# Towards a Model of Urban Evolution Part IV: Evolutionary (Formetic) Distance—An Interpretation of Yelp Review Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Encoding Yelp Data in TUEM

- Annex (95)—High income predominately residential with retail;
- Bathurst Manor (34)—Middle income bedroom community;
- Bay Street Corridor (76)—Middle to high income mixed commercial and residential;
- Church-Yonge Corridor (75)—Middle income with retail;
- Danforth (66)—Middle income with retail;
- Junction Area (90)—Middle and low income with retail;
- Palmerston–Little Italy (80)—Middle income residential;
- Waterfront Communities-The Island (77)—Middle income with retail and commercial;
- Wychwood (94)—Middle to high income residential.

- Time stamp.
- Business ID: a unique identifier for the business being reviewed.
- Neighbourhood ID: a unique identifier for the neighbourhood in which the business is located. There are 140 neighbourhoods in Toronto.
- User ID: a unique identifier for the reviewer. There are 73,504 unique reviewers in this set.
- Categories: one or more categories, from the Yelp taxonomy of business categories, that the business is classified as. There are 854 unique categories (excluding top level categories) in this Yelp dataset.

- Spatial Areas (C): a spatial area c corresponds to a Toronto neighbourhood.
- Forms (P): a form p corresponds to a unique Yelp business ID.
- Groups (G): a group g corresponds to a unique User ID, i.e., reviewer.
- Activities (A): an activity a corresponds to the implicit activity of reviewing.

## 3. Formeme and Signature Distances

_{1}, f

_{2}): measures the formetic distance between formemes f

_{1}and f

_{2}.

**Axiom**

**1.**

_{1}, f

_{1}) = 0.

**Axiom**

**2.**

_{1}, f

_{2}) = fdist(f

_{2}, f

_{1}).

**Axiom**

**3.**

_{1}, f

_{2}) + fdist(f

_{2}, f

_{3}) ≥ fdist(f

_{1}, f

_{3}).

_{1}and F

_{2}:

_{1}, F

_{2}): measures the similarity between formeme sets F

_{1}and F

_{2}.

**Axiom**

**4.**

_{1}, F

_{1}) = 0.

**Axiom**

**5.**

_{1}, F

_{2}) = Fdist (F

_{2}, F

_{1}).

**Axiom**

**6.**

_{1}, F

_{2}) + Fdist (F

_{2}, F

_{3}) ≥ Fdist (F

_{1}, F

_{3}).

_{1}and F

_{2}, i.e., the more similar they are, the closer the value of the fraction is to one. We then subtract the fraction from zero to get the distance, i.e., a distance of zero implies the faction is one and the F

_{1}and F

_{2}share the same elements.

## 4. Signature Distances: Unaggregated Data

#### 4.1. Longitudinal Analysis

**Number of non-unique elements in component:**total number of elements across the three components, P, A and G, of H.**Number of unique elements in component:**total number of unique elements across the three components, P, A and G, of H.**Intersection of elements with prior year:**total number of unique elements across the three components, P, A and G, in the intersection of this year’s elements (metric #1) with the prior year.**Union of elements with prior year:**total number of unique elements across the three components, P, A and G, in the union of this year’s elements (metric #1) with the prior year.**Intersection %**: Percentage of unique elements that are common to this year’s metric #1 and the prior year.**Cumulative intersection since year 1**: total number of unique elements across the three components, P, A and G, in the intersection of this year’s elements (metric #1) with**all**prior years.**Cumulative Intersection %:**Percentage of unique elements that are common to this year’s metric #1 and all prior years.

#### 4.2. Transversal Distance

- The lines listing the neighourhoods specify the number of unique elements for each of the components P, G, and A.
- Intersection of elements specifies the number of unique elements in the intersection of the two neighbourhoods.
- The union of elements specifies the number of unique elements in the union.
- The intersection % specifies the number of unique elements in the intersection divided by the number in the union.

## 5. Signature Distances: Aggregated Forms

- Form f: single business category;
- Activity a: Review—same for all formemes;
- Group g: group ID—the reviewer’s unique User ID;
- Weight w.

- -
- <category 1, Review, Group 28, 0.333>
- -
- <category 2, Review, Group 28, 0.333>
- -
- <category 3, Review, Group 28, 0.333>

#### 5.1. Longitudinal Distance

#### 5.1.1. Longitudinal Case: Waterfront Communities-The Island (77)

**Neighbourhood Venue (Form) Changes.**Examination of the Waterfront data shows that greater than 80% of the reviews from one year to the next are for the same categories of venues, whereas over the six year period the cumulative intersection of venue categories reviewed drops to approximately 50%, possibly reflecting an evolution in the categories of venues in the neighbourhood over the six year period. Within the restaurant industry, the decrease in intersecting venues is consistent with the average life span of a restaurant—the majority do not last more than a year and those that do, 70% will close within five years (https://yourbusiness.azcentral.com/average-life-span-restaurant-6024.html, accessed on 17 January 2022). This is validated by the cumulative intersection of non-aggregated forms (venues) in year 6 of Table 9 of 20%, implying that many restaurants have probably closed, but still greater than the average. Nevertheless, the analysis also indicates that the neighbourhood retains a sizable share of its orientation over the period, with the churn in particular businesses matched by a greater stability in the types of businesses present. In other words, the genome U for the neighbourhood influences the persistence of venue categories which in turn influences a persistence in the activities associated with them. Although some change in the actual activities in Hunome H occur, the persisted impact of U is clearly felt.

