Mining knowledge-sharing sites for viral marketing

article2002KDD1,852 citations

Proposes a computationally efficient probabilistic framework to mine social influence from knowledge-sharing platforms and optimize continuous marketing spend across individuals while accounting for the costs of gathering network data.

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Traditional direct marketing targets customers based solely on their individual characteristics and expected purchase behavior. This conventional strategy overlooks the significant social influence that customers exert on one another's purchasing choices, often leading to suboptimal campaign decisions and missed profit opportunities in markets characterized by strong network effects. At the same time, earlier computational methods designed to optimize viral marketing were too computationally demanding to scale to large commercial audiences and were restricted to basic binary decisions, such as deciding whether or not to send a fixed promotion.

The article develops and evaluates a highly scalable, linear probabilistic framework to determine optimal viral marketing plans from online knowledge-sharing data. It specifically aims to optimize continuously variable marketing expenditures per customer while accounting for partial or costly network information.

To evaluate this framework, the authors analyzed real-world data from the consumer review site Epinions, utilizing a network of over 75,000 users and 500,000 trust relationships within the "Kids & Family" category. By formulating customer interactions as a linear model, the authors derived a closed-form calculation of each individual's total influence across the network, known as the network effect. This method was compared against traditional direct marketing and earlier non-linear viral models across several cost structures, continuous expenditure levels, and simulated conditions of incomplete network knowledge.

The analysis produced several critical findings. First, viral marketing consistently outperformed direct marketing across all test scenarios, generating substantially higher profits; notably, at higher marketing costs where direct marketing chose to market to nobody, viral marketing remained profitable. Second, the linear formulation dramatically reduced computational time from approximately 100 hours required by previous search methods to just 1.05 seconds, enabling scalability to customer bases of hundreds of millions. Third, enabling continuously variable marketing expenditures increased profits by up to 41% compared to binary marketing by tailoring investment to individual responsiveness. Fourth, the model proved exceptionally robust to missing data: having knowledge of only 5% of network connections captured approximately 69% of the maximum potential profit increase over direct marketing. Finally, when acquiring network data under a constrained research budget, prioritizing queries toward customers with the highest observed network effect produced up to tenfold greater profit lift compared to random surveying.

These findings indicate that organizations can significantly lower customer acquisition costs and increase promotional returns by incorporating social network value into their marketing models. Because the influence distribution follows a highly skewed power law, marketing budgets can be concentrated on a small fraction of influential nodes to drive widespread organic adoption across the rest of the customer base. Furthermore, the immense computational efficiency of the linear formulation allows enterprises to perform real-time optimization without requiring costly high-performance computing infrastructure.

Organizations operating in peer-influenced markets should transition from strictly demographic-based direct marketing to influence-aware viral strategies. When customer relationship maps are absent, companies should actively invest limited market research funds to uncover connections starting with the most central, high-influence individuals. For scalable execution, practitioners should query candidates in batches (such as groups of 100), which yields virtually identical profit performance at a fraction of the computational and operational overhead.

Decision-makers should consider several limitations and exercise appropriate caution. The empirical validation relied on a single product category, treated consumer reviews as a proxy for product purchases, and assumed equal influence among all trusted peers. Additionally, the model assumes marketing revenue is constant across interventions; scenarios involving steep price discounts may introduce minor profit overestimations between 1% and 10%. Nevertheless, confidence in the overarching findings remains high, as the qualitative superiority and robustness of the viral optimization framework hold firmly across varying network densities and cost assumptions.

University of Washington association rules binary decision computational efficiency viral marketing knowledge-sharing sites collaborative filtering

Richardson et al (2002).pdf

Paper: Mining the network value of customers, Pedro M. Domingos et al. (2001). This foundational paper introduced the concept of customer network value and the core probabilistic modeling framework that the source explicitly extends to continuous marketing spend and partial network knowledge.
Paper: Item-based collaborative filtering recommendation algorithms, Badrul Sarwar et al. (2001). It provides the foundational collaborative filtering methodology for modeling customer preferences and relationships that underpins data mining on knowledge-sharing and product review sites.
Paper: Empirical Analysis of Predictive Algorithms for Collaborative Filtering, John S. Breese et al. (1998). It establishes key probabilistic and model-based algorithms for learning user preferences from sparse review and rating data essential for mining customer networks.

