# Modalflow: Cross-Origin Flow Data Visualization for Urban Mobility

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## Abstract

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## 1. Introduction

- A visualization system with coordinated views derived from a set of considerations about the nature of pervasive and traditional data sources,
- The distribution-aware selection tooltip: an enhancement for selection techniques.
- The sinusoidal flow encoding: a new encoding for bidirectional and multivariate flows as edges of a graph.
- A validation of our approach with a case study using real-world cross-origin datasets.

## 2. Related Work

## 3. Design Requirements

#### 3.1. Domain Problem

#### 3.2. Considerations on Cross-Origin Dataset Comparison

#### 3.3. Requirements

## 4. Materials and Methods

#### 4.1. Data

- W is a waypoint matrix, where every column represents a directed flow between two areas of the city, and every rows represents a tower. Thus, each cell ${w}_{ij}$ contains the number of times that tower i appears in the trajectories in flow j.
- A and B are positive low-rank matrices that express the associations between k latent dimensions and each tower (A) and flow (B).
- L is a k-rank labeling matrix where ${l}_{ij}$ is 1 if tower i is associated to mode of transportation j, 0 otherwise. This labeling enables aligning latent dimensions with mode of transportation usage in a semi-supervised way, as some towers are strictly associated to specific modes of transportation due to urban infrastructure surrounding it (see Ref. [42] for details).
- ⊙ is the Hadamard product operator.

#### 4.2. General Layout

#### 4.3. Color Coding

#### 4.4. Ternary Plot

#### 4.5. Scatterplot

#### 4.6. OD Matrix

#### 4.7. Flow Map with Sinusoidal Encoding

#### 4.8. Edge Bundling

## 5. Results

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Ternary color scale construction schema (

**a**) and resulting colormap (

**b**) used to encode mode split across views.

**Figure 3.**Selection over different datasets in the scatterplot is facilitated by our distribution-aware selection tool. A range selected in one scatterplot is not merely transposed to a, which would probably end in an empty selection, but linearly transformed into b, according to the grid automatically defined based on the distribution of each dataset.

**Figure 4.**Sinusoidal encoding design space and working schema. Left: Bidirectional flow encoding alternatives: (

**a**) straight; (

**b**) arched; and, (

**c**) sinusoidal, which projects a third dimension into perspective, differentiating in- and outflows in the vertical dimension. Right: schematic view of incoming and outgoing flows at a certain node. Flow direction becomes quickly distinguishable thanks to the sinusoidal flow encoding.

**Figure 5.**Pervasive (

**a**) and survey (

**b**) flows at night time. Each circle is an origin-destination pair, its area the flow magnitude, with color coded mode split. Highlighted are the different overall shapes present in their distribution.

**Figure 6.**XDR (

**a**) and survey (

**b**) flows at morning peak 1 at municipal aggregation level. Even at a time period where they show a similar total flow magnitude, the sampling density is different.

**Figure 7.**One day of mobility according to a travel survey (EOD) and a pervasive (XDR) dataset, visualized as flow maps on Modalflow.

**Figure 8.**Zone-level OD matrix of XDR (

**a**) and survey (

**b**) flows for the night valley period. Sparser measures and an over representation of intramunicipal flows can be appreciated in the survey.

**Figure 9.**Comparison of survey (

**EOD**) and pervasive (

**XDR**) data with geographic bundling by mode of transportation.

**Figure 10.**XDR (

**a**) and survey (

**b**) flows aggregated by origin municipality positioned on the ternary plot according to mean trip mode split (also encoded by background color), with radius encoding total magnitude.

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**MDPI and ACS Style**

Pérez-Messina, I.; Graells-Garrido, E.; Lobo, M.J.; Hurter, C. Modalflow: Cross-Origin Flow Data Visualization for Urban Mobility. *Algorithms* **2020**, *13*, 298.
https://doi.org/10.3390/a13110298

**AMA Style**

Pérez-Messina I, Graells-Garrido E, Lobo MJ, Hurter C. Modalflow: Cross-Origin Flow Data Visualization for Urban Mobility. *Algorithms*. 2020; 13(11):298.
https://doi.org/10.3390/a13110298

**Chicago/Turabian Style**

Pérez-Messina, Ignacio, Eduardo Graells-Garrido, María Jesús Lobo, and Christophe Hurter. 2020. "Modalflow: Cross-Origin Flow Data Visualization for Urban Mobility" *Algorithms* 13, no. 11: 298.
https://doi.org/10.3390/a13110298