**Neighbourhood Reviewer (Group) Changes.**From one year to the next there is about 10% repeat reviewers-the same person will generate at least one review each year over a two year period. However, over the six years the number of people who submit reviews for each of the years reduces to 0.3%. Hence, the reviewer population appears to be transient, which is consistent with the Waterfront being a tourist area. The Waterfront therefore illustrates a type of urban evolution where the population of local formemes is likely adapted to the expectations of a mobile tourist population of users.

#### 5.1.2. Longitudinal Case: Annex (95)

#### 5.1.3. Observations

#### 5.2. Transversal Distance

#### 5.2.1. Transversal Case: Annex (95)—Church-Yonge Corridor (75)

#### 5.2.2. Transversal Case: Annex (95)—Bathurst Manor (34)

#### 5.2.3. Transversal Case: Annex (95)—Waterfront Communities-The Island (77)

## 6. Signature Distances: Aggregating Groups

- The aggregate group whose defining forms contained the formeme’s form;
- the aggregate group with the largest number of forms used to define the aggregate group.

#### 6.1. Longitudinal Distance

#### 6.1.1. Waterfront Communities-The Island (77)

#### 6.1.2. Annex (95)

#### 6.2. Transversal Distance

#### 6.2.1. Transversal Case: Annex (95)—Bathurst Manor (34)

#### 6.2.2. Transversal Case: Annex (95)—Waterfront Communities-The Island (77)

#### 6.2.3. Transversal Case: Annex (95)—Hurch-Yonge Corridor (75)

## 7. Transversal Distances between Toronto and Montreal Neighbourhoods

## 8. Discussion

**Is Formetic Distance meaningful?**

“is a small, semi-suburban and scenic neighbourhood, … there’s some scenic spots and great parks, … a bit out of the way from the busier parts of the city, … isn’t a place where you go to party, … one of the parts of the city where the middle-aged and elderly might outnumber the younger folks. A lot of families move out here to settle and buy homes for the long run. As such, many of the residents of this area are long-term inhabitants who want to enjoy the feeling of suburbia but still be close to downtown, … bit out of place, especially since there are some industrial zones nearby, … find restaurants, drugstores and groceries. Though there aren’t too many choices for amenities overall …” (https://nexthome.ca/neighbourhoods/montreal-sault-au-recollet/142959/, accessed on 27 January 2021)

**Is aggregating individuals from different cities into the same group valid?**

^{2}indicate that between 31 and 55% of the variation in the weighted intersection of groups observed in the Yelp data can be explained by the weighted intersection of forms. Therefore, our exploration of the correlation between the intersection of forms and groups seems to confirm that our aggregation of individuals from different cities based on their reviewing activity is valid.

**What does Yelp data tell us about the Model?**

**What does the model tell us about Yelp data?**

## 9. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Formal Model

_{i}: the ith formeme in U

_{i}[p]: the set of forms in the ith formeme in U

_{i}[a]: the set of activities in the ith formeme in U

_{i}[g]: the set of groups in the ith formeme in U

_{i}: the ith formeme in H

_{i}[p]: the set of physical forms in the ith formeme in H

_{i}[a]: the set of activities in the ith formeme in H

_{i}[g]: the set of groups in the ith formeme in H

_{i}h

_{i}[p] set of all forms in H

_{i}h

_{i}[a] set of all activities in H

_{i}h

_{i}[g] set of all groups in H

_{i}|formeme(h

_{i})} for some space c at time t

- formeme that communicates a fragment of a genome. This fragment may be assimilated by another spatial area, first as a change to hunome H, and if it survives, eventually as a change to U;
- the source of the signal a spatial area receives. Where a signal comes from affects how it is received;
- method of communication. A formeme may be communicated in more than one way, and depending on the method of communication, the signal may travel only within c (intra-spatial signal), or between c’s (inter-spatial signal), or both (bi-spatial signal);
- the capacity of a signal to alter the recoding costs in the area that receives the signal; and
- the number of times the signal has been received. A signal that is received with a high frequency may have a higher probability of assimilation in H.

