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Forecasting success via early adoptions analysis: A data-driven study

  • Giulio Rossetti ,

    Roles Conceptualization, Data curation, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – original draft

    giulio.rossetti@isti.cnr.it

    Affiliation Knowledge Discovery and Data Mining Laboratory, ISTI-CNR, Pisa, Italy

  • Letizia Milli,

    Roles Investigation, Methodology, Software, Validation, Visualization, Writing – original draft

    Affiliations Knowledge Discovery and Data Mining Laboratory, ISTI-CNR, Pisa, Italy, Computer Science Department, University of Pisa, Pisa, Italy

  • Fosca Giannotti,

    Roles Conceptualization, Funding acquisition, Supervision

    Affiliation Knowledge Discovery and Data Mining Laboratory, ISTI-CNR, Pisa, Italy

  • Dino Pedreschi

    Roles Conceptualization, Funding acquisition, Supervision, Writing – original draft

    Affiliation Computer Science Department, University of Pisa, Pisa, Italy

Forecasting success via early adoptions analysis: A data-driven study

  • Giulio Rossetti, 
  • Letizia Milli, 
  • Fosca Giannotti, 
  • Dino Pedreschi
PLOS
x

Abstract

Innovations are continuously launched over markets, such as new products over the retail market or new artists over the music scene. Some innovations become a success; others don’t. Forecasting which innovations will succeed at the beginning of their lifecycle is hard. In this paper, we provide a data-driven, large-scale account of the existence of a special niche among early adopters, individuals that consistently tend to adopt successful innovations before they reach success: we will call them Hit-Savvy. Hit-Savvy can be discovered in very different markets and retain over time their ability to anticipate the success of innovations. As our second contribution, we devise a predictive analytical process, exploiting Hit-Savvy as signals, which achieves high accuracy in the early-stage prediction of successful innovations, far beyond the reach of state-of-the-art time series forecasting models. Indeed, our findings and predictive model can be fruitfully used to support marketing strategies and product placement.

1 Introduction

Every day, new artists appear on the music scene, new products are launched onto retail markets, new restaurants and businesses open up. Every day, people make choices: which artists to listen to, which items to buy at the supermarket, which restaurants to visit. Consumers’ choices determine which innovations (artists, products, businesses) will reach success and achieve large diffusion, and which ones will not. To reach success, innovations need to reach/target the right adopters. Several classical studies [13] analyzed the different phases of product’s lifecycle, from the first appearance on the market to vanishing. Rogers [4] described a peculiar family of adopters: the innovators, e.g., the ones that adopt an innovation before it becomes mainstream, the ones that do not need peer pressure to make their choice. From a different, psychological perspective, Tetlock et al. [5, 6] recently identified another exciting niche of individuals, called super-forecasters, that continuously make correct predictions of future events (in controlled Q&A experiments). Tetlock’s study, which ran over a number of years, aimed to understand whether people could predict an explicit yes/no time-limited question. To make predictions, the forecasters were explicitly allowed to prepare themselves researching the particular topics they were asked about. Moreover, forecasters were allowed to change their predictions as time goes by to match their evolving feelings about the outcome as the deadline for the question grew closer. Citing [6], super-forecasters are

“[..] people whose analytic ability is considerably better than random (or who, in financial analyst terms, “beat the market”)”

namely, all those individuals able to provide the correct answers on a regular basis, thus making predictions having a precision far above the average.

In this work we address a question at the intersection of the two lines above: are there innovators with passive super-forecaster abilities? Or equivalently, are there users that consistently adopt, before others, innovations that will later reach success? To answer such questions, we adopt a data-driven approach evaluated on two real datasets of supermarket transactions and musical listenings.

Differently, from Tetlock’s approach, we do not ask users to express their forecast whether an innovation will be a success; we observe what and when they adopt (buy or listen) in the recorded transactions. Indeed, the niche of users we target—we call them Hit-Savvy—do not train themselves to produce a correct guess. Conversely, they regularly chose to adopt innovations (we will refer to them as “items”) that are likely to reach success in the future. Such difference is profound: adoption choices of Hit-Savvy are not driven by the desired outcome as for Tetlock’s super-forecasters (i.e., early-adopters who listen to novel music do not necessarily do so because they think the artist will be successful) but by personal taste.

The first contribution of our study, described in Section 2, is the discovery that Hit-Savvy do exist and that their peculiar behaviour perdure through time. We empirically observe in our data a niche of innovators that exhibit a surprising propensity to adopt future successful artists and products prevalently: moreover, such Hit-Savvy tend to last in time, retaining their ability for months or even years.

Moving from such results we addressed a question whose answer can deeply impact marketing strategies: can Hit-Savvy be used to predict whether an innovation in the early stage of its lifecycle will reach success in the future? Our second contribution, illustrated in Section 3, answer such question by describing a predictive analytical process that, using Hit-Savvy as signals, achieves high accuracy in the early-stage prediction of successful innovations. In Section 4, we validate our method on the previously analyzed datasets observing high precision and recall of successful items prediction, far beyond the state-of-the-art models based on time series forecasting.

We believe that our data-driven study sheds a new light at the intersection of two increasingly important themes, discussed in Section 5: the diffusion of innovations and the science of success. Finally, Section 6 concludes the paper introducing future directions of research.

2 Successful items and their adopters

Super-forecasters are ubiquitous still not easy to spot. Given a set of questions regarding future events each one of us, specialist or not can make his prediction: however, only a handful of people will be able to correctly guess the future more than the average. This peculiar minority, driven by chance or intuition, is strictly tied to the type of questions asked and to the definition we adopt to identify successful answers. In the classic scenario offered by Tetlock’s work [5], successful answers are those that capture the exact outcome of an event (e.g., the fact that a particular conflict ended, or that a bill has been approved by the Congress), while super-forecasters are those individuals able to correctly guess such outcome before it happened.