Paper: Maximizing the spread of influence through a social network, David Kempe et al. (2003). This seminal work builds directly on Domingos and Richardson's viral marketing formulation by formalizing influence maximization under submodular cascade models with provable greedy approximation guarantees.
Paper: Cost-effective outbreak detection in networks, J. Leskovec et al. (2007). It develops the CELF algorithm for submodular optimization under arbitrary node costs, extending the budgeted viral marketing problem explored in the source.
Paper: Efficient influence maximization in social networks, Wei Chen et al. (2009). It advances scalable influence maximization algorithms and heuristic evaluations to overcome the computational bottlenecks of viral marketing in large-scale social networks.
Paper: Everyone's an influencer: quantifying influence on twitter, Eytan Bakshy et al. (2011). It evaluates the empirical predictability and cost-effectiveness of influencer-based viral marketing strategies on large-scale real-world social network diffusion cascades.
Paper: Group formation in large social networks: membership, growth, and evolution, L. Backstrom et al. (2006). It examines structural determinants of social contagion and group formation in digital networks, offering an empirical basis for the influence mechanisms modeled in viral marketing.

Cover for Mining knowledge-sharing sites for viral marketing

Abstract

Viral marketing takes advantage of networks of influence among customers to inexpensively achieve large changes in behavior. Our research seeks to put it on a firmer footing by mining these networks from data, building probabilistic models of them, and using these models to choose the best viral marketing plan. Knowledge-sharing sites, where customers review products and advise each other, are a fertile source for this type of data mining. In this paper we extend our previous techniques, achieving a large reduction in computational cost, and apply them to data from a knowledge-sharing site. We optimize the amount of marketing funds spent on each customer, rather than just making a binary decision on whether to market to him. We take into account the fact that knowledge of the network is partial, and that gathering that knowledge can itself have a cost. Our results show the robustness and utility of our approach.

Topics

association rules binary decision computational efficiency knowledge-sharing probabilistic models viral marketing customer review network architecture knowledge discovery

Keywords

viral marketing knowledge-sharing sites collaborative filtering social network knowledge discovery probabilistic models heuristic search data mining

1. INTRODUCTION
2. THE MODEL
3. INFERENCE AND SEARCH
4. MINING KNOWLEDGE-SHARING SITES
5. EXPERIMENTS
5.1 Profits and Network Values
5.2 Speed
5.3 Continuous Marketing Actions
5.4 Incomplete Network Knowledge
5.4.1 Viral marketing is robust
5.4.2 Acquiring new network knowledge
6. RELATED WORK
7. FUTURE WORK
8. CONCLUSION
9. ACKNOWLEDGEMENTS
10. REFERENCES
11. APPENDIX

Knowls

Knowl 1 — Linear Probabilistic Model of Network Customer Influence
model/method
Let a market consist of $n$ potential customers, where $X_i \in \{0, 1\}$ is a Boolean random variable indicating whether customer $i$ purchases a product described by an attribute vector $\mathbf{Y}$ . Let $M_i$ denote the marketing action targeted at customer $i$ , and let $\mathbf{M} = (M_1, \dots, M_n)$ be the global marketing plan. Customer $i$ has a set of neighbors $N_i \subseteq \{X_1, \dots, X_n\} \setminus \{X_i\}$ who directly influence them, with non-negative influence weights $w_{ij} \ge 0$ satisfying $\sum_{X_j \in N_i} w_{ij} = 1$ (and $w_{ij} = 0$ if $j \notin N_i$ ).

The probability that customer $i$ purchases the product combines an intrinsic internal probability $P_0(X_i = 1 \mid \mathbf{Y}, M_i)$ and a linear combination of neighbor purchasing probabilities:

$P(X_i = 1 \mid \mathbf{Y}, \mathbf{M}) = \beta_i P_0(X_i = 1 \mid \mathbf{Y}, M_i) + (1 - \beta_i) \sum_{X_j \in N_i} w_{ij} P(X_j = 1 \mid \mathbf{Y}, \mathbf{M})$

where $\beta_i \in [0, 1]$ is a self-reliance coefficient parameterizing customer $i$ 's independence from social influence. This self-referential linear system can be solved iteratively to compute all global adoption probabilities $P(X_i = 1 \mid \mathbf{Y}, \mathbf{M})$ starting from initial values $P^{(0)}(X_i = 1 \mid \mathbf{Y}, \mathbf{M}) = P_0(X_i = 1 \mid \mathbf{Y}, M_i)$ .
Knowl 2 — Customer Network Effect and Fixed-Point Recurrence
theoretical result
The network effect $\Delta_i(\mathbf{Y})$ of customer $i$ for a product with attributes $\mathbf{Y}$ is defined as the total marginal change in purchase probability across the entire network (including customer $i$ ) resulting from a unit change in customer $i$ 's intrinsic probability $P_0(X_i = 1 \mid \mathbf{Y}, M_i)$ under the unmarketed null plan $\mathbf{M}_0 = (0, \dots, 0)$ :

