In addition to the broader modes of substitution outlined in Table \ref{table:technology_categories}, other technologies have been identified as 'non-starters': these are marginalised technologies that were never mass commercialised (such as wire recorders or chain printers). In many cases these technologies could have been adapted for the target markets considered but were either never used or failed to demonstrate the required features, or performance and cost improvements necessary to warrant further development beyond initial trials. Non-starters are excluded in this study, as the analysis that follows classifies individual technologies based on training technologies that are known to have been successfully commercialised, and as such it is not believed their inclusion would influence the results presented here, although non-starters would need to be included for predicting the commercial success or failure of emerging technologies in the first instance \cite{Sood_2005}.
Based on Constant's hypothesis regarding scientific and technological anomalies and their influence on the mode of technological substitution, this paper looks to test whether bibliometric measures of scientific and technological development can provide an indication of the mode of adoption likely to occur. Constant's conceptual model theorises that presumptive technological anomalies emerge from scientific insights before a functional failure has occurred. Consequently, this study theorises that in order to identify cases of technological substitution arising from presumptive anomaly a classification scheme would need to be able to identify if a functional failure already exists, and if new scientific discoveries have preceded such a failure. As a result, the classification scheme needs to consider:
  1. a population’s perception of the current rate of scientific development in observed domains \cite{II_1973}
  2. a population’s perception of the current rate of technological development in observed domains \cite{II_1973}

Measuring perceptions of limits of science and technology

Many indicators of science and technological progress have been developed in the fields of bibliometrics and scientometrics in recent decades. Whilst these have largely been developed for the purposes of identifying and targeting gaps in existing knowledge, as well as for determining the effectiveness of funding in specific fields of research, they also provide a systematic approach to compare development trends across a broad range of scientific domains. When attempting to measure science it is however important to ensure that any measurements taken are suitable indicators of the development characteristics that are being studied. In this regard conceptual distinctions exist between scientific activity, scientific production, and  scientific progress \cite{Martin_1996}. In this study, the emphasis is not on assessing the performance or influence on technical direction of a specific set of papers, but rather to gauge the adoption of the field as a whole. As technology diffusion models also rely on non-invested parties being made aware of scientific and technological progress, communication and promotion of scientific research are important factors to include in adoption processes \cite{Bass_2004}. Adoption is equally dependent on perceptions of current scientific and technological rates of progress (shaped by social and political pressures, as well as technical), rather than the actual rates of progress (shaped by technical contributions to knowledge). Lastly, diffusion effects are population size, word-of-mouth, and time dependent \cite{Bass_2004}. As a result, measures of scientific production are felt to be a more relevant  indication of likelihood to adopt than measures of scientific progress in this study.