_{i}|s

_{i}= <f, r, c, sf, cm, n>}

_{i}has been received from c during the time span of the signature

_{i}: the ith signal in S

_{i}[f]: is the Formeme f of the ith signal

_{i}[r]: is the recoding cost transform

_{i}[c]: is the spatial area from which the signal originates

_{i}[cm]: is the communication methods of the ith signal

_{i,}[n]: is the frequency of the ith signal

_{i}s

_{i}[p] set of all forms in S

_{i}s

_{i}[a] set of all activities in S

_{i}s

_{i}[g] set of all groups in S

_{i}s

_{i}[f] set of all formemes in S

## Appendix B. Aggregate Groups

Group ID | Yelp Categories | Group Size |

Group-1 | [‘American (New)’, ‘Bars’] | 7135 |

Group-2 | [‘American (New)’, ‘Breakfast & Brunch’] | 5475 |

Group-3 | [‘American (New)’, ‘Canadian (New)’] | 9337 |

Group-4 | [‘American (Traditional)’, ‘Bars’] | 7124 |

Group-5 | [‘American (Traditional)’, ‘Canadian (New)’] | 5675 |

Group-6 | [‘Bars’, ‘Breakfast & Brunch’] | 9845 |

Group-7 | [‘Bars’, ‘Burgers’] | 5485 |

Group-8 | [‘Bars’, ‘Cafes’] | 5093 |

Group-9 | [‘Bars’, ‘Canadian (New)’] | 12,015 |

Group-10 | [‘Bars’, ‘Cocktail Bars’] | 5216 |

Group-11 | [‘Bars’, ‘Coffee & Tea’] | 6709 |

Group-12 | [‘Bars’, ‘Italian’] | 7428 |

Group-13 | [‘Bars’, ‘Japanese’] | 6398 |

Group-14 | [‘Bars’, ‘Lounges’] | 5344 |

Group-15 | [‘Bars’, ‘Pubs’] | 9029 |

Group-16 | [‘Bars’, ‘Sandwiches’] | 5703 |

Group-17 | [‘Bars’, ‘Specialty Food’] | 5103 |

Group-18 | [‘Breakfast & Brunch’, ‘Canadian (New)’] | 8484 |

Group-19 | [‘Breakfast & Brunch’, ‘Coffee & Tea’] | 6466 |

Group-20 | [‘Breakfast & Brunch’, ‘Italian’] | 5701 |

Group-21 | [‘Breakfast & Brunch’, ‘Sandwiches’] | 5565 |

Group-22 | [‘Cafes’, ‘Coffee & Tea’] | 5689 |

Group-23 | [‘Canadian (New)’, ‘Coffee & Tea’] | 5520 |

Group-24 | [‘Canadian (New)’, ‘Italian’] | 5910 |

Group-25 | [‘Canadian (New)’, ‘Pubs’] | 5280 |

Group-26 | [‘Coffee & Tea’, ‘Desserts’] | 5143 |

Group-27 | [‘Ethnic Food’, ‘Specialty Food’] | 5061 |

Group-28 | [‘Italian’, ‘Pizza’] | 5874 |

Group-29 | [‘Japanese’, ‘Sushi Bars’] | 7071 |

Group-30 | [‘American (New)’, ‘Bars’, ‘Canadian (New)’] | 6863 |

Group-31 | [‘American (New)’, ‘Breakfast & Brunch’, ‘Canadian (New)’] | 5258 |

Group-32 | [‘American (Traditional)’, ‘Bars’, ‘Canadian (New)’] | 5031 |

Group-33 | [‘Bars’, ‘Breakfast & Brunch’, ‘Canadian (New)’] | 6658 |

Group-34 | [‘Bars’, ‘Canadian (New)’, ‘Italian’] | 5057 |

Group-35 | [‘Bars’, ‘Canadian (New)’, ‘Pubs’] | 5280 |

## References

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Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Yr 6 | |
---|---|---|---|---|---|---|

Yr 1 | 0.536 | 0.649 | 0.743 | 0.81 | 0.84 | |

Yr 2 | 0.582 | 0.698 | 0.781 | 0.816 | ||

Yr 3 | 0.597 | 0.713 | 0.76 | |||

Yr 4 | 0.592 | 0.669 | ||||

Yr 5 | 0.549 | |||||

Yr 6 |

Year (1096) | Dist. from Prior Year | Dist. from Year 1 | Waterfront Communities-The Island (77) Exp # 10.0 | P | G | A | Total |
---|---|---|---|---|---|---|---|

1 | Number of non-unique elements in component | 4031 | 4031 | 4031 | 12,093 | ||

Number of unique elements in component | 644 | 1723 | 1 | 2368 | |||

2 | 0.536 | 0.536 | Number of non-unique elements in component | 4462 | 4462 | 4462 | 13,386 |

Number of unique elements in component | 709 | 2275 | 1 | 2985 | |||

Intersection of elements with prior year | 511 | 399 | 1 | 911 | |||

Union of elements with prior year | 842 | 3599 | 1 | 4442 | |||

Intersection % | 60.7 | 11.1 | 100.0 | 20.5 | |||

Cumulative intersection since year 1 | 511 | 399 | 1 | 911 | |||

Cumulative union since year 1 | 842 | 3599 | 1 | 4442 | |||

Cumulative Intersection % | 60.7 | 11.1 | 100.0 | 20.5 | |||

3 | 0.582 | 0.649 | Number of non-unique elements in component | 5798 | 5798 | 5798 | 17,394 |

Number of unique elements in component | 809 | 3190 | 1 | 4000 | |||

Intersection of elements with prior year | 569 | 507 | 1 | 1077 | |||

Union of elements with prior year | 949 | 4958 | 1 | 5908 | |||

Intersection % | 60.0 | 10.2 | 100.0 | 18.2 | |||

Cumulative intersection since year 1 | 430 | 196 | 1 | 627 | |||

Cumulative union since year 1 | 1013 | 6170 | 1 | 7184 | |||

Cumulative Intersection % | 42.4 | 3.2 | 100.0 | 8.7 | |||

4 | 0.597 | 0.743 | Number of non-unique elements in component | 8054 | 8054 | 8054 | 24,162 |

Number of unique elements in component | 838 | 4692 | 1 | 5531 | |||

Intersection of elements with prior year | 636 | 640 | 1 | 1277 | |||

Union of elements with prior year | 1011 | 7242 | 1 | 8254 | |||

Intersection % | 62.9 | 8.8 | 100.0 | 15.5 | |||

Cumulative intersection since year 1 | 373 | 117 | 1 | 491 | |||

Cumulative union since year 1 | 1150 | 10,024 | 1 | 11,175 | |||

Cumulative Intersection % | 32.4 | 1.2 | 100.0 | 4.4 | |||

5 | 0.592 | 0.81 | Number of non-unique elements in component | 11,463 | 11,463 | 11,463 | 34,389 |

Number of unique elements in component | 938 | 6567 | 1 | 7506 | |||

Intersection of elements with prior year | 683 | 999 | 1 | 1683 | |||

Union of elements with prior year | 1093 | 10,260 | 1 | 11,354 | |||

Intersection % | 62.5 | 9.7 | 100.0 | 14.8 | |||

Cumulative intersection since year 1 | 332 | 82 | 1 | 415 | |||

Cumulative union since year 1 | 1306 | 15,221 | 1 | 16,528 | |||

Cumulative Intersection % | 25.4 | 0.5 | 100.0 | 2.5 | |||

6 | 0.549 | 0.84 | Number of non-unique elements in component | 12,699 | 12,699 | 12,699 | 38,097 |