$\Delta_i(\mathbf{Y}) = \sum_{j=1}^n \frac{\partial P(X_j = 1 \mid \mathbf{Y}, \mathbf{M}_0)}{\partial P_0(X_i = 1 \mid \mathbf{Y}, M_i)}$

Because the underlying influence propagation is linear, $\Delta_i(\mathbf{Y})$ is independent of the marketing actions applied to other customers and satisfies the recurrence relation:

$\Delta_i^{(k)}(\mathbf{Y}) = \sum_{j=1}^n (1 - \beta_j) w_{ji} \Delta_j^{(k-1)}(\mathbf{Y})$

initialized with $\Delta_i^{(0)}(\mathbf{Y}) = 1$ for all $i \in \{1, \dots, n\}$ , where $w_{ji}$ represents the influence customer $i$ exerts on neighbor $j$ , and $\beta_j$ is customer $j$ 's self-reliance parameter. Evaluating this recurrence until convergence requires $O(|E|)$ operations per iteration, where $|E|$ is the number of non-zero directed influence edges in the social network, and empirically reaches a fixed point within 10 to 20 iterations. The calculation is mathematically equivalent to computing the dominant eigenvector of the transposed influence matrix, analogous to PageRank on the reversed influence graph.
Knowl 3 — Optimal Continuous Marketing Action under Diminishing Returns
model/method
When marketing intensity is a continuous decision variable $M_i = z \in [0, 1]$ (where $z=0$ represents no marketing action), the cost of marketing is modeled as $c(z) = c_1 z$ with constant marginal cost $c_1 > 0$ . The marketing intervention scales the customer's baseline purchasing probability via an exponentially asymptotic diminishing-returns function:

$P_0(X_i = 1 \mid \mathbf{Y}, M_i = z) = \alpha(z) P_0(X_i = 1 \mid \mathbf{Y}, M_i = 0)$

$\alpha(z) = \alpha_\infty + (1 - \alpha_\infty) e^{-\lambda z}$

where $\alpha_\infty > 1$ is the asymptotic multiplier achievable as $z \to \infty$ , and $\lambda > 0$ controls the rate of convergence $(\alpha(0) = 1)$ .

The immediate change in customer $i$ 's purchasing probability is $\Delta P_i(z, \mathbf{Y}) = \beta_i (\alpha(z) - 1) P_0(X_i = 1 \mid \mathbf{Y}, M_i = 0)$ , where $\beta_i$ is customer $i$ 's self-reliance. Under a constant revenue per sale $r$ , the total expected lift in profit across the network is:

$ELP_{i, \text{total}}^z(\mathbf{Y}, \mathbf{M}) = r \Delta_i(\mathbf{Y}) \Delta P_i(z, \mathbf{Y}) - c(z)$

Setting $\frac{d}{dz} ELP_{i, \text{total}}^z(\mathbf{Y}, \mathbf{M}) = 0$ yields a closed-form unique global maximum for the optimal continuous marketing allocation $z_i^*$ :