Patent-based technology forecasting

The use of patents for forecasting technology development trends, and the close links to economic activity, has evolved considerably since the earliest literature was published on measuring innovation from patent statistics by the likes of Schmookler and Scherer in the 1960s \cite{Schmookler_1966,scherer1965firm}. More recent publications have expanded these early concepts and have demonstrated on numerous occasions how patterns in historic patent data can be used to build predictions of future development trends, including the use of partially complete or mined datasets when historical data is not yet available. Many of these studies attempt to assess the development maturity of a given technology (not to be confused with measures of commercial market adoption) against commonly recognised milestones and features in observed technology evolution patterns. Chief amongst these is comparison to Arthur Little's Technology Life Cycle (TLC) \cite{little1981strategic}. Comprising four stages (emergence, growth, maturity, and saturation) Little's framework describes a means of measuring technological development efforts relative to a technology's competitive impact and progress in transitioning from product to process-based innovation. Classically TLC studies have relied on a simple count of patent records to determine the maturity of technologies on this scale. However, contesting the accuracy and reliability of matching a single patent indicator against pre-determined growth curves, Watts, Porter, and Haupt advocated the use of multiple patent metrics in their technology evaluations \cite{Watts_1997,Haupt_2007}. Building on this, Gao demonstrated the use of a trained nearest neighbour classifier, based on thirteen extracted patent data dimensions, to assess a technology's life cycle progress \cite{Gao_2013}. This was followed more recently by Lee's proposal for the use of a stochastic method based on multiple patent indicators and a hidden Markov model (i.e. an unsupervised machine learning technique) to estimate the probability of a technology being at a certain stage of its life cycle \cite{Lee_2016}. In parallel to these extensions to sets of indicators and pattern recognition techniques, the use of text-mining approaches to improve the speed, relevance, and accuracy, of patent analysis methods have been demonstrated by Ranaei's automatic retrieval of patent records for forecasting the development of electric and hydrogen vehicles \cite{Ranaei_2016}. Similarly, patent content clustering techniques for technology forecasting purposes have also been explored by the works of Trappey and Daim \cite{Trappey_2011,Daim_2006}. Daim's analysis illustrated how technology forecasting results for emerging technologies can be improved by combining patent-based statistics with bibliometric clustering and citation analysis techniques for the purpose of data acquisition (as a proxy indicator for technology diffusion when historical data is not present). However, being able to determine the technical readiness of a new technology is only part of the technology forecasting problem. The other critical aspect that must then be considered is the market adoption of the technology once it has been commercialised. Here Daim's work subsequently coupled the patent-based and academic literature data-mining techniques employed with the use of system dynamics modelling as a means of exploring causal relationships and non-linear behaviours in technology diffusion. Based on these works, the current study looks to combine the recent advances made in pattern recognition applications with a simplified version of Adner's technology substitution framework.

Methodology

There is a range of possible techniques that can be used for gauging the progress of technological development. In this study, bibliometric data has been used based on patent records as this has become a well-established means of assessment for both industry market comparisons and government policy setting purposes. An overview of the considerations taken in to account in method selection and development are discussed below.

Bibliometric data

Patent data has been sourced from the Questel-Orbit patent search platform in this analysis. More specifically, the full FamPat database was queried in this study, which groups related invention-based patents filed in multiple international jurisdictions into families of patents. Some of the core functionalities behind this search engine are outlined in \cite{Questel_Orbit_2000}. This platform is accessed by subscribers via an online search engine that allows complex patent record searches to be structured, saved, and exported in a variety of formats. A selection of keywords, dates, or classification categories are used in this search engine to build relevant queries for a given technology (this process is discussed in more detail in section \ref{108157}). The provided search terms are then matched in the title, abstract, and key content of all family members included in a FamPat record, although unlike title and abstract searches, key contents searches (which include independent claims, advantages, drawbacks, and the main patent object) are limited to only English language publications.

Statistical comparisons of time series

This study considers 23 technologies, defined in Table \ref{table:search_terms}, where literature evidence has been identified to classify the particular mode of technology substitution observed. The evidence and process used in this categorisation is outlined in detail in \cite{marr2018}. Using bibliometric analysis methods it is possible to extract a variety of historical trends for any technologies of interest, effectively generating a collection of time series data points associated with a given technology (these multidimensional time series datasets are referred to here as 'technology profiles'). This raises the question of how best to compare dissimilar bibliometric technology profiles in an unbiased manner in order to investigate whether literature based technology substitution groupings can be determined using a classification system built on the assumptions given in section \ref{585124}. In particular, comparisons of technology time series can be subject to one or more areas of dissimilarity: time series may be based on different number of observations (e.g. covering different time spans), be out of phase with each other, may be subject to long-term and shorter term cyclic trends, be at different stages through the Technology Life Cycle (or be fluctuating between different stages) \cite{little1981strategic}, or be representative of dissimilar industries. As such, a body of work already exists on the statistical comparison of time series, and in particular time series classification methods \cite{lin2012pattern}. Most modern pattern recognition and classification techniques emerging from the machine learning and data science domains broadly fall within the categories of supervised, semi-supervised, or unsupervised learning approaches. Related to this, an overview of current preprocessing, statistical significance testing, classification, feature alignment, clustering, cross-validation, and functional data analysis techniques for time series is provided in Appendix A for further details of the considerations addressed in this study's methodology beyond those discussed directly in section \ref{330519}.