Number of unique elements in component | 989 | 7596 | 1 | 8586 | |||

Intersection of elements with prior year | 757 | 1254 | 1 | 2012 | |||

Union of elements with prior year | 1170 | 12,909 | 1 | 14,080 | |||

Intersection % | 64.7 | 9.7 | 100.0 | 14.3 | |||

Cumulative intersection since year 1 | 300 | 54 | 1 | 355 | |||

Cumulative union since year 1 | 1438 | 21,085 | 1 | 22,524 | |||

Cumulative Intersection % | 20.9 | 0.3 | 100.0 | 1.6 |

Annex (95) | Bathurst Manor (34) | Church-Yonge Corridor (75) | Danforth (66) | Junction Area (90) | Palmerston-Little Italy (80) | Waterfront Communities-The Island (77) | Wychwood (94) | |
---|---|---|---|---|---|---|---|---|

Annex (95) | 0.997 | 0.736 | 0.96 | 0.948 | 0.824 | 0.81 | 0.936 | |

Bathurst Manor (34) | 0.998 | 0.975 | 0.982 | 0.993 | 0.998 | 0.983 | ||

Church-Yonge Corridor (75) | 0.967 | 0.958 | 0.857 | 0.771 | 0.952 | |||

Danforth (66) | 0.822 | 0.926 | 0.98 | 0.834 | ||||

Junction Area (90) | 0.899 | 0.974 | 0.796 | |||||

Palmerston-Little Italy (80) | 0.901 | 0.882 | ||||||

Waterfront Communities-The Island (77) | 0.967 | |||||||

Wychwood (94) |

Exp # 10.0 | P | G | A | Total |
---|---|---|---|---|

Annex (95) | 447 | 963 | 1 | 1411 |

Bathurst Manor (34) | 4 | 11 | 1 | 16 |

Intersection of elements | 0 | 5 | 1 | 6 |

Union of elements | 451 | 969 | 1 | 1421 |

Intersection % | 0.0 | 0.5 | 100.0 | 0.4 |

Exp # 10.0 | P | G | A | Total |
---|---|---|---|---|

Annex (95) | 447 | 963 | 1 | 1411 |

Church-Yonge Corridor (75) | 437 | 1176 | 1 | 1614 |

Intersection of elements | 0 | 373 | 1 | 374 |

Union of elements | 884 | 1766 | 1 | 2651 |

Intersection % | 0.0 | 21.1 | 100.0 | 14.1 |

Exp # 10.0 | P | G | A | Total |
---|---|---|---|---|

Annex (95) | 447 | 963 | 1 | 1411 |

Waterfront Communities-The Island (77) | 644 | 1723 | 1 | 2368 |

Intersection of elements | 0 | 426 | 1 | 427 |

Union of elements | 1091 | 2260 | 1 | 3352 |

Intersection % | 0.0 | 18.8 | 100.0 | 12.7 |

Active Life | Financial Services | Local Services | Real Estate |

Arts & Entertainment | Food | Mass Media | Religious Organizations |

Automotive | Health & Medical | Nightlife | Restaurants |

Beauty & Spas | Home Services | Pets | Shopping |

Education | Hotels & Travel | Professional Services | |

Event Planning & Services | Local Flavor | Public Services & Government |

Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Yr 6 | |
---|---|---|---|---|---|---|

Yr 1 | 0.471 | 0.591 | 0.701 | 0.778 | 0.803 | |

Yr 2 | 0.53 | 0.661 | 0.754 | 0.782 | ||

Yr 3 | 0.563 | 0.684 | 0.722 | |||

Yr 4 | 0.559 | 0.622 | ||||

Yr 5 | 0.494 | |||||

Yr 6 |

Year (1096) | Dist. from Prior Year | Dist. from Year 1 | Waterfront Communities-The Island (77) Exp # 10.1 | P | G | A | Total |
---|---|---|---|---|---|---|---|

1 | Number of non-unique elements in component | 11,891 | 11,891 | 11,891 | 35,673 | ||

Number of unique elements in component | 313 | 1720 | 1 | 2034 | |||

2 | 0.471 | 0.471 | Number of non-unique elements in component | 12,927 | 12,927 | 12,927 | 38,781 |

Number of unique elements in component | 334 | 2271 | 1 | 2606 | |||

Intersection of elements with prior year | 289 | 399 | 1 | 689 | |||

Union of elements with prior year | 358 | 3592 | 1 | 3951 | |||

Intersection % | 80.7 | 11.1 | 100.0 | 17.4 | |||

Cumulative intersection since year 1 | 289 | 399 | 1 | 689 | |||

Cumulative union since year 1 | 358 | 3592 | 1 | 3951 | |||

Cumulative Intersection % | 80.7 | 11.1 | 100.0 | 17.4 | |||

3 | 0.53 | 0.591 | Number of non-unique elements in component | 16,278 | 16,278 | 16,278 | 48,834 |

Number of unique elements in component | 376 | 3188 | 1 | 3565 | |||

Intersection of elements with prior year | 316 | 507 | 1 | 824 | |||

Union of elements with prior year | 394 | 4952 | 1 | 5347 | |||

Intersection % | 80.2 | 10.2 | 100.0 | 15.4 | |||

Cumulative intersection since year 1 | 277 | 196 | 1 | 474 | |||

Cumulative union since year 1 | 400 | 6161 | 1 | 6562 | |||

Cumulative Intersection % | 69.2 | 3.2 | 100.0 | 7.2 | |||

4 | 0.563 | 0.701 | Number of non-unique elements in component | 22,715 | 22,715 | 22,715 | 68,145 |