$z_i^* = \max\left(0, \min\left(1, -\frac{1}{\lambda} \ln \left( \frac{c_1}{r \Delta_i(\mathbf{Y}) \beta_i \lambda (\alpha_\infty - 1) P_0(X_i = 1 \mid \mathbf{Y}, M_i = 0)} \right)\right)\right)$
Knowl 4 — Active Network Knowledge Acquisition Algorithm
algorithm
When social network connectivity is initially unknown or incomplete, a marketer with a fixed research budget can iteratively acquire neighbor relationships by querying users. Because customers with high network effects exert the largest total influence on the market, discovering their outgoing trust edges yields the highest expected increase in profit lift.
Input: Set of customers $V = \{1, \dots, n\}$ , observed edge set $E_{obs}$ , query budget $B$ , batch size $K$ , product attributes $\mathbf{Y}$ , model parameters $\beta, c_1, r, \alpha_\infty, \lambda$
Output: Recommended marketing plan $\mathbf{M}^* = (z_1^*, \dots, z_n^*)$
$Q \leftarrow \emptyset$
while $|Q| < B$ do
    for each $i \in V$ do
        Compute $\Delta_i(\mathbf{Y})$ on the graph $(V, E_{obs})$ via fixed-point iteration
    end for
     $S \leftarrow$ top $\min(K, B - |Q|)$ customers in $V \setminus Q$ ranked by $\Delta_i(\mathbf{Y})$ in descending order
    for each $u \in S$ do
        Query customer $u$ to reveal their trusted neighbor set $N_u$
        for each $v \in N_u$ do
             $E_{obs} \leftarrow E_{obs} \cup \{(u, v)\}$
        end for
         $Q \leftarrow Q \cup \{u\}$
    end for
end while
for each $i \in V$ do
    Compute final network effect $\Delta_i(\mathbf{Y})$ on $(V, E_{obs})$
     $z_i^* \leftarrow \max\left(0, \min\left(1, -\frac{1}{\lambda} \ln \left( \frac{c_1}{r \Delta_i(\mathbf{Y}) \beta_i \lambda (\alpha_\infty - 1) P_0(X_i = 1 \mid \mathbf{Y}, M_i = 0)} \right)\right)\right)$
end for
return $\mathbf{M}^* = (z_1^*, \dots, z_n^*)$
Querying customers in batches of $K = 100$ runs 100 times faster than querying individuals one at a time, with an average profit lift penalty of only 0.008.

Knowl 5 — Profit Comparison Across Marketing Strategies and Costs

data/table

The table compares global expected profits across marketing strategies on the Epinions dataset (category 'Kids & Family') under varying marketing cost parameters ( $c$ for Boolean actions, $c_1$ for continuous actions) with baseline parameters $\alpha = 2$ (or $\alpha_\infty = 2$ , $\lambda = 5$ ), unit revenue $r_0 = r_1 = r(z) = 1$ , and self-reliance $\beta_i = 0.5$ .

Marketing Scenario	$c=0.1$ ( $c_1=0.1$ )	$c=0.01$ ( $c_1=0.01$ )	$c=0.001$ ( $c_1=0.001$ )
No Marketing	37.78	37.78	37.78
Direct Marketing (Boolean)	37.78	42.71	66.08
Viral Marketing (Boolean)	47.25	60.54	70.23
Direct Marketing (Continuous)	37.84	51.71	68.38
Viral Marketing (Continuous)	51.14	63.23	71.28
Lift over Boolean Viral Marketing	3.89 (41.08%)	2.69 (11.82%)	1.05 (3.24%)

When the marketing cost is a large fraction of revenue ( $c = 0.1$ ), direct marketing chooses to market to nobody because individual purchase probabilities are too low to offset marketing cost in isolation. Viral marketing generates substantially higher profits by accounting for network value. Continuous marketing actions consistently outperform Boolean actions across all cost settings because continuous optimization tailors the spend per customer to balance marginal cost against diminishing marginal returns.

Knowl 6 — Robustness of Viral Marketing to Incomplete Network Knowledge
empirical result
When social network edges are missing uniformly at random, viral marketing remains robust and retains most of its profit advantages over direct marketing:
1. Knowing only 5% of the total network edges allows the viral marketing optimization algorithm to capture 69% of the full-knowledge profit lift over direct marketing.
2. The expected profit lift estimated by the algorithm on a partial network systematically underestimates the actual lift realized when the marketing plan is executed on the complete real-world network.
This robustness arises because uniform random edge removal preserves the relative ranking of customer connectivity and network effects: nodes with high network value in the subsampled network remain high-value nodes in the true full graph.
Knowl 7 — Skewed Distribution of Customer Network Values in Knowledge-Sharing Networks
empirical result
On the Epinions web of trust (comprising 75,888 users and approximately 500,000 directed trust edges), the distribution of customer network values is highly skewed and follows a Zipfian power-law distribution. A small minority of users possess disproportionately large network influence, while the vast majority have negligible network value.

For example, the single highest-value user in the dataset has a normalized network value of 22,000 (meaning marketing to this individual produces an expected revenue lift equivalent to marketing to 22,000 average customers in isolation without costs), directly influences 784 users, and exhibits a baseline purchasing probability of 0.03 (23 times the population average). This extreme concentration of influence enables viral marketing to achieve broad network adoption by targeting only a small, highly influential subset of users.
Knowl 8 — Computational Scalability of the Linear Viral Marketing Model
empirical result
The linear formulation of social influence decouples the calculation of customer network effects from the specific marketing decisions applied to other nodes. As a result, finding the optimal marketing plan does not require heuristic combinatorial search over the space of joint plans.