Method selection

Based on the technology classification problem considered, the bibliometric data available, and the methods discussed in Appendix A the following methods have been selected for use in this analysis:

Technology Life Cycle stage matching process

For those technologies where evidence for determining the transitions between different stages of the Technology Life Cycle has either not been found or is incomplete, a nearest neighbour pattern recognition approach has been employed based on the work of Gao \cite{Gao_2013} to locate the points where shifts between cycle stages occur. However, for the specific technologies considered in this paper, literature evidence has been identified for the transitions between stages, and so the nearest neighbour methodology is not discussed further here.

Identification of significant patent indicator groups

In order to identify those bibliometric indicator groupings that could form the basis of a data-driven technology classification model a combination of Dynamic Time Warping and the 'Partitioning Around Medoids' (PAM) variant of K-Medoids clustering has been applied in this study. For the initial feature alignment and distance measurement stages of this process, Dynamic Time Warping is still widely recognised as the classification benchmark to beat (see Appendix A), and so this study does not look to advance the feature alignment processes used beyond this. Unlike the Technology Life Cycle stage matching process which is based on a well-established technology maturity model, this study is assuming that a classification system based on the modes of substitution outlined in section \ref{585124} is not intrinsically valid. For this reason an unsupervised learning approach has been adopted here to enable human biases to be eliminated in determining whether a classification system based on presumptive technological substitution is valid or not, before subsequently defining a classification rule system. In doing so this additionally means that labelling of predicted clusters can be carried out even if labels are only available for a small number of observed samples representative of the desired classes, or potentially even if none of the observed samples are absolutely defined. This is of particular use if this technique is to be expanded to a wider population of technologies, as obtaining evidence of the applicable mode of substitution that gave rise to the current technology can be a time-consuming process, and in some cases the necessary evidence may not be publicly available (e.g. if dealing with commercially sensitive performance data). As such, clustering can provide an indication of the likely substitution mode of a given technology without the need for prior training on technologies that belong to any given class. Under such circumstances this approach could be applied without the need for collecting performance data, providing that the groupings produced by the analysis are broadly identifiable from inspection as being associated with the suspected modes of substitution (this is of course made easier if a handful of examples are known, but means that this is no longer a hard requirement).
The 'PAM' variant of K-Medoids is selected here over hierarchical clustering since the expected number of clusters is known from the literature, and keeping the number of clusters fixed allows for easier testing of how frequently predicted clusters align with expected groupings. Additionally, a small sample of technologies is evaluated in this study, and as a result computational expense is not likely to be significant in using the 'PAM' variant of K-Medoids  over Hierarchical clustering approaches. It is also worth noting that by evaluating the predictive performance of each subset of patent indicator groupings independently it is possible to spot and rank commonly recurring patterns of subsets, which is not possible when using approaches such as Linear Discriminant Analysis which can assess the impact of individual predictors, but not rank the most suitable combinations of indicators.

Ranking of significant patent indicator groups

As the number of technologies considered in this study is relatively small, exhaustive cross-validation approaches provide a feasible means to rank the out-of-sample predictive capabilities of those bibliometric indicator subsets that have been identified as producing significant correlations to expected in-sample technology groupings. As such, leave-p-out cross-validation approaches are applied for this purpose, whilst also reducing the risk of over-fitting in the following model building phases \cite{Arlot_2010}.

Model building

The misalignment in time between life cycle stages relative to other technologies can make it difficult to identify common features in time series. This is primarily because this phase variance risks artificially inflating data variance, skewing the driving principal components and often disguising underlying data structures \cite{Marron_2015}. Consequently, due to the importance of phase variance when comparing historical trends for different technologies, and the coupling that exists between adjacent points in growth and adoption curves, functional linear regression is selected here to build the technology classification model developed in this study (see notes on Functional Data Analysis in Appendix A for further details).