Predicting diffusion of innovations with self-organisation and machine learning

The main subject of this master's thesis was predicting diffusion of innovations. The prediction was done in a special case: product has been available in some countries, and based on its diffusion in those countries the prediction is done for other countries. The prediction was based on finding similar countries with Self-Organizing Map~(SOM), using parameters of countries. Parameters included various economical and social key figures. SOM was optimised for different products using two different methods: (a) by adding diffusion information of products to the country parameters, and (b) by weighting the country parameters based on their importance for the diffusion of different products. A novel method using Differential Evolution (DE) was developed to solve the latter, highly non-linear optimisation problem. Results were fairly good. The prediction method seems to be on a solid theoretical foundation. The results based on country data were good. Instead, optimisation for different products did not generally offer clear benefit, but in some cases the improvement was clearly noticeable. The weights found for the parameters of the countries with the developed SOM optimisation method were interesting, and most of them could be explained by properties of the products.

Biomedical Event Extraction with Machine Learning

Biomedical natural language processing (BioNLP) is a subfield of natural language processing, an area of computational linguistics concerned with developing programs that work with natural language: written texts and speech. Biomedical relation extraction concerns the detection of semantic relations such as protein-protein interactions (PPI) from scientific texts. The aim is to enhance information retrieval by detecting relations between concepts, not just individual concepts as with a keyword search. In recent years, events have been proposed as a more detailed alternative for simple pairwise PPI relations. Events provide a systematic, structural representation for annotating the content of natural language texts. Events are characterized by annotated trigger words, directed and typed arguments and the ability to nest other events. For example, the sentence “Protein A causes protein B to bind protein C” can be annotated with the nested event structure CAUSE(A, BIND(B, C)). Converted to such formal representations, the information of natural language texts can be used by computational applications. Biomedical event annotations were introduced by the BioInfer and GENIA corpora, and event extraction was popularized by the BioNLP'09 Shared Task on Event Extraction. In this thesis we present a method for automated event extraction, implemented as the Turku Event Extraction System (TEES). A unified graph format is defined for representing event annotations and the problem of extracting complex event structures is decomposed into a number of independent classification tasks. These classification tasks are solved using SVM and RLS classifiers, utilizing rich feature representations built from full dependency parsing. Building on earlier work on pairwise relation extraction and using a generalized graph representation, the resulting TEES system is capable of detecting binary relations as well as complex event structures. We show that this event extraction system has good performance, reaching the first place in the BioNLP'09 Shared Task on Event Extraction. Subsequently, TEES has achieved several first ranks in the BioNLP'11 and BioNLP'13 Shared Tasks, as well as shown competitive performance in the binary relation Drug-Drug Interaction Extraction 2011 and 2013 shared tasks. The Turku Event Extraction System is published as a freely available open-source project, documenting the research in detail as well as making the method available for practical applications. In particular, in this thesis we describe the application of the event extraction method to PubMed-scale text mining, showing how the developed approach not only shows good performance, but is generalizable and applicable to large-scale real-world text mining projects. Finally, we discuss related literature, summarize the contributions of the work and present some thoughts on future directions for biomedical event extraction. This thesis includes and builds on six original research publications. The first of these introduces the analysis of dependency parses that leads to development of TEES. The entries in the three BioNLP Shared Tasks, as well as in the DDIExtraction 2011 task are covered in four publications, and the sixth one demonstrates the application of the system to PubMed-scale text mining.