In our scenario, however, the valuable individuals we are searching for possess different characteristics w.r.t. Tetlock’s super-forecasters, and are subject to different constraints as well:

  • Firstly, the niche of individuals we target do not actively train themselves to produce predictions but, by chance or luck, are constantly involved in the adoption of successful items;
  • Secondly, conversely from super-forecasters, to be Hit-Savvy it is not sufficient to correctly “guess” the future but it is mandatory to do so before others do.

Moreover, if in Tetlock’s experiment each question has one and only correct answer (yes or no) in our settings the success of an artist, a product, as well as an idea, can be measured in multiple ways (i.e. considering a musician it can be the number of disks sold, the volume of his fanbase as well as how long took for his name to became easily recognizable from the public).

We can say that to identify Hit-Savvy we need to fix at least two domain-specific notions: (i) what it means for an item to be a successful one, and (ii) who are the innovators, i.e., those users that adopt an item before others do.

In this section, firstly we introduce the datasets we used in our experimental analysis, 2.1, then we propose two alternative definitions of success, 2.2. Finally, we describe a methodology tailored to identify Hit-Savvy, 2.3, and briefly discuss some of their properties, 2.4.

2.1 Experimental data

This paper describes the analytical results of a data-driven investigation, for this reason as a first step it is mandatory to introduce the datasets analyzed.

  • Last.fm: Last.fm (http://www.lastfm.com) is an online social network platform where users can share their music tastes and discover new artists and genres. The crawled dataset is composed of two years (2010-2012) of listenings for 70K UK users: we considered only novel artists having at least 500 listenings. The data, involving users weekly artist listening charts, were collected in compliance with Last.fm API Terms Of Service (https://www.last.fm/api/tos).
  • Coop: Market Basket Data from the largest Italian retail Company; our dataset span over a year (Jan-Dec 2011) and is extracted from a seven years long itemised timestamped transaction records. We considered only novel products launched into the market within such temporal window, e.g., those for which no transaction records were present in the complete dataset until the selected period.

All the user related information of both datasets—namely, Last.fm and Coop user identifiers—were anonymized after collection, and before the analysis, to comply with the sharing policies of the services.

Table 1 are provided the details of both datasets. We model them as adoption logs, , temporal ordered sets of triples of the form < a, g, t > where aA is an adopter, gG is the adopted item (the innovation) and t is the adoption time (i.e. <Jon, ACDC, 6/1/2017>).

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Table 1. Datasets’ details.

We report the time units used to build adoption trends: raw adoption log data of both datasets have a more fine grained time-scales as specified in dataset description.

https://doi.org/10.1371/journal.pone.0189096.t001

2.2 Defining success

Success is a concept not easy to quantify: indeed, several factors both exogenous (i.e., artist’s prizes or social impact) and endogenous (i.e., purchases’ volumes) can be used to measure it. To identify and characterize Hit-Savvy, we compare a few definitions of success: to guarantee context independency and objectiveness of our analysis we will focus only on endogenous ones. Indeed, the most straightforward way to measure the success is by looking at volumes: the number of listeners of an artist, as well as the number of purchases of an item, can be seen as natural proxies to evaluate and compare the attention received by different items of the same type. However, the volume is not the only way to capture success: another essential information is given by how adoptions spread over time. In order to identify a success measure alternative to volume, we analyzed the available data and devise a data-driven methodology that separate trend-successful items from trend-unsuccessful ones. The adoption trend (AT) of an item describes how its adoptions unfold through time: we can define it as,

Definition 1 (Adoption Trend) Given an item g its adoption trend τ is a time series in which τ(t) identifies the percentage x of the total adoptions of g occurred at time t.

As an example, consider an artist A and all its listeners during the observed period: the adoption trend of A describes, for each month, the percentage of listeners that listened A for the first time.

Indeed, the time unit chosen to define the adoption trend is context dependent. It is important to notice that reducing the temporal granularity of a given adoption trend (i.e., moving from a monthly scale to a weekly one) its overall shape will remain the same, only its smoothness will be affected. In our scenarios, to reduce noisy fluctuations while modeling adoption trends, we impose a weekly unit for Coop and a monthly one for Last.fm.

Starting from each adoption log, we extracted items’ adoption trends and profiled them to identify recurrent patterns. To do so, we used k-means clustering with Dynamic Time Warping (DTW [7, 8]) as the distance function. We executed k-means using as a feature vector for each item g its observed trend τ. The study of cluster quality through SSE (Sum of Squared Errors) identifies, on both datasets, k = 2 as the optimal k-means parameter value. The medoids (i.e., cluster profiles) of the two well-separated clusters describe peculiar shapes: one expressing a sudden drop of the adoption rate, the other capturing an expanding trend. Fig 1 shows the medoids obtained on Last.fm, Coop ones behaving alike. In the same figure, we also report the Last.fm medoids for k = 3 and k = 4. In the latter scenarios, the additional profiles identify specializations of one of the medoids obtained for k = 2: in particular, they capture growing trends whose peak is shifted w.r.t. the one observed in the optimal solution and, most importantly, they do not describe novel previously unseen trend shapes. Several different clustering strategies can be employed to identify adoption trends families: we employed k-means with DTW since such methodology is widely used for clustering time series data. Indeed, we also tested a variant of k-means, namely k-shape [9], explicitly designed to group together similarly shaped time series. The results we obtained with such approach were indeed comparable to the k-means (both in the optimal number of clusters as well as shapes identified) ones, however, since k-shape implements a distance function that does not allineate shifted time series we choose to maintain the former approach as default clustering strategy.

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Fig 1. Last.fm trends analysis.

