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Abstract Understanding relationships between different products in a market system and predicting how changes in design impact their market position can be instrumental for companies to create better products. We propose a graph neural network-based method for modeling relationships between products, where nodes in a network represent products and edges represent their relationships. Our modeling enables a systematic way to predict the relationship links between unseen products for future years. When applied to a Chinese car market case study, our method based on an inductive graph neural network approach, GraphSAGE, yields double the link prediction performance compared to an existing network modeling method—exponential random graph model-based method for predicting the car co-consideration relationships. Our work also overcomes scalability and multiple data type-related limitations of the traditional network modeling methods by modeling a larger number of attributes, mixed categorical and numerical attributes, and unseen products. While a vanilla GraphSAGE requires a partial network to make predictions, we augment it with an “adjacency prediction model” to circumvent the limitation of needing neighborhood information. Finally, we demonstrate how insights obtained from a permutation-based interpretability analysis can help a manufacturer understand how design attributes impact the predictions of product relationships. Overall, this work provides a systematic data-driven method to predict the relationships between products in a complex network such as the car market. 

Statistical network models have been used to study the competition among different products and how product attributes influence customer decisions. However, in existing research using network-based approaches, product competition has been viewed as binary (i.e., whether a relationship exists or not), while in reality, the competition strength may vary among products. In this paper, we model the strength of the product competition by employing a statistical network model, with an emphasis on how product attributes affect which products are considered together and which products are ultimately purchased by customers. We first demonstrate how customers’ considerations and choices can be aggregated as weighted networks. Then, we propose a weighted network modeling approach by extending the valued exponential random graph model to investigate the effects of product features and network structures on product competition relations. The approach that consists of model construction, interpretation, and validation is presented in a step-by-step procedure. Our findings suggest that the weighted network model outperforms commonly used binary network baselines in predicting product competition as well as market share. Also, traditionally when using binary network models to study product competitions and depending on the cutoff values chosen to binarize a network, the resulting estimated customer preferences can be inconsistent. Such inconsistency in interpreting customer preferences is a downside of binary network models but can be well addressed by the proposed weighted network model. Lastly, this paper is the first attempt to study customers’ purchase preferences (i.e., aggregated choice decisions) and car competition (i.e., customers’ co-consideration decisions) together using weighted directed networks. 

Graph representation learning has revolutionized many artificial intelligence and machine learning tasks in recent years, ranging from combinatorial optimization, drug discovery, recommendation systems, image classification, social network analysis to natural language understanding. This paper shows their efficacy in modeling relationships between products and making predictions for unseen product networks. By representing products as nodes and their relationships as edges of a graph, we show how an inductive graph neural network approach, named GraphSAGE, can efficiently learn continuous representations for nodes and edges. These representations also capture product feature information such as price, brand, and engineering attributes. They are combined with a classification model for predicting the existence of a relationship between any two products. Using a case study of the Chinese car market, we find that our method yields double the F-1 score compared to an Exponential Random Graph Model-based method for predicting the co-consideration relationship between cars. While a vanilla Graph-SAGE requires a partial network to make predictions, we augment it with an ‘adjacency prediction model’ to circumvent this limitation. This enables us to predict product relationships when no neighborhood information is known. Finally, we demonstrate how a permutation-based interpretability analysis can provide insights on how design attributes impact the predictions of relationships between products. Overall, this work provides a systematic method to predict the relationships between products in a complex engineering system.

 

Abstract Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: an imbalanced dataset containing more of certain shapes or physical properties can be detrimental to the efficacy of data-driven approaches. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that (1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property spaces and (2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET allows the trade-off between shape and property diversity so that subsets can be tuned for various applications. Through the design of 2D metamaterials with target displacement profiles, we demonstrate that smaller, diverse subsets can indeed improve the search process as well as structural performance. By eliminating inherent overlaps in a dataset of 3D unit cells created with symmetry rules, we also illustrate that our flexible method can distill unique subsets regardless of the metric employed. Our diverse subsets are provided publicly for use by any designer. 

Abstract Collaborative work often benefits from having teams or organizations with heterogeneous members. In this paper, we present a method to form such diverse teams from people arriving sequentially over time. We define a monotone submodular objective function that combines the diversity and quality of a team and proposes an algorithm to maximize the objective while satisfying multiple constraints. This allows us to balance both how diverse the team is and how well it can perform the task at hand. Using crowd experiments, we show that, in practice, the algorithm leads to large gains in team diversity. Using simulations, we show how to quantify the additional cost of forming diverse teams and how to address the problem of simultaneously maximizing diversity for several attributes (e.g., country of origin and gender). Our method has applications in collaborative work ranging from team formation, the assignment of workers to teams in crowdsourcing, and reviewer allocation to journal papers arriving sequentially. Our code is publicly accessible for further research. 

Abstract Design researchers have long sought to understand the mechanisms that support creative idea development. However, one of the key challenges faced by the design community is how to effectively measure the nebulous construct of creativity. The social science and engineering communities have adopted two vastly different approaches to solving this problem, both of which have been deployed throughout engineering design research. The goal of this paper was to compare and contrast these two approaches using design ratings of nearly 1000 engineering design ideas. The results of this study identify that while these two methods provide similar ratings of idea quality, there was a statistically significant negative relationship between these methods for ratings of idea novelty. In addition, the results show discrepancies in the reliability and consistency of global ratings of creativity. The results of this study guide the deployment of idea ratings in engineering design research and evidence. 

Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: An imbalanced dataset containing more of certain shapes or physical properties than others can be detrimental to the efficacy of the approaches and any models built on those sets. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that 1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property space, and 2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET allows the trade-off between shape and property diversity so that subsets can be tuned for various applications. Through the design of 2D metamaterials with target displacement profiles, we demonstrate that smaller, diverse subsets can indeed improve the search process as well as structural performance. We also apply METASET to eliminate inherent overlaps in a dataset of 3D unit cells created with symmetry rules, distilling it down to the most unique families. Our diverse subsets are provided publicly for use by any designer.

 

Statistical network models allow us to study the co-evolution between the products and the social aspects of a market system, by modeling these components and their interactions as graphs. In this paper, we study competition between different car models using network theory, with a focus on how product attributes (like fuel economy and price) affect which cars are considered together and which cars are finally bought by customers. Unlike past work, where most systems have been studied with the assumption that relationships between competitors are binary (i.e., whether a relationship exists or not), we allow relationships to take strengths (i.e., how strong a relationship is). Specifically, we use valued Exponential Random Graph Models and show that our approach provides a significant improvement over the baselines in predicting product co-considerations as well as in the validation of market share. This is also the first attempt to study aggregated purchase preference and car competition using valued directed networks.

 

Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. Traditionally, the primary goal of such models is to maximize a linear function of the constituent matches (e.g., linear social welfare maximization) subject to some constraints. Recent work has studied a new goal of balancing whole-match diversity and economic efficiency, where the objective is instead a monotone submodular function over the matching. Basic versions of this problem are solvable in polynomial time. In this work, we prove that the problem of simultaneously maximizing diversity along several features (e.g., country of citizenship, gender, skills) is NP-hard. To address this problem, we develop the first combinatorial algorithm that constructs provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide a Mixed-Integer Quadratic formulation for the same problem and show that our method guarantees optimal solutions and takes less computation time for a reviewer assignment application. The source code is made available at https://github.com/faezahmed/diverse_matching.