Sentence Compression with Supervised Machine Learning

The subject of the thesis is automatic sentence compression with machine learning, so that the compressed sentences remain both grammatical and retain their essential meaning. There are multiple possible uses for the compression of natural language sentences. In this thesis the focus is generation of television program subtitles, which often are compressed version of the original script of the program. The main part of the thesis consists of machine learning experiments for automatic sentence compression using different approaches to the problem. The machine learning methods used for this work are linear-chain conditional random fields and support vector machines. Also we take a look which automatic text analysis methods provide useful features for the task. The data used for machine learning is supplied by Lingsoft Inc. and consists of subtitles in both compressed an uncompressed form. The models are compared to a baseline system and comparisons are made both automatically and also using human evaluation, because of the potentially subjective nature of the output. The best result is achieved using a CRF - sequence classification using a rich feature set. All text analysis methods help classification and most useful method is morphological analysis. Tutkielman aihe on suomenkielisten lauseiden automaattinen tiivistäminen koneellisesti, niin että lyhennetyt lauseet säilyttävät olennaisen informaationsa ja pysyvät kieliopillisina. Luonnollisen kielen lauseiden tiivistämiselle on monta käyttötarkoitusta, mutta tässä tutkielmassa aihetta lähestytään television ohjelmien tekstittämisen kautta, johon käytännössä kuuluu alkuperäisen tekstin lyhentäminen televisioruudulle paremmin sopivaksi. Tutkielmassa kokeillaan erilaisia koneoppimismenetelmiä tekstin automaatiseen lyhentämiseen ja tarkastellaan miten hyvin erilaiset luonnollisen kielen analyysimenetelmät tuottavat informaatiota, joka auttaa näitä menetelmiä lyhentämään lauseita. Lisäksi tarkastellaan minkälainen lähestymistapa tuottaa parhaan lopputuloksen. Käytetyt koneoppimismenetelmät ovat tukivektorikone ja lineaarisen sekvenssin mallinen CRF. Koneoppimisen tukena käytetään tekstityksiä niiden eri käsittelyvaiheissa, jotka on saatu Lingsoft OY:ltä. Luotuja malleja vertaillaan Lopulta mallien lopputuloksia evaluoidaan automaattisesti ja koska teksti lopputuksena on jossain määrin subjektiivinen myös ihmisarviointiin perustuen. Vertailukohtana toimii kirjallisuudesta poimittu menetelmä. Tutkielman tuloksena paras lopputulos saadaan aikaan käyttäen CRF sekvenssi-luokittelijaa laajalla piirrejoukolla. Kaikki kokeillut teksin analyysimenetelmät auttavat luokittelussa, joista tärkeimmän panoksen antaa morfologinen analyysi.

Evaluation of Machine Learning Classifiers for Mobile Network Intrusion Detection Systems

Mobile malwares are increasing with the growing number of Mobile users. Mobile malwares can perform several operations which lead to cybersecurity threats such as, stealing financial or personal information, installing malicious applications, sending premium SMS, creating backdoors, keylogging and crypto-ransomware attacks. Knowing the fact that there are many illegitimate Applications available on the App stores, most of the mobile users remain careless about the security of their Mobile devices and become the potential victim of these threats. Previous studies have shown that not every antivirus is capable of detecting all the threats; due to the fact that Mobile malwares use advance techniques to avoid detection. A Network-based IDS at the operator side will bring an extra layer of security to the subscribers and can detect many advanced threats by analyzing their traffic patterns. Machine Learning(ML) will provide the ability to these systems to detect unknown threats for which signatures are not yet known. This research is focused on the evaluation of Machine Learning classifiers in Network-based Intrusion detection systems for Mobile Networks. In this study, different techniques of Network-based intrusion detection with their advantages, disadvantages and state of the art in Hybrid solutions are discussed. Finally, a ML based NIDS is proposed which will work as a subsystem, to Network-based IDS deployed by Mobile Operators, that can help in detecting unknown threats and reducing false positives. In this research, several ML classifiers were implemented and evaluated. This study is focused on Android-based malwares, as Android is the most popular OS among users, hence most targeted by cyber criminals. Supervised ML algorithms based classifiers were built using the dataset which contained the labeled instances of relevant features. These features were extracted from the traffic generated by samples of several malware families and benign applications. These classifiers were able to detect malicious traffic patterns with the TPR upto 99.6% during Cross-validation test. Also, several experiments were conducted to detect unknown malware traffic and to detect false positives. These classifiers were able to detect unknown threats with the Accuracy of 97.5%. These classifiers could be integrated with current NIDS', which use signatures, statistical or knowledge-based techniques to detect malicious traffic. Technique to integrate the output from ML classifier with traditional NIDS is discussed and proposed for future work.

Retinal Image Analysis Using Machine Vision

The topic of this thesis is studying how lesions in retina caused by diabetic retinopathy can be detected from color fundus images by using machine vision methods. Methods for equalizing uneven illumination in fundus images, detecting regions of poor image quality due toinadequate illumination, and recognizing abnormal lesions were developed duringthe work. The developed methods exploit mainly the color information and simpleshape features to detect lesions. In addition, a graphical tool for collecting lesion data was developed. The tool was used by an ophthalmologist who marked lesions in the images to help method development and evaluation. The tool is a general purpose one, and thus it is possible to reuse the tool in similar projects.The developed methods were tested with a separate test set of 128 color fundus images. From test results it was calculated how accurately methods classify abnormal funduses as abnormal (sensitivity) and healthy funduses as normal (specificity). The sensitivity values were 92% for hemorrhages, 73% for red small dots (microaneurysms and small hemorrhages), and 77% for exudates (hard and soft exudates). The specificity values were 75% for hemorrhages, 70% for red small dots, and 50% for exudates. Thus, the developed methods detected hemorrhages accurately and microaneurysms and exudates moderately.