Cluster medoids identified by k-means with DTW for K in [2, 3, 4]. SSE analysis identifies k = 2 as the best choice. The trends identified for k = 3, 4 do not unveil novel trend shapes, but only specialize the ones identified for k = 2.

https://doi.org/10.1371/journal.pone.0189096.g001

Since by construction the areas under trend curves are all equals to 1, we cannot compare the adopters’ volumes directly starting from items’ adoption trends. To understand if there exists a correlation between the shape of the adoption trend of one item and its adoption volume, we analyzed how volumes distribute w.r.t. the two clusters. The results, reported in Fig 2, show a clear tendency: items having expanding trends tend, on average, to have a broader diffusion than the others.

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Fig 2. trends analysis.

Comparison of volumes of expanding and contracting trends on Last.fm dataset (a) and Coop (b).

https://doi.org/10.1371/journal.pone.0189096.g002

Notice that, to avoid biases while computing trend clusters as well as the need of temporal normalization, in this phase we employed only those items that were continuously adopted for at least half of the observed period (i.e., 1 year for Last.fm, 6 months for Coop). Thus, our data-driven definition of success discriminate successful and unsuccessful items by the shape of their trends:

Definition 2 (Successful trends) Successful trends are the ones describing an increase of adoption rate through time capturing an expansion of individual items’ adopter base: e.g., all trends whose second derivative has negative value.

Definition 3 (Unsuccessful trends) Unsuccessful trends are the ones in which the adoption rate do not increase considerably over time or even reach an early maximum only to start to decrease rapidly: e.g., all trends whose second derivative has positive value.

Following the previous example, an artist A will be considered successful if his adoption trend is concave, meaning that, as time goes by a growing number of individuals decided to listen to his music. Conversely, if A’s diffusion trend follows a convex shape, he will be considered unsuccessful since most of his adoptions happened early and he was unable to attract novel listeners as time goes by.

Independently from the success definition used, in the following, we will call Hits the successful items and Flops the unsuccessful ones. Moreover, we identify with HG the set of Hits and with FG the set of Flops.

Indeed, an entirely data-driven classification of items based on their adoption trends has an evident drawback: by definition, it cannot be considered universal nor transferable across different contexts. The proposed methodology can be applied to every kind of adoption log: however, it is possible that different data will generate clusters whose medoids profoundly differs from the patterns we identified in our analysis (both in number and shapes). In such scenarios we fall in an “out-of-sample” configuration w.r.t. the ones we encountered in both Last.fm and Coop: to move forward with the predictive model definition it will be thus necessary to label the identified clusters identifying a characteristic able to discriminate the item within them.

2.3 Identify Hit-Savvy

Once fixed the success definitions we can start searching for Hit-Savvy. To do so, we need to: (i) identify those adopters that adopt before the others successful items (the innovators) and (ii) measure their propensity to repeat such behavior in time.

Innovators.

The classic approach used when addressing the problem of segmenting the customers of an item w.r.t. the time of their adoption lies in leveraging the definitions given by Rogers [4]. Rogers’ segmentation, which assumes a normal distribution shape for a generic adoption trend, defines the innovators as the first 2.5% of the item adopters. Since our data-driven analysis revealed the absence of such peculiar distribution of adoptions we decided to employ an alternative more conservative method to identify such interesting segment of the population. We thus define:

Definition 4 (Innovators) Given an adoption trend τ of an item g we consider innovators all those adopters that adopt g strictly before the global maxima of τ.

The proposed definition does not impose a fixed threshold and applies to all the different trends that can be observed in real data. Indeed, this criterion potentially generates a wider set of innovators than the Rogers’ one: for these reasons, to support our alternative definition, in Section 4.1 we will compare it with Roger’s while predicting successful items.

Hit-Savvy.

Once identified the innovators we need to quantify their intrinsic individual propensity to adopt Hits. To do so we define HF-propensity:

Definition 5 (HF-Propensity) Given an adopter a and (i) f the number of Flops he adopted, (ii) h the number of the Hits he adopted as innovator and (iii) k the number of Hits he adopted after they reach their global maxima, the HF-propensity of a is: (1) HF lies in [−1, 1]: its value is maximised when a adopts only Hits as innovator, minimised when his adoptions regard prevalently Flops as well as Hits but as latecomer.

Once fixed a way to measure the propensity toward the exclusive adoption of successful items we can formally define the Hit-Savvy:

Definition 6 (Hit-Savvy) Given an adoption log , a set of successful items HG we define Hit-Savvy all those adopters aA for which HF > 0.

The farther the HF-propensity value is from 0, the stronger the Hit-Savvy strength: we identify with HT the set of Hit-Savvy and with FT the set of Flop-adopters (e.g. adopters having HF < 0). Adopters having HF = 0 are considered neutral signals since they do not show any special propensity toward neither Hits nor Flops. In the following analysis, we will discard neutral adopters since they cannot be considered discriminatory indicators.

Indeed, since the HF measure is not weighted on the number of adoptions, an adopter that has adopted a single successful (unsuccessful) items will receive the highest (lowest) value in the range. Even though this choice appears to be counterintuitive, such scenario represents a rare event in the data we analyzed and, most importantly, it does not affect the semantics we search for while defining our Hit-Savvy. An adopter must be considered a Hit-Savvy even if he only adopted a single item among thousands available if, later on, such item reached success. Indeed, it is likely that such adopter will not be able to contribute to identifying successful items in the future due to his reduced adoption activity. However, his behavior is similar to all other Hit-Savvy. As previously discussed Hit-Savvy, conversely from Tetlock’s super-forecasters, are not driven by the desire to identify successful items: they only chose to adopt something that they like or need.

