Implementing a concept network model

Abstract

The same concept can mean different things or be instantiated in different forms, depending on context, suggesting a degree of flexibility within the conceptual system. We propose that a feature-based network model can be used to capture and predict this flexibility. We modeled individual concepts (e.g., BANANA, BOTTLE) as graph-theoretical networks, in which properties (e.g., YELLOW, SWEET) were represented as nodes and their associations as edges. In this framework, networks capture within-concept statistics that reflect how properties relate to one another across instances of a concept. We extracted formal measures of these networks that capture different aspects of network structure, and explored whether a concept's network structure relates to its flexibility of use. To do so, we compared network measures to a text-based measure of semantic diversity, as well as to empirical data from a figurative-language task and an alternative-uses task. We found that network-based measures were predictive of the text-based and empirical measures of flexible concept use, highlighting the ability of this approach to formally capture relevant characteristics of conceptual structure. Conceptual flexibility is a fundamental attribute of the cognitive and semantic systems, and in this proof of concept we reveal that variations in concept representation and use can be formally understood in terms of the informational content and topology of concept networks.

Keywords: Conceptual flexibility; Conceptual knowledge; Network science.

Figures

Fig 1:. A visualization of network topologies and measures.

Networks are defined in terms of nodes (circles) and edges (lines). Network topologies fall into three main categories: (A) regular, (B) small-world, and (C) random (Watts & Strogatz, 1998). Most naturally evolving networks exhibit small-world topology, including neural networks and language networks. Regular and small-world networks have high clustering. (D) Modularity reflects the extent to which a network can be partitioned into a set of densely-connected “modules”, represented here in distinct colors. (E) Some nodes participate in multiple modules, reflecting a diversity of connections: this is captured in a “diversity coefficient.” A diverse node (yellow) participates in multiple modules (green, purple), whereas other nodes (grey) do not exhibit these diverse connections. (F) A network has strong core-periphery structure if it can be characterized in terms of a single densely-connected “core” (yellow) and a sparsely-connected “periphery” (grey).

Fig 2:. Visualizing the Chocolate Network.

(A) The chocolate concept can be broken down into a range of subordinates, which can each be defined as a property vector (columns). Each property can also be defined as a vector (rows), which can be used to calculate within-concept property relationships. Only a small set of subordinates and properties are shown here for simplicity. (B) A simple schematic of the chocolate network that reveals a selection of potential property relationships. Certain properties might cluster together in the chocolate network, for example edible, sweet, brown, creamy, and messy, liquid, hot. (C) The actual chocolate network we constructed based on the empirical property statistics. Our constructed chocolate network was binarized (threshold=90%) in order to reduce the number of properties to ease visualization. Properties are arranged in order of degree (number of links), from low degree (white) to high degree (blue). Image generated using cytoscape (Shannon et al., 2003).

Figure 3:. Example images used to generate test data in classification analysis.

Test data used in the classification analysis were generated from participants who made property judgments on images of conceptual exemplars. Yellow cross indicates object to be considered. Example images for grass (top) and cookie (bottom).

Figure 4:. Simile Ratings.

The relationship between simile meaningfulness and familiarity ratings for target similes (blue) and control similes. As expected, the high-apt control similes (red) were rated as more meaningful than the moderate-apt control similes (pink). The range of meaningfulness and familiarity ratings for our target similes subsumes the range of the control similes. Since meaningfulness and familiarity were highly correlated, we averaged these measures to create a single measure of simile goodness.

Figure 5:. Classification results.

We ran a range of classification analyses using different numbers of eigen-dimensions from our concept networks. Classification was successful using ≥ 1 dimensions in both Set 1 and Set 2. Classification performance increased as more dimensions were added, such that performance of the network-models reached performance of the vector-based models (single data points).

Figure 6:. Network predictors of Semantic Diversity.

Semantic diversity measures calculated using word co-occurrence statistics (Hoffman et al., 2013) were (A) positively predicted by core-periphery structure (r=0.71, p=0.003), and (B) negatively predicted by network clustering (r=−0.70, p=0.004).

Figure 7:. Results of bootstrap analyses.

(A) Distributions of correlations between SemD and network measures when multiple networks are constructed using subsets of (A) subordinates or (B) properties. The positive relationship between core-periphery structure and SemD is robust to variations in subordinates and properties; the negative relationship between network clustering and SemD is robust to variations in subordinates and properties.

Figure 8:. Network predictors of creative concept use.

(A) Network diversity positively predicted the goodness of similes including the target concept in the vehicle position. (B) Network diversity negatively predicted the creativity of initial responses in an alternative use task.

Fig 9:. Predicting Conceptual Combination.

(A) The within-concept feature statistics of banana are encoded in its concept network. These data can also be used to define a transition probability matrix that encodes the probabilities that activation will spread from one node to another. We can use these data in a (e.g., random walk) spreading activation model in order to predict network states in different contexts. For example, we can predict the state of the banana network during adjective-noun combinations: here the adjectives “green” and “soft” are represented as single-node activations. (B) Activating a single node will cause the spread of activation throughout the network according to the transition probabilities. For example, activating the green node (in “green banana”) will likely cause activation of firm and sweet (top), whereas activating the soft node (in “soft banana”) will likely cause activation of brown and sweet (bottom). Thus, the structure of the banana network enables the activation of a range of states, subsequently generating varied, yet appropriate, representations of bananas.