Number of unique elements in component | 377 | 4689 | 1 | 5067 | |||

Intersection of elements with prior year | 351 | 639 | 1 | 991 | |||

Union of elements with prior year | 402 | 7238 | 1 | 7641 | |||

Intersection % | 87.3 | 8.8 | 100.0 | 13.0 | |||

Cumulative intersection since year 1 | 272 | 117 | 1 | 390 | |||

Cumulative union since year 1 | 415 | 10,013 | 1 | 10,429 | |||

Cumulative Intersection % | 65.5 | 1.2 | 100.0 | 3.7 | |||

5 | 0.559 | 0.778 | Number of non-unique elements in component | 33,404 | 33,404 | 33,404 | 100,212 |

Number of unique elements in component | 399 | 6564 | 1 | 6964 | |||

Intersection of elements with prior year | 360 | 999 | 1 | 1360 | |||

Union of elements with prior year | 416 | 10,254 | 1 | 10,671 | |||

Intersection % | 86.5 | 9.7 | 100.0 | 12.7 | |||

Cumulative intersection since year 1 | 270 | 82 | 1 | 353 | |||

Cumulative union since year 1 | 438 | 15,207 | 1 | 15,646 | |||

Cumulative Intersection % | 61.6 | 0.5 | 100.0 | 2.3 | |||

6 | 0.494 | 0.803 | Number of non-unique elements in component | 37,211 | 37,211 | 37,211 | 111,633 |

Number of unique elements in component | 422 | 7592 | 1 | 8015 | |||

Intersection of elements with prior year | 373 | 1253 | 1 | 1627 | |||

Union of elements with prior year | 448 | 12,903 | 1 | 13,352 | |||

Intersection % | 83.3 | 9.7 | 100.0 | 12.2 | |||

Cumulative intersection since year 1 | 264 | 54 | 1 | 319 | |||

Cumulative union since year 1 | 470 | 21,068 | 1 | 21,539 | |||

Cumulative Intersection % | 56.2 | 0.3 | 100.0 | 1.5 |

Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Yr 6 | |
---|---|---|---|---|---|---|

Yr 1 | 0.47 | 0.571 | 0.663 | 0.709 | 0.727 | |

Yr 2 | 0.531 | 0.642 | 0.695 | 0.715 | ||

Yr 3 | 0.559 | 0.631 | 0.658 | |||

Yr 4 | 0.531 | 0.57 | ||||

Yr 5 | 0.496 | |||||

Yr 6 |

Year (1096) | Dist. from Prior Year | Dist. from Year 1 | Annex (95) Exp # 10.1 | P | G | A | Total |
---|---|---|---|---|---|---|---|

1 | Number of non-unique elements in component | 5060 | 5060 | 5060 | 15,180 | ||

Number of unique elements in component | 246 | 962 | 1 | 1209 | |||

2 | 0.47 | 0.47 | Number of non-unique elements in component | 5188 | 5188 | 5188 | 15,564 |

Number of unique elements in component | 250 | 1231 | 1 | 1482 | |||

Intersection of elements with prior year | 214 | 230 | 1 | 445 | |||

Union of elements with prior year | 282 | 1963 | 1 | 2246 | |||

Intersection % | 75.9 | 11.7 | 100.0 | 19.8 | |||

Cumulative intersection since year 1 | 214 | 230 | 1 | 445 | |||

Cumulative union since year 1 | 282 | 1963 | 1 | 2246 | |||

Cumulative Intersection % | 75.9 | 11.7 | 100.0 | 19.8 | |||

3 | 0.531 | 0.571 | Number of non-unique elements in component | 6637 | 6637 | 6637 | 19,911 |

Number of unique elements in component | 258 | 1573 | 1 | 1832 | |||

Intersection of elements with prior year | 226 | 228 | 1 | 455 | |||

Union of elements with prior year | 282 | 2576 | 1 | 2859 | |||

Intersection % | 80.1 | 8.9 | 100.0 | 15.9 | |||

Cumulative intersection since year 1 | 206 | 88 | 1 | 295 | |||

Cumulative union since year 1 | 308 | 3251 | 1 | 3560 | |||

Cumulative Intersection % | 66.9 | 2.7 | 100.0 | 8.3 | |||

4 | 0.559 | 0.663 | Number of non-unique elements in component | 8596 | 8596 | 8596 | 25,788 |

Number of unique elements in component | 279 | 2201 | 1 | 2481 | |||

Intersection of elements with prior year | 232 | 277 | 1 | 510 | |||

Union of elements with prior year | 305 | 3497 | 1 | 3803 | |||

Intersection % | 76.1 | 7.9 | 100.0 | 13.4 | |||

Cumulative intersection since year 1 | 198 | 44 | 1 | 243 | |||

Cumulative union since year 1 | 330 | 5076 | 1 | 5407 | |||

Cumulative Intersection % | 60.0 | 0.9 | 100.0 | 4.5 | |||

5 | 0.531 | 0.709 | Number of non-unique elements in component | 9973 | 9973 | 9973 | 29,919 |

Number of unique elements in component | 282 | 2722 | 1 | 3005 | |||

Intersection of elements with prior year | 241 | 357 | 1 | 599 | |||

Union of elements with prior year | 320 | 4566 | 1 | 4887 | |||

Intersection % | 75.3 | 7.8 | 100.0 | 12.3 | |||

Cumulative intersection since year 1 | 188 | 21 | 1 | 210 | |||

Cumulative union since year 1 | 354 | 7267 | 1 | 7622 | |||

Cumulative Intersection % | 53.1 | 0.3 | 100.0 | 2.8 | |||

6 | 0.496 | 0.727 | Number of non-unique elements in component | 11,027 | 11,027 | 11,027 | 33,081 |