2.4 Hit-Savvy: Who are they?

Once fixed both the success definitions and the criterion to identify Hit-Savvy several questions arise: (i) do Hit-Savvy exist? (ii) how many of them are we able to identify? To better highlight the impact different success definitions have on Hit-Savvy we compare four of them: three based on volume (V10, V20, V30) that define as Hits respectively the top-10%, top-20%, and top-30% most adopted items, and AT, the data-driven trend-based we proposed. We can observe in Table 2 that, disregarding the dataset and the success definition used, HF-propensity often identifies as Hit-Savvy less than 1% of the total adopters: a niche of individuals still able to adopt a high percentage of Hits. In particular, the induced coverages fluctuate across the 12-42% on Last.fm and the 4-9% on Coop when success is defined as a function of volume, while they reach respectively the 22% and 79% if success is modeled using AT. In Fig 3 (top) we show the binned distributions of the HF-propensity for the identified Hit-Savvy while varying the success definition. For both Last.fm and Coop, a neat peak for low HF-propensity scores emerges (in the range (0, 0.1]), implying that it is very rare to identify within Hit-Savvy adopters that adopt Hits exclusively. Moreover, all the analyzed success definitions induce similar right skewed long tail shaped distributions for such indicator, thus not excluding the existence of few, precious, very strong Hit-Savvy.

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Fig 3. Hit-Savvy: HF-propensity and active periods.

Hit-Savvy vs. HF-propensity in Last.fm (top left) and Coop (top right). Distribution of Hit-Savvy’ active periods length for Last.fm (bottom left) and Coop (bottom right).

https://doi.org/10.1371/journal.pone.0189096.g003

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Table 2. Hit-Savvy statistics.

For each dataset and success definition are reported: the number of Hit-Savvy |HT|, the number of successful items |H| and the coverage induced on them by Hit-Savvy. Within bracket are reported their percentage over all the adopters and items respectively.

https://doi.org/10.1371/journal.pone.0189096.t002

Indeed, our experiments suggest that Hit-Savvy exist. To understand if they can be fruitfully used to forecast success, we still need to answer an important question: for how long a generic Hit-Savvy adopt as such? So far we computed the HF-propensity for each adopter over his complete history of adoptions: to understand if a Hit-Savvy adopts as such only few random times across his history or stably performs prevalently Hit adoptions as an innovator, we computed his HF-propensity on a weekly basis. Let be the ordered list of weekly HF-propensity of the adopter aA and [t0, …, tn] the weeks in which a makes at least an adoption, we define as Hit-Savvy’s active period the average number of consecutive weeks in having HF-propensity greater than 0. In Fig 3 (bottom) we show the probability distribution of Hit-Savvy’ active periods computed on both datasets varying the success definitions. Two clear patterns emerge: (i) as happened for the HF-propensity score we observe peaked long-tailed distributions (having their modes within 5-10 weeks in Last.fm and 5-6 weeks on Coop) and, (ii) AT is able to guarantee the identification of Hit-Savvy with the longest active periods (∼80 and ∼45 weeks on, respectively Last.fm and Coop).

3 Predicting success

Certainly, the road to success is not an easy one. To decide, by observing only a short time-bounded adoption log, if a novel item is destined to become a Hit (or be doomed to be just another of many Flops) we need to extract meaningful information from known examples and to design a reliable forecasting model. Music companies, as well as online music providers (Spotify, Apple Music…), can greatly benefit from being able to discriminate Hit artists from Flop ones during the early stages of their distribution so to design ad-hoc marketing and advertising strategies. Hit-Savvy play a huge role in this process: being able to identify a sufficiently broad and stable group of individuals capable of spotting success before others is one of the dreams of every marketing department. Indeed, we have seen that different definitions of success generate different sets of Hit-Savvy that vary both in volume and stability. Volume-based definitions, even if immediate and of natural formulation, have an unpleasant drawback: the reduced set of positive, successful items they define causes the identification of very few and volatile Hit-Savvy. Such reduced set of special users, although being very strong signal for success, are usually not enough to make predictions: for this reason in the following, we will adopt our data-driven trend-based definition of success to formulate our predictive model. The approach we propose, Hits&Flops (code available at https://goo.gl/f36Unv), follows a simple rationale: identify the smallest set of Hit-Savvy, as well as Flop-adopters, that allow discriminating Hits from Flops and leverage them to make predictions. Our predictive model, namely Hits&Flops, can be applied independently from the chosen success definition.

3.1 Hits&Flops: Learning Hitters and Floppers

So far we have measured the adopters propensity toward Hits and Flops and thus transformed them into indicators. Our aim is now to use such indicators to forecast the success of novel, previously unseen, items. As we have seen in 2.4 HF-propensity distributions is right skewed in both datasets: since we aim to reduce the noise weak signals can generate while used to make prediction we target the minimum sets of Hit-Savvy as well as of Flop-adopters able to discriminate both Hits and Flops.

The task of identifying such subsets can be naturally formulated as a Weighted Multi-Set Coverage (WMSC) problem. To comply with WMSC, we build two bipartite graphs: one connecting each Hit-Savvy in HT to the successful items he adopted, and the other connecting each Flop-adopters in FT to his unsuccessful items. On each of such topologies, we search for the subset of adopters that guarantees a constrained minimum coverage of the connected items. A valid coverage needs to satisfy the WMSC formulation: where xi, yj, ei,j are binary variables modelling each potential adopter (belonging to the adopter set ), item adopted (belonging to the item set ), and edge of the bipartite graph. The first constraint ensures that a selected adopter contributes to the coverage of each of the item he adopts. The second constraint ensures that selected adopters cover at least β% of the sum of all incoming edges to each item. The third constraint ensures that the selected adopters collectively cover at least α% of the set of items.

We designed a greedy approach to solving WMSC (Algorithm 1) that selects a subset of adopters which satisfies the α and β thresholds. In order to easily manage adoption log structures, in the pseudocode we make use of the following notation: let aA be an adopter, gG an item, A*A and G*G two sets then, (i) ω(a, G*) identifies the set of items in G* adopted by a and, (ii) ψ(g, A*) identifies the adopters of g within A*.

