one based on the position of the rings.

Design options: density

• The last design option is to consider the density of the elements in the layout.

• A related aspect with density is spacefilling.

Density

• The density of the marks is used to represent an overview of the maximum number of elements with very high information density.

• A maximally dense layout has point marks that are only a single pixel in size, and line marks that are only a single pixel in width.

• The minimum size of the marks implies that only channels associated to spatial position and color can be used in the visual encoding.

• This type of representations are often used to represent the source code statistics.

System example that implements density: Tarantula [Jones et al. 02]

Spacefilling• With spacefilling, all the available space in the layout is used.• Bidimensional marks are often used to represent items and

containment marks to establish relationships between items.• The possibility that the colored area is large enough to be perceived

by observers in a relevant way increases maximizing the space available for color encoding.

• Another advantage is that the required space to represent an item is usually large enough to incorporate a label.

• One disadvantage is that you can not use the color white for the empty space without explicit visual elements.

• They are used in systems with very high information density.

Spacefilling

References• Tamara Munzner. Visualization Analysis and Design. A K Peters Visualization

Series. CRC Press. Oct 2014.• [Gapminder]: www.gapminder.org• [Byr08]: Lee Byron y Martin Wattenberg, “Stacked graphs. Geometry &

Aesthetics” IEEE Trans. on Visualization and Computer Graphics 14(6): 1245-1252, 2008. leebyron.com/else/streamgraph leebyron.com/what/boxoffice

leebyron.com/what/lastfm• [Seo02]: Jinwook Seo y Ben Shneiderman, “Interactively exploring hierarchical

clustering results”, IEEE Computer 35(7): 80-86, 2002.• [Chi]: Manuela Chessa www.pspc.unige.it/~manuela/?page_ide=136• [Wickham et al. 12]: Hadley Wickham et al. “Glyph-maps for visually exploring

temporal patterns in climate data and models”. Environmetrics 23(5): 382-393, 2012.

• [Diehl et al. 10]: Stephan Diehl et al. “Uncovering strengths and weaknesses of radial visualizations – an empirical approach”. IEEE Trans. On Visualization and Computer Graphics. 16(6): 935-942, 2010.

• [Jones et al. 02]: James A. Jones et al. “Visualization of test information to assist fault localization”. In Proc. Intl. Conf. on Software Engineering (ICSE), 467-477, 2002.

Comparison between rectilinear and radial arrangements [Wickam et al 12]

Comparison between rectilinear and radial arrangements [Wickam et al 12]

Comparison between rectilinear and radial arrangements [Wickam et al 12]

Comparison between rectilinear and radial arrangements [Wickam et al 12]

Comparison between rectilinear and radial arrangements [Wickam et al 12]

Comparison between rectilinear and radial arrangements [Diehl et al 10]