Number of unique elements in component | 300 | 3054 | 1 | 3355 | |||

Intersection of elements with prior year | 254 | 416 | 1 | 671 | |||

Union of elements with prior year | 328 | 5360 | 1 | 5689 | |||

Intersection % | 77.4 | 7.8 | 100.0 | 11.8 | |||

Cumulative intersection since year 1 | 184 | 13 | 1 | 198 | |||

Cumulative union since year 1 | 367 | 9680 | 1 | 10,048 | |||

Cumulative Intersection % | 50.1 | 0.1 | 100.0 | 2.0 |

Annex (95) | Bathurst Manor (34) | Church-Yonge Corridor (75) | Danforth (66) | Junction Area (90) | Palmerston-Little Italy (80) | Waterfront Communities-The Island (77) | Wychwood (94) | |
---|---|---|---|---|---|---|---|---|

Annex (95) | 0.995 | 0.53 | 0.935 | 0.908 | 0.7 | 0.668 | 0.899 | |

Bathurst Manor (34) | 0.996 | 0.973 | 0.98 | 0.99 | 0.998 | 0.976 | ||

Church-Yonge Corridor (75) | 0.947 | 0.927 | 0.757 | 0.593 | 0.919 | |||

Danforth (66) | 0.706 | 0.876 | 0.966 | 0.759 | ||||

Junction Area (90) | 0.835 | 0.955 | 0.704 | |||||

Palmerston-Little Italy (80) | 0.84 | 0.814 | ||||||

Waterfront Communities-The Island (77) | 0.948 | |||||||

Wychwood (94) |

P | G | A | Total | |
---|---|---|---|---|

Annex (95) | 246 | 962 | 1 | 1209 |

Church-Yonge Corridor (75) | 249 | 1176 | 1 | 1436 |

Intersection | 173 | 373 | 1 | 547 |

Union | 332 | 1765 | 1 | 2098 |

Intersection % | 52.1% | 21.1% | 100% | 26.1% |

P | G | A | Total | |
---|---|---|---|---|

Annex (95) | 246 | 962 | 1 | 1209 |

Bathurst Manor (34) | 11 | 11 | 1 | 23 |

Intersection | 6 | 5 | 1 | 12 |

Union | 251 | 968 | 1 | 1220 |

Intersection % | 2.4% | 0.5% | 100% | 1% |

P | G | A | Total | |
---|---|---|---|---|

Annex (95) | 246 | 962 | 1 | 1209 |

Waterfront Communities-The Island (77) | 313 | 1720 | 1 | 2034 |

Intersection | 182 | 426 | 1 | 609 |

Union | 377 | 2256 | 1 | 2634 |

Intersection % | 48.3% | 18.9% | 100% | 23.1% |

Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Yr 6 | |
---|---|---|---|---|---|---|

Yr 1 | 0.204 | 0.364 | 0.539 | 0.67 | 0.703 | |

Yr 2 | 0.308 | 0.497 | 0.64 | 0.676 | ||

Yr 3 | 355 | 0.537 | 0.58 | |||

Yr 4 | 366 | 0.433 | ||||

Yr 5 | 0.238 | |||||

Yr 6 |

Year | Distance from Prior Year | Distance from Year 1 | Waterfront Communities-The Island (77) Exp # 11 | P | G | A | Total |
---|---|---|---|---|---|---|---|

1 | Number of non-unique elements in component | 2398 | 2398 | 2398 | 7194 | ||

Number of unique elements in component | 313 | 418 | 1 | 732 | |||

2 | 0.204 | 0.204 | Number of non-unique elements in component | 3016 | 3016 | 3016 | 9048 |

Number of unique elements in component | 334 | 579 | 1 | 914 | |||

Intersection of elements with prior year | 289 | 39 | 1 | 329 | |||

Union of elements with prior year | 358 | 958 | 1 | 1317 | |||

Intersection % | 80.7 | 4.1 | 100.0 | 25.0 | |||

Cumulative intersection since year 1 | 289 | 39 | 1 | 329 | |||

Cumulative union since year 1 | 358 | 958 | 1 | 1317 | |||

Cumulative Intersection % | 80.7 | 4.1 | 100.0 | 25.0 | |||

3 | 0.308 | 0.364 | Number of non-unique elements in component | 3922 | 3922 | 3922 | 11,766 |

Number of unique elements in component | 376 | 806 | 1 | 1183 | |||

Intersection of elements with prior year | 316 | 45 | 1 | 362 | |||

Union of elements with prior year | 394 | 1340 | 1 | 1735 | |||

Intersection % | 80.2 | 3.4 | 100.0 | 20.9 | |||

Cumulative intersection since year 1 | 277 | 33 | 1 | 311 | |||

Cumulative union since year 1 | 400 | 1713 | 1 | 2114 | |||

Cumulative Intersection % | 69.2 | 1.9 | 100.0 | 14.7 | |||

4 | 0.355 | 0.539 | Number of non-unique elements in component | 5308 | 5308 | 5308 | 15,924 |

Number of unique elements in component | 377 | 1265 | 1 | 1643 | |||

Intersection of elements with prior year | 351 | 48 | 1 | 400 | |||

Union of elements with prior year | 402 | 2023 | 1 | 2426 | |||

Intersection % | 87.3 | 2.4 | 100.0 | 16.5 | |||

Cumulative intersection since year 1 | 272 | 33 | 1 | 306 | |||

Cumulative union since year 1 | 415 | 2921 | 1 | 3337 | |||

Cumulative Intersection % | 65.5 | 1.1 | 100.0 | 9.2 | |||

5 | 0.366 | 0.67 | Number of non-unique elements in component | 7125 | 7125 | 7125 | 21,375 |