Algorithm 1 WMSC greedy

Require: B = (A, G*): bipartite graph composed by adopters A, and items G*; c a sorting strategy based on degree and HF-propensity; α global coverage threshold; β local coverage threshold.

1: Indicators = [ ], covered_items = [ ]

2: As = sort(A, c)

3: for a ∈ As do

4:  if |covered_items| < α |G*| then

5:   Ga = ω(a, G*)

6:   for g ∈ Ga do

7:    if |ψ(g, Indicators)| < β degree(g) then

8:     if a ∉ Indicators then

9:      Indicators.add(a)

10:    else if g ∉ covered_items then

11:     covered_items(g)

12:  else

13:   return Indicators

14: return [ ]

Our greedy approach takes care to sort the adopters to be selected for the covering: it selects the adopters maximizing their degree and HF-propensity to cover Hits and maximizing their degree while minimizing their HF-propensity to cover Flops. Doing so, we impose the identification of a local maximum composed by highly discriminative Hit-Savvy (Flop-adopters). In Fig 4 is shown the WMSC coverage for a simple bipartite graph: in the toy example, to simplify the analysis, the HF-propensity is considered equal for all the adopters (e.g. only a degree ordering is exploited in the selection phase). Since the α and β parameters deeply affect the coverage produced by WMSC, to identify the optimal HT and FT subsets we instantiate multiple runs of WMSC applying a grid search strategy. Such strategy results in two sets of solutions: (i) one for Hit-coverages, with HT0, …, HTnHT and, (ii) the other for Flop-coverages with FT0, …, FTnFT. Given a valid solution , let HiH be a the subset of items covered by adopters in HTi. Symmetrically, given a valid solution , let FjF be a the subset of items covered by adopters in FTj. Among the solutions within and we select HTi and FTj that maximise |Hi| and |Fj| while having minimal cardinality: we call them and . Such selection procedure acts as a feedback control loop that implicitly supports the identification the optimal values of α and β among the ones tested by the grid search strategy.

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Fig 4. WMSC toy example.

WMSC with α = β = 0.6: in red the selected adopters, in green the covered items.

https://doi.org/10.1371/journal.pone.0189096.g004

Finally, we call Hitters all the filtered and reliable Hit-Savvy within . Symmetrically, we call Floppers all the Flop-adopters within .

3.2 Hits&Flops: Forecast model

Once learned the Hitters and Floppers to predict whether a novel item will be either a Hit or a Flop we proceed as follows.

For each successful item gH let π(g) be the number of its adopters in and Π the probability distribution of π(g) across all the items in H. Symmetrically, for each unsuccessful item gF let δ(g) be the number its adopters in and Δ the probability distribution of δ(g) across all the items in F. We call () a user specified threshold over Π (Δ).

We define the Hits&Flops predictor as a two step procedure:

  1. Specialized classification. Two distinct classifiers are built: one to forecast Hits (leveraging set and Π distribution), the other to forecast Flops (leveraging the set and Δ distribution).
  2. Synthesis. A meta-classifier combines the predictions of specialized classifiers and generates the final prediction for each novel item.

Let g* be a previously unseen item and A* the set of its adopters during a limited time window starting from its first appearance: the rationale behind the specialized predictors is the following:

Definition 7 (Hits-classifier) returns a positive class (Hit) iff where π(g*) is computed over .

Definition 8 (Flops-classifier) , returns a positive class (Flop) iff where δ(g*) is computed over .

Since those classifiers give only partial predictions their outcomes need to be combined by a meta-classifier:

Definition 9 (Hits&Flops) Given the Hits and Flops predictors and , we define the rule based meta-classifier as:

  1. if and , g* is a future Hit;
  2. if and , g* is a future Flop;
  3. if and :
    1. if , g* is a future Hit;
    2. if , the observed adoptions are still not enough to make a forecast;
    3. otherwise g* is a future Flop;
  4. otherwise, the observed adoptions are still not enough to make a forecast.

To exemplify the rules of the meta-classifier in Fig 5 are depicted the distributions Π and Δ on Last.fm. The first (second) rule identifies an item g* having π(g*) = b (π(g*) = a) at the right (left) of , and δ(g*) = c (δ(g*) = d) at the left (right) of . In these cases, the meta-classifier returns the positive class identified by the corresponding classifier. The third rule models the situation in which both the classifiers return a positive class for the item g* (in the example, π(g*) = b and δ(g*) = d). In this case, the meta-classifier will return the class identified by the greater distance between the thresholds and the corresponding value of π(g*) or δ(g*) (in the specific case will classify g* as Flop, since ), and in case the two distances are equivalent, it will not return a classification. Finally, the fourth rule models the case in which both the classifiers do not return a positive guess (in the example, π(g*) = a and δ(g*) = c). In this case, a classification is not provided: since we are dealing with partial observations we choose not to classify the instances for which we do not have enough data.

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Fig 5. Probability distributions Π and Δ.

The thresholds are identified with and respectively.

https://doi.org/10.1371/journal.pone.0189096.g005

We designed a meta-classifier, avoiding the use of classic approaches (e.g., Decision Trees) since the peculiar formulation of the problem allows, in the absence of sufficient observations, to suspend the class prediction (generating a “third”, temporary, class that is not described by any example in the training set). In the following, we adopted as and the median values of the two distributions after a stage of parameters tuning that highlighted their ability to guarantee highest predictive performances on training and test sets of the analyzed datasets. Indeed, being a data-driven analysis, different datasets could require different thresholds values to fine-tune the classification process. For such reason, in our framework, we leave and as model parameters, allowing the analyst to fit them to the distributions observed in the data as well as to specific analytical needs.

4 Evaluation

In 4.1 we apply Hits&Flops on both Last.fm and Coop datasets and compare its predictions with the ones produced by its competitors. In 4.2, we statistically validate the significance of our results. Finally, in 4.3 an in-depth analysis of the Last.fm case study is provided.