Offset-print mottling measurement using machine vision

Mottling is one of the key defects in offset-printing. Mottling can be defined as unwanted unevenness of print. In this work, diameter of a mottle spot is defined between 0.5-10.0 mm. There are several types of mottling, but the reason behind the problem is still not fully understood. Several commercial machine vision products for the evaluation of print unevenness have been presented. Two of these methods used in these products have been implemented in this thesis. The one is the cluster method and the other is the band-pass method. The properties of human vision system have been taken into account in the implementation of these two methods. An index produced by the cluster method is a weighted sum of the number of found spots, and an index produced by band-pass method is a weighted sum of coefficients of variations of gray-levels for each spatial band. Both methods produce larger indices for visually poor samples, so they can discern good samples from the poor ones. The difference between the indices for good and poor samples is slightly larger produced by the cluster method. 11 However, without the samples evaluated by human experts, the goodness of these results is still questionable. This comparison will be left to the next phase of the project.

Machine Learning and Clinical Text. Supporting Health Information Flow

Fluent health information flow is critical for clinical decision-making. However, a considerable part of this information is free-form text and inabilities to utilize it create risks to patient safety and cost-­effective hospital administration. Methods for automated processing of clinical text are emerging. The aim in this doctoral dissertation is to study machine learning and clinical text in order to support health information flow.First, by analyzing the content of authentic patient records, the aim is to specify clinical needs in order to guide the development of machine learning applications.The contributions are a model of the ideal information flow,a model of the problems and challenges in reality, and a road map for the technology development. Second, by developing applications for practical cases,the aim is to concretize ways to support health information flow. Altogether five machine learning applications for three practical cases are described: The first two applications are binary classification and regression related to the practical case of topic labeling and relevance ranking.The third and fourth application are supervised and unsupervised multi-class classification for the practical case of topic segmentation and labeling.These four applications are tested with Finnish intensive care patient records.The fifth application is multi-label classification for the practical task of diagnosis coding. It is tested with English radiology reports.The performance of all these applications is promising. Third, the aim is to study how the quality of machine learning applications can be reliably evaluated.The associations between performance evaluation measures and methods are addressed,and a new hold-out method is introduced.This method contributes not only to processing time but also to the evaluation diversity and quality. The main conclusion is that developing machine learning applications for text requires interdisciplinary, international collaboration. Practical cases are very different, and hence the development must begin from genuine user needs and domain expertise. The technological expertise must cover linguistics,machine learning, and information systems. Finally, the methods must be evaluated both statistically and through authentic user-feedback.

Threat modeling a factory environment using Microsoft Security Development Lifecycle methodology

The number of security violations is increasing and a security breach could have irreversible impacts to business. There are several ways to improve organization security, but some of them may be difficult to comprehend. This thesis demystifies threat modeling as part of secure system development. Threat modeling enables developers to reveal previously undetected security issues from computer systems. It offers a structured approach for organizations to find and address threats against vulnerabilities. When implemented correctly threat modeling will reduce the amount of defects and malicious attempts against the target environment. In this thesis Microsoft Security Development Lifecycle (SDL) is introduced as an effective methodology for reducing defects in the target system. SDL is traditionally meant to be used in software development, principles can be however partially adapted to IT-infrastructure development. Microsoft threat modeling methodology is an important part of SDL and it is utilized in this thesis to find threats from the Acme Corporation’s factory environment. Acme Corporation is used as a pseudonym for a company providing high-technology consumer electronics. Target for threat modeling is the IT-infrastructure of factory’s manufacturing execution system. Microsoft threat modeling methodology utilizes STRIDE –mnemonic and data flow diagrams to find threats. Threat modeling in this thesis returned results that were important for the organization. Acme Corporation now has more comprehensive understanding concerning IT-infrastructure of the manufacturing execution system. On top of vulnerability related results threat modeling provided coherent views of the target system. Subject matter experts from different areas can now agree upon functions and dependencies of the target system. Threat modeling was recognized as a useful activity for improving security.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Learning Preferences with Kernel-Based Methods

Learning of preference relations has recently received significant attention in machine learning community. It is closely related to the classification and regression analysis and can be reduced to these tasks. However, preference learning involves prediction of ordering of the data points rather than prediction of a single numerical value as in case of regression or a class label as in case of classification. Therefore, studying preference relations within a separate framework facilitates not only better theoretical understanding of the problem, but also motivates development of the efficient algorithms for the task. Preference learning has many applications in domains such as information retrieval, bioinformatics, natural language processing, etc. For example, algorithms that learn to rank are frequently used in search engines for ordering documents retrieved by the query. Preference learning methods have been also applied to collaborative filtering problems for predicting individual customer choices from the vast amount of user generated feedback. In this thesis we