Number of unique elements in component | 399 | 1700 | 1 | 2100 | |||

Intersection of elements with prior year | 360 | 61 | 1 | 422 | |||

Union of elements with prior year | 416 | 2904 | 1 | 3321 | |||

Intersection % | 86.5 | 2.1 | 100.0 | 12.7 | |||

Cumulative intersection since year 1 | 270 | 33 | 1 | 304 | |||

Cumulative union since year 1 | 438 | 4541 | 1 | 4980 | |||

Cumulative Intersection % | 61.6 | 0.7 | 100.0 | 6.1 | |||

6 | 0.238 | 0.703 | Number of non-unique elements in component | 8703 | 8703 | 8703 | 26,109 |

Number of unique elements in component | 422 | 2091 | 1 | 2514 | |||

Intersection of elements with prior year | 373 | 67 | 1 | 441 | |||

Union of elements with prior year | 448 | 3724 | 1 | 4173 | |||

Intersection % | 83.3 | 1.8 | 100.0 | 10.6 | |||

Cumulative intersection since year 1 | 264 | 33 | 1 | 298 | |||

Cumulative union since year 1 | 470 | 6529 | 1 | 7000 | |||

Cumulative Intersection % | 56.2 | 0.5 | 100.0 | 4.3 |

Yr 1 | Yr 2 | Yr 3 | Yr 4 | Yr 5 | Yr 6 | |
---|---|---|---|---|---|---|

Yr 1 | 0.207 | 0.302 | 0.456 | 0.535 | 0.562 | |

Yr 2 | 0.286 | 0.449 | 0.53 | 0.556 | ||

Yr 3 | 0.334 | 0.429 | 0.459 | |||

Yr 4 | 0.284 | 0.342 | ||||

Yr 5 | 0.243 | |||||

Yr 6 |

Year | Distance from Prior Year | Distance from Year 1 | Annex (95) Exp # 11 | P | G | A | Total |
---|---|---|---|---|---|---|---|

1 | Number of non-unique elements in component | 1369 | 1369 | 1369 | 4107 | ||

Number of unique elements in component | 246 | 220 | 1 | 467 | |||

2 | 0.207 | 0.207 | Number of non-unique elements in component | 1629 | 1629 | 1629 | 4887 |

Number of unique elements in component | 250 | 287 | 1 | 538 | |||

Intersection of elements with prior year | 214 | 36 | 1 | 251 | |||

Union of elements with prior year | 282 | 471 | 1 | 754 | |||

Intersection % | 75.9 | 7.6 | 100.0 | 33.3 | |||

Cumulative intersection since year 1 | 214 | 36 | 1 | 251 | |||

Cumulative union since year 1 | 282 | 471 | 1 | 754 | |||

Cumulative Intersection % | 75.9 | 7.6 | 100.0 | 33.3 | |||

3 | 0.286 | 0.302 | Number of non-unique elements in component | 2072 | 2072 | 2072 | 6216 |

Number of unique elements in component | 258 | 386 | 1 | 645 | |||

Intersection of elements with prior year | 226 | 39 | 1 | 266 | |||

Union of elements with prior year | 282 | 634 | 1 | 917 | |||

Intersection % | 80.1 | 6.2 | 100.0 | 29.0 | |||

Cumulative intersection since year 1 | 206 | 30 | 1 | 237 | |||

Cumulative union since year 1 | 308 | 816 | 1 | 1125 | |||

Cumulative Intersection % | 66.9 | 3.7 | 100.0 | 21.1 | |||

4 | 0.334 | 0.456 | Number of non-unique elements in component | 2758 | 2758 | 2758 | 8274 |

Number of unique elements in component | 279 | 607 | 1 | 887 | |||

Intersection of elements with prior year | 232 | 41 | 1 | 274 | |||

Union of elements with prior year | 305 | 952 | 1 | 1258 | |||

Intersection % | 76.1 | 4.3 | 100.0 | 21.8 | |||

Cumulative intersection since year 1 | 198 | 30 | 1 | 229 | |||

Cumulative union since year 1 | 330 | 1378 | 1 | 1709 | |||

Cumulative Intersection % | 60.0 | 2.2 | 100.0 | 13.4 | |||

5 | 0.284 | 0.535 | Number of non-unique elements in component | 3278 | 3278 | 3278 | 9834 |

Number of unique elements in component | 282 | 709 | 1 | 992 | |||

Intersection of elements with prior year | 241 | 45 | 1 | 287 | |||

Union of elements with prior year | 320 | 1271 | 1 | 1592 | |||

Intersection % | 75.3 | 3.5 | 100.0 | 18.0 | |||

Cumulative intersection since year 1 | 188 | 30 | 1 | 219 | |||

Cumulative union since year 1 | 354 | 2030 | 1 | 2385 | |||

Cumulative Intersection % | 53.1 | 1.5 | 100.0 | 9.2 | |||

6 | 0.243 | 0.562 | Number of non-unique elements in component | 4022 | 4022 | 4022 | 12,066 |