On the full Epinions network of 75,888 customers, the linear model computes the globally optimal marketing plan in 1.05 seconds. Under equivalent conditions, non-linear influence models require approximately 100 hours using single-pass heuristic search, or 10 to 15 minutes when employing inference approximations. The linear model's per-iteration computational complexity scales linearly with the number of non-zero edges in the influence graph.
Knowl 9 — Degeneracy of Continuous Marketing under Linear Response Functions
theoretical result
If the marketing response function $\alpha(z)$ is strictly linear in the marketing action $z$ (i.e., $\alpha(z) = \alpha z$ ) and marketing cost is linear ( $c(z) = c_1 z$ ), continuous-valued marketing optimization mathematically degenerates to Boolean marketing ( $z_i^* \in \{0, 1\}$ ).

Under linear response and linear cost, the marginal net profit with respect to $z$ is constant for any customer. If the expected marginal benefit of marketing to customer $i$ exceeds the marginal cost at any $z > 0$ , it exceeds the cost for all $z$ , making the boundary value $z = 1$ strictly optimal. If marginal cost exceeds marginal benefit, $z = 0$ is optimal. Consequently, non-linear diminishing returns functions (such as exponential asymptotic functions) are necessary for continuous marketing allocations to yield non-trivial intermediate marketing levels.
Knowl 10 — Profit Overestimation for Price Discounts in Linear Viral Marketing
limitation
The closed-form decoupling of customer network effects assumes a constant unit revenue $r(z) = r$ . In marketing campaigns where the marketing action involves a price discount, unit revenue decreases with marketing intensity ( $r_1 < r_0$ or $r'(z) < 0$ ).

When unit revenue is decreasing, the linear model overestimates the revenue generated by downstream network adoptions, which can lead to a slightly sub-optimal marketing plan. Empirically, this overestimation error ranges between 1% and 10% of total profits, though the resulting marketing plan still consistently outperforms direct marketing.

Coverage note — None was omitted; all key theoretical models, optimization formulas, algorithms, empirical results, dataset characteristics, and limitations were captured.

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Citation

MLA

Richardson, M., and P. Domingos. “Mining Knowledge-sharing Sites for Viral Marketing”. Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2002, pp. 61–70, https://doi.org/10.1145/775047.775057.

APA

Richardson, M., & Domingos, P. (2002). Mining knowledge-sharing sites for viral marketing. Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 61–70. https://doi.org/10.1145/775047.775057

Chicago

Richardson, M., and P. Domingos. 2002. “Mining Knowledge-sharing Sites for Viral Marketing”. Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 61–70. https://doi.org/10.1145/775047.775057.

Harvard

Richardson, M. and Domingos, P. (2002) “Mining knowledge-sharing sites for viral marketing”, Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp. 61–70. Available at: https://doi.org/10.1145/775047.775057.

Vancouver

1. Richardson M, Domingos P (2002) Mining knowledge-sharing sites for viral marketing. In: Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 61–70

BibTeX

@inproceedings{Richardson_2002, series={KDD02}, title={Mining knowledge-sharing sites for viral marketing}, url={http://dx.doi.org/10.1145/775047.775057}, DOI={10.1145/775047.775057}, booktitle={Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining}, publisher={ACM}, author={Richardson, Matthew and Domingos, Pedro}, year={2002}, month=July, pages={61–70}, collection={KDD02} }

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Mining knowledge-sharing sites for viral marketing

Abstract

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Knowls

Knowl 1 — Linear Probabilistic Model of Network Customer Influence

Knowl 2 — Customer Network Effect and Fixed-Point Recurrence

Knowl 3 — Optimal Continuous Marketing Action under Diminishing Returns

Knowl 4 — Active Network Knowledge Acquisition Algorithm

Knowl 5 — Profit Comparison Across Marketing Strategies and Costs

Knowl 6 — Robustness of Viral Marketing to Incomplete Network Knowledge

Knowl 7 — Skewed Distribution of Customer Network Values in Knowledge-Sharing Networks

Knowl 8 — Computational Scalability of the Linear Viral Marketing Model

Knowl 9 — Degeneracy of Continuous Marketing under Linear Response Functions

Knowl 10 — Profit Overestimation for Price Discounts in Linear Viral Marketing

References

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