# Advanced Industry Specialization (Product Complexity Index, PCI)

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<summary>Definition</summary>

The Advanced Industry Specialization metric measures how specialized and advanced a region’s industries are, based on the knowledge, skills, and technology required to produce their goods and services. High specialization reflects industries that are innovation-driven, highly competitive, and difficult to replicate—such as aerospace or biotech. Rather than measuring whether an industry is simply better, PCI captures how distinct or unique it is within the broader economic landscape. Regions with strong industry specialization attract R\&D investment, drive technological progress, and enhance global competitiveness.

Compared to the other Economic Strategy KPIs, PCI focuses on quality of knowledge—revealing which industries require deep specialization, advanced technologies, or unique combinations of capabilities.

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<summary>Navigation</summary>

The main map view displays anonymized businesses as geolocated nodes, color-coded by their NAICS sector and sized by revenue. In the Advanced Industry Specialization module, color intensity reflects specialization:

* Blue = High complexity (specialized, innovation-intensive industries)
* Red = Low complexity (common, less specialized sectors)

Selecting a business or sector on the map reveals its 6-digit NAICS classification, PCI score, and filters the sidebar visualizations by the city it is located in:

1. Specialization Treemap - Displays sectors by size (revenue in euro) and PCI score (blue to red gradient). Clicking a box highlights that sector across all views.
2. Specialization Positioning Chart (Growth Readiness vs. Specialization) - Plots each industry by Industry Growth Readiness (PDI, x-axis) and Advanced Specialization (PCI, y-axis), following four-quadrant analysis.
   1. Top-right (Q1): Thriving sectors – complex and well-integrated
   2. Bottom-right (Q2): Traditional sectors – embedded but less complex
   3. Top-left (Q3): Emerging sectors – complex but less established
   4. Bottom-left (Q4): At-risk sectors – low complexity and low integration
3. Specialization Network Map - Shows how highly specialized (blue) or less complex (red) businesses cluster across the city. Well-positioned sectors tend to cluster centrally.

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<summary>Methodology</summary>

The PCI score is calculated using a data-driven model of economic activity across cities, measuring how uniquely an industry appears and coexists with others in different urban contexts.

1. Economic Presence Matrix Creation – Construct a binary matrix that indicates whether each industry is present in each city based on business activity data.
2. Diversity and Ubiquity Calculation – Compute how many industries each city has (diversity) and how many cities host each industry (ubiquity).
3. Industry Co-occurrence Mapping – Compare all pairs of industries to determine how often they appear together in the same cities, normalized by the diversity of those cities and the ubiquity of the industries.
4. Complexity Inference – Industries that appear mostly in diverse cities with other rare industries are assigned higher complexity scores.
5. Sector Score Assignment – Each NAICS-coded industry is assigned a PCI value, which is used to color business nodes across the map and drive positioning in the platform’s strategic quadrant analysis.

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<summary>Calculation</summary>

$$M^{P}*{p, p'} = \sum*{c} \frac{M\_{cp} \cdot M\_{cp'}}{\kappa\_{c,0} \cdot \kappa\_{p,0}}$$

Where:

* $$M\_{cp}$$ = Binary value indicating whether industry p is present in city c
* $$\kappa\_{c,0} = \sum\_{p} M\_{cp}$$= Number of industries in city c (diversity)
* $$\kappa\_{p,0} = \sum\_{c} M\_{cp}$$ = Number of cities where industry p is present (ubiquity)
* $$M^{P}\_{p, p'}$$ =  Normalized co-occurrence value between industries p and p’

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<summary>Interpretation</summary>

High PCI scores represent industries that are rare and typically found in economically diverse, innovation-driven environments. These sectors tend to:

* Require specialized knowledge, talent, and infrastructure
* Drive research, development, and technological advancement
* Anchor long-term competitiveness and global differentiation

Low PCI scores represent common, easily replicable sectors with lower specialization requirements. These may still play essential roles but offer less strategic economic leverage. This metric can be used to prioritize high-value industries for investment, R\&D, and urban strategy—especially when planning innovation districts or identifying anchor sectors.

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