Number of unique elements in component | 300 | 943 | 1 | 1244 | |||

Intersection of elements with prior year | 254 | 47 | 1 | 302 | |||

Union of elements with prior year | 328 | 1605 | 1 | 1934 | |||

Intersection % | 77.4 | 2.9 | 100.0 | 15.6 | |||

Cumulative intersection since year 1 | 184 | 30 | 1 | 215 | |||

Cumulative union since year 1 | 367 | 2913 | 1 | 3281 | |||

Cumulative Intersection % | 50.1 | 1.0 | 100.0 | 6.6 |

nnex (95) | Bathurst Manor (34) | Bay Street Corridor (76) | Church-Yonge Corridor (75) | Danforth (66) | Junction Area (90) | Palmerston-Little Italy (80) | Waterfront Communities-The Island (77) | Wychwood | |
---|---|---|---|---|---|---|---|---|---|

x (95) | 0.994 | 0.443 | 0.37 | 0.917 | 0.883 | 0.623 | 0.585 | 0.874 | |

nor (34) | 0.996 | 0.995 | 0.958 | 0.969 | 0.988 | 0.997 | 0.968 | ||

Bay Street Corridor (76) | 0.338 | 0.942 | 0.921 | 0.739 | 0.425 | 0.914 | |||

Church-Yonge Corridor (75) | 0.933 | 0.908 | 0.697 | 0.482 | 0.897 | ||||

Danforth (66) | 0.505 | 0.823 | 0.958 | 0.602 | |||||

Junction Area (90) | 0.774 | 0.943 | 0.535 | ||||||

Palmerston-Little Italy (80) | 0.812 | 0.743 | |||||||

Waterfront Communities-The Island (77) | 0.938 | ||||||||

Wychwood (94) |

Exp # 11 | P | G | A | Total |
---|---|---|---|---|

Annex (95) | 246 | 220 | 1 | 467 |

Bathurst Manor (34) | 11 | 4 | 1 | 16 |

Intersection of elements | 6 | 2 | 1 | 9 |

Union of elements | 251 | 222 | 1 | 474 |

Intersection % | 2.4 | 0.9 | 100.0 | 1.9 |

Exp # 11-2 | P | G | A | Total |
---|---|---|---|---|

Annex (95) | 246 | 220 | 1 | 467 |

Waterfront Communities-The Island (77) | 313 | 418 | 1 | 732 |

Intersection of elements | 182 | 42 | 1 | 225 |

Union of elements | 377 | 596 | 1 | 974 |

Intersection % | 48.3 | 7.0 | 100.0 | 23.1 |

Exp # 11 | P | G | A | Total |
---|---|---|---|---|

Annex (95) | 246 | 220 | 1 | 467 |

Church-Yonge Corridor (75) | 259 | 257 | 1 | 517 |

Intersection of elements | 173 | 41 | 1 | 215 |

Union of elements | 332 | 436 | 1 | 769 |

Intersection % | 52.1 | 9.4 | 100.0 | 28.0 |

**Table 24.**Transversal Distances between Neighborhoods in Toronto and Montreal for Year 1–Aggregated Forms and Groups.

Annex (95) | Bathurst Manor (34) | Bay Street Corridor (76) | Lachine-Ouest | René-Lévesque | Sainte-Marie | |
---|---|---|---|---|---|---|

Annex (95) | 0.994 | 0.488 | 1.0 | 0.565 | 0.962 | |

Bathurst Manor (34) | 0.996 | 0.974 | 0.994 | 0.931 | ||

Bay Street Corridor (76) | 1.0 | 0.627 | 0.973 | |||

Lachine-Ouest | 0.999 | 0.994 | ||||

René-Lévesque | 0.952 | |||||

Sainte-Marie |

Exp # 12 | P | G | A | Total |
---|---|---|---|---|

Annex (T) | 258 | 766 | 1 | 1025 |

René-Lévesque (M) | 273 | 993 | 1 | 1267 |

Intersection of elements | 174 | 155 | 1 | 330 |

Union of elements | 357 | 1604 | 1 | 1962 |

Intersection % | 48.7 | 9.7 | 100.0 | 16.8 |

Intersection % in Annex (T) | 67.4 | 20.2 | 100.0 | 32.2 |

Intersection % in René-Lévesque (M) | 63.7 | 15.6 | 100.0 | 26.0 |

Exp # 12 | P | G | A | Total |
---|---|---|---|---|

Bay Street Corridor (76) | 327 | 1133 | 1 | 1461 |

René-Lévesque | 273 | 993 | 1 | 1267 |

Intersection of elements | 201 | 218 | 1 | 420 |

Union of elements | 399 | 1908 | 1 | 2308 |

Intersection % | 50.4 | 11.4 | 100.0 | 18.2 |

Intersection % in Annex (T) | 61.4 | 19.2 | 100.0 | 28.7 |

Intersection % in René-Lévesque (M) | 73.6 | 22.0 | 100.0 | 33.1 |

Year | Form (P) | Group (G) | ||
---|---|---|---|---|

Annex | Waterfront | Annex | Waterfront | |

2 | 75.9 | 80.7 | 7.6 | 4.1 |

3 | 66.9 | 69.2 | 3.7 | 1.9 |

4 | 60 | 65.5 | 2.2 | 0.7 |

5 | 53.1 | 61.6 | 1.5 | 0.7 |

6 | 50.1 | 56.2 | 1.0 | 0.5 |

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## Share and Cite

**MDPI and ACS Style**

Fox, M.S.; Silver, D.; Silva, T.; Zhang, X.
Towards a Model of Urban Evolution Part IV: Evolutionary (Formetic) Distance—An Interpretation of Yelp Review Data. *Urban Sci.* **2022**, *6*, 86.
https://doi.org/10.3390/urbansci6040086

**AMA Style**

Fox MS, Silver D, Silva T, Zhang X.
Towards a Model of Urban Evolution Part IV: Evolutionary (Formetic) Distance—An Interpretation of Yelp Review Data. *Urban Science*. 2022; 6(4):86.
https://doi.org/10.3390/urbansci6040086

**Chicago/Turabian Style**

Fox, Mark S., Daniel Silver, Thiago Silva, and Xinyi Zhang.
2022. "Towards a Model of Urban Evolution Part IV: Evolutionary (Formetic) Distance—An Interpretation of Yelp Review Data" *Urban Science* 6, no. 4: 86.
https://doi.org/10.3390/urbansci6040086