4.1 Experimental results

We tested Hits&Flops against two different classes of competitors: (i) time-series forecasting and (ii) innovator based supervised learning predictors. A classic time-series based strategy to address our problem is to (i) reconstruct (forecast) a complete trend moving from its partial observation, (ii) estimate its distance from the medoids of the previously identified clusters and (iii) assign it to the closest one, thus determining if the new item will be either a Hit or a Flop. To do so, we adopt as a first set of competitors two time-series forecasting techniques: one that takes into account seasonality while reconstructing the adoption trend, Fast Fourier Transform (FFT), and one that does not, Moving Average (MA).

Hits&Flops does not only generates predictions for novel items: it also identifies the sets of Hitters and Floppers, valuable adopters that can be monitored and used to influence marketing strategies. For this reason, we tested our predictive approach also against competitors able to produce such valuable byproduct. In particular, we compared to the following innovator-based supervised learning strategies:

  1. ER: the prediction is made using only the innovators extracted with the 2.5% Rogers’ threshold. For this approach, an item will be defined a Hit iff at least one of its observed adopters is a known Hit-Savvy, a Flop otherwise;
  2. ER-H&F: the initial HT set for Hits&Flops is identified by using the threshold proposed by Rogers (e.g., the first 2.5% of the item adopters);
  3. HA-H&F: a variant of Hits&Flops in which the coverage on the bipartite graph is obtained not through the proposed WMSC heuristic but by selecting the top-k scorers of Hubs&Authorities [10](where the optimal k is identified using the same procedure to optimize α and β);

To evaluate the effectiveness of the aforementioned strategies we design our experiments temporally dividing each dataset into a training set (items that appear for the first time within the first 60% of the dataset observation period) and test set (items appearing for the first time in the residual 40%). We considered as partial observation windows for the items of the test set respectively: 2 months in Last.fm and 4 weeks in Coop.

Hits&Flops.

First of all, we need to justify the rationale behind the proposed approach: why not to use directly HF-propensity scores to make predictions? To answer such question, we built a simple classifier that exploits directly the indicators, as computed in 2.3, by combining them linearly. In such scenario, a novel item will be labeled as Hit if the sum of the HF-propensities of its observed adopters is greater than 0, Flop otherwise. Unfortunately, such approach is not able to make predictions for Hits due to the highly unbalance among the computed indicators (Hit-Savvy are always less than 1%). The introduction of the WMSC step is a way to address such unbalance: are then and sufficient to make predictions without leveraging the meta-classifier? We use the HF-propensity scores for adopters in such sets to compute the same linear combinations: even in this case we get very low Recall on the Hit class: 0.023 on Last.fm and 0.061 on Coop. Such low performances are due to the right skewness of the HF-propensity distribution for Floppers which tends, conversely from Hitters, to be polarized toward extreme values.

Comparative analysis.

Table 3 report the performances of the proposed approach as well as of its competitors on the two datasets. Time series forecasting approaches, either susceptible to seasonality (FFT) or not (MA), are constantly outperformed by Hits&Flops. Moreover, we can observe two distinct, but related phenomena: (i) FFT always shows higher reliability while predicting Hits (higher PPV and Recall) w.r.t. MA and (ii) MA always outperforms FFT while predicting Flops (higher NPV and Specificity). Such results are consistent with the patterns expressed by the trends belonging each cluster: Flops are not subject to seasonality since their trends experience a contraction.Hits, conversely, are characterized by manifold trends that can have multiple local minima and maxima.

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Table 3. PPV, NPV, Recall and Specificity comparison for the analyzed forecasting approaches.

https://doi.org/10.1371/journal.pone.0189096.t003

Focusing our attention on the innovators-based methods, we observe that the ER approach does not obtain any valuable results w.r.t. the precision of the predictions (i.e., low scores of PPV and NPV). Due to the non-gaussian adoption distribution of the analyzed datasets, the choice of identifying the innovators with a fixed 2.5% threshold and to use them—without further refinement—to forecast success leads to overestimating the Flops (as indicated by the values of Recall and Specificity). To understand if the innovators identified by ER are still valuable, we build upon them a modified version of our model, namely ER-H&F. Since we aim to achieve high predictive precision especially in the prediction of successful items (PPV score) and guarantee that we can correctly identify a significative percentage of them, we can state that our method is always capable of outperforming such competitor. The limitation of ER-H&F, inherited from ER, is due to the choice of identifying innovators using a fixed threshold. However, ER-H&F outperforms ER. Such result confirms that not all innovators are good indicators of success and, as shown by the experimental results, our methodology is capable of recognizing and exploiting the ones which can be reliably used as signals to make predictions. Moreover, considering the results provided by HA-H&F we observe how this variant is able to reach high PPV and Specificity at the cost of very low NPV and Recall. This latter result highlights that the proposed WMSC greedy solution which, conversely from Hubs&Authorities, takes into account HF-propensity plays an important role in the definition of the Flop classifier. In conclusion, Hits&Flops is always able to outperform the competitors producing effective predictions. Moreover, in the performed experiments our meta-classifier is able to assign a class to, respectively, 97% new artists in Last.fm and 94.4% new Coop products (among the ones covered by the Hit-Savvy and identified in Section 2.4).

4.2 Null model analysis

The main hypothesis behind Hits&Flops is that there are very special adopters, the Hit-Savvy, which tend to choose and adopt prevalently successful items. To validate that the results obtained from our case studies are statistically significant, we need to prove that they are driven not by chance but, conversely, by adopters’ explicit behaviors. To do so, we perturbed our datasets, executed Hits&Flops on the outcome of such process and statistically tested the results obtained against the ones we obtain on real data. The randomisation we applied targeted adopters choices while preserving two important characteristics of the original data: (i) the adoption trend distribution for each item (e.g., Flops and Hits remained as such); (ii) the original number of adoptions and relative temporal distribution for each adopter.

The performed transformation acts as our Null Model (its pseudocode is reported in Algorithm 2): it ensures that both adopters and items maintain their characteristic distributions, by destroying only the temporal sequence of adoptions and individuals choice on the item to adopt. The final adoption log describes adopters that choose items without any particular personal preference. In detail, Algorithm 2 takes as inputs two maps and which relates, respectively, each adopter and each pair < item, time > to their number of adoptions. Such procedure builds a matrix of size and populates it by randomly selecting indices from the two maps, taking care of maintaining the defined constraints.

Algorithm 2 Null Model Generator

Require: : map of adopternumber of items; : map of <item, time > → number of adoptions.

1: m = matrix(, )

2: while > 0 and > 0 do

3:  a = random(.key)

4:  < g, t > = random(.key)

5:  m[a][< g, t >] += 1

6:  [a] -= 1, [< g, t >] -= 1

7:  if [a] == 0 then

8:   .remove(a)

9:  if [< g, t >] == 0 then

10:   .remove(< g, t >)

11: model = []

12: for (a, < g, t >) ∈ m do

13:  if model[a][< g, t >] > 0 then

14:   model.append(a, g, t)

15: return model

Statistical significance.

We generated 10 different null models for each dataset which were used to instantiate Hits&Flops following a 10-fold cross-validation strategy, thus testing it over 100 different combinations of training-test sets. In Table 3 with NM are identified the average performances of our approach on the transformed data, along with their standard deviations. Computing the z-test to compare the performances achieved by Hits&Flops on real data and null model generated ones we obtain the values shown in Table 4. Given the low standard deviation on the null models, the z-scores obtained reach values that are remarkably far from the ones given by Hits&Flops: we can thus conclude that the results obtained by Hits&Flops on real data are statistically significant. As an example, the value 61.0 for PPV (Positive Precision) in Last.fm dataset in Table 4 means that Hits&Flops’ Precision is 61.0 Null Model’s Standard Deviations far from the Null Model Precision’ average (). We then reject the null hypothesis that the observed performances can be explained by the null model.

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Table 4. H&F z-test.

The lowest z-score obtained, 5.4, lead to a p-value (one-sided) of 3.332e-8: z-scores higher than 8.3 lead to p-value equals to 0.

https://doi.org/10.1371/journal.pone.0189096.t004

4.3 Case study: Last.fm

In order to better discuss the performances of Hits&Flops here we focus on its results on the Last.fm dataset. We analyze this particular scenario because Last.fm adoption logs are very dense and accurate and the concept of novel item (new artist) is crisp and not affected by biases such as the brand-effect in the retail market data. Indeed, in a retail market scenario, the success of a new product (i.e., a new type of “pasta”) is often strictly related to the overall success of its brand (i.e., “Barilla”). Due to such dependency, on average, it is not easy to separate real novel Hits from those products whose success is due to the users’ attachment to a brand.

One of the main questions that arise when forecasting novel artists’ success is: for how long do I need to observe his listeners to make a reliable prediction? To study the effect that time has on the predictive performances of Hits&Flops, we run it on Last.fm varying the observation period for novel artists. We report in Fig 6 (left) the trends of PPV, NPV, Recall, and Specificity obtained applying our model with increasingly longer observation periods (ranging from 1 month to 1 year). We notice that the main effect of a protracted observation is to introduce variability on Recall: with more observations, we are likely to identify a higher percentage of Hits preserving a high PPV and NPV. Conversely, Specificity stabilizes on the long run. Hence, for this specific case study, the optimal observation window can be reasonably fixed at 2 months since, with such settings, we observe the best predictive power. Such results are due to the fact that rely on few observations lowers the probability of encounter Hitters adoptions (and thus identify Hits) while, on the other hand, excessively extend the observation window is likely to induce over-representations of Floppers.

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Fig 6. Predictive accuracy stability.

Predictive accuracy varying the observation period for the Last.fm dataset (left). Stability of Hitters and Floppers sets across time: the analyzed models were learned with a 9-15 split using a sliding window (right).

https://doi.org/10.1371/journal.pone.0189096.g006

Next, we split our data using an incremental temporal window to represent the past—while maintaining the identified optimal observation window length. We learn our model on those artists (and related listening) that appear during the first 3-6-9-12 and 15 months and forecast the success of the artists listened for the first time in the remaining period. As shown in Table 5, our methodology correctly identifies Hits with high precision and recall with a relatively short training. In particular, Hits&Flops is able to maximize our target measures by learning the model on those artists that are listened for the first time during the first 9 months.

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Table 5. Hits&Flops predictive performances when dealing with different temporal splits.

Each column identifies a different split of observed 24 months: e.g., S6 stands for 6 months of training, 18 of test. In bold the best scores for PPV and TPR.

https://doi.org/10.1371/journal.pone.0189096.t005

Once identified the best split strategy to learn our model, e.g., S9 in Table 5, we focus on the primary byproduct of our approach: the Hitters and Floppers sets. To characterize the stability of such sets, once fixed the splitting strategy, we learn Hits&Flops on several consecutive extractions obtained with a sliding window of fixed width. Fig 6 (right) shows, for both indicators, their similarity across time (continuous lines) and w.r.t. the first extraction (dashed lines). First of all, we observe that set stability is high: (i) consecutive Hitter sets do not change more than 40% and (ii) consecutive Flopper sets shown a Jaccard between 0.3 and 0.6. Conversely, we notice that, as expected, global stability (computed as the Jaccard among each new set and the first one) tends to decrease with time. In particular, after 9 months from model learning only 30% of original Hitters are still useful to predict successful artists. Our indicators are volatile and need to be updated incrementally to guarantee high predictive power, thus confirming what we observed while analyzing the distribution of active periods of Hit-Savvy.

At the end, who are the unexpected Flops among Last.fm artists? They are almost all the ones that receive huge media exposure (i.e., participants to music reality shows) that after their early explosion are not able to maintain the public engagement. Conversely, successful artists are the ones able to nurture their public by incrementally enter in the Last.fm scene with few individual tracks.

5 Related works

Our work is situated at the intersection of two intense research areas: (i) the identification and analysis of Hit-Savvy and Innovators and, (ii) the forecast of Success.

Super-forecasters, Trend-Setter and innovators

The term super-forecaster has appeared only recently, primarily thanks to the seminal works of Tetlock [5, 6]. In [11] the authors theorized that the most successful forecasters did tend to have advanced degrees and a greater degree of general political knowledge. In [12] are studied the forecasts of 208 experts on the results of 15 treatments involving monetary and non-monetary motivators in a real-effort task: in such context, the authors identified super-forecasters among the non-experts who outperformed the experts w.r.t effort, confidence and revealed ability. As we have shown, super-forecaster can be seen as a very special subset of adopters: among the first studies on the adoptions of novel products [1, 2] hypothesized that the adoption trend distribution was likely to grow as an exponential toward an asymptote. In 1943, [3] theorised the existence of five categories of adopters: Innovators, Early adopters, Early majority, Late majority and Laggards. Rogers, in [4], revise such formulation defining adoption thresholds to separate the five categories: moving from the assumption of a normal distribution of adoption trends, he identifies the innovators with the first 2.5% of the adopters. As today, Rogers’ studies hold a predominant role within the study of information diffusion [13]: however, several models were proposed as alternative [14, 15]. In particular, as shown from the current work, three weakness of such model are often highlighted [16, 17]: (i) it is not justified empirically or analytically; (ii) it assumes that the adoption trend is normally distributed; (iii) the threshold is univocally defined for all the possible products. In recent years problem of identify innovators has lived a second youth: diffusion of Memes [18], social prominence analysis [19], discovery of innovation communities [20] as well as identification of Trend-Setter [2124] are only a few of the network studies which exploit [25] or model [26] techniques aimed at identifying key users that are able to influence the diffusion of a product, content or idea over a social network. Although being related Hit-Savvy and Trend-Setter carry different semantics: where a Hit-Savvy is a passive actor that operates on the basis of its personal taste, a Trend-Setter is often defined as an active one that with his own choice aims to influence his peers. Indeed in a real-world scenario it is not easy to separate the former—which we can see as taste-maker—from the latter—that conversely are taste-spotter [27]. However, in the absence of a static/dynamic graph describing interactions among individuals and of an explicit/measurable index of causality/peer pressure, Hit-Savvy offer a less demanding definition than Trend-Setters, applicable, as in our cases, in a mean-field context.

Science of success

One of the most intriguing challenges for data science is to forecast, given a partial observation, the future evolution of a phenomenon. Thanks to the growing availability of social data, sportive accomplishments [2830], online habits [31] as well as, scientific publications [3234] and professional accomplishments [3537] new opportunities emerges for discovering the hidden patterns of success. Predictive models are also designed to facilitate the diffusion and adoption of innovations: machine learning literature has witnessed the increase of works in which are proposed context-specific models to suggest novel products to targeted adopters, as in [38]. Moreover, to identify success is necessary to be able to classify innovations relying on partial data. Finally, in [39] the authors propose a simple and effective method to provide uncertainty estimates for early classification of time series.

6 Conclusions

In this work we studied the Hit-Savvy, those special adopters having a propensity to adopt successful items. Our contribution was threefold: (i) firstly measure the intrinsic propensity of adopters toward Hit items, thus identifying the Hit-Savvy; (ii) we then analyze such special users on two different real-world datasets and observe their properties; (iii) finally we define a method that exploits Hit-Savvy to predict the future success of innovations given only partial observations of their adoptions.Hits&Flops does not depend on the success definition used to identify the Hit-Savvy and, our results showed that it is able to achieve high predictive performance thus being applicable to support marketing campaigns of novel items. Moreover, we validate the statistical significance of our approach against a null model concluding that the results obtained are due to the peculiar adoption behaviors of the identified Hit-Savvy. Given the obtained results we plan, as future works, to investigate if a specialization of our approach in a given context (i.e., learn it for a well-defined music genre or product segment) can lead to even more interesting performances. Finally, it would be interesting to understand if the social relationships among adopters, as well as exogenous definitions of success, can be used to characterize Hit-Savvy better. Moreover, leveraging detailed information on adopters interactions could allow a data-driven support for the study of the relations among Hit-Savvy and Trend-Setters.

Supporting information

S1 Fig. Coop trends analysis.

Cluster medoids identified by k-means with DTW. Also for this dataset, the medoids are well-separated and describe characteristic shapes: one expressing a sudden drop of the adoption rate (identified by a dashed blue line), the other capturing an expanding trend (identified by a red line).

https://doi.org/10.1371/journal.pone.0189096.s001

(PDF)

S2 Fig. Coop trend volumes.

Comparison of volumes of expanding and contracting trends. The results show the same tendency of Last.fm dataset: items having expanding trends tend, on average, to have a broader diffusion than the others.

https://doi.org/10.1371/journal.pone.0189096.s002

(PDF)

S3 Fig. Coop predictive accuracy.

Predictive accuracy varying the observation period for the Coop dataset. We notice that the main effect of a protracted observation is to introduce variability on Recall and Specificity; with more observations, we are likely to identify a higher percentage of Hits preserving a high PPV and NPV. For this specific case study, the optimal observation window can be reasonably fixed at 4 weeks since, with such settings, we can observe the best predictive power.

https://doi.org/10.1371/journal.pone.0189096.s003

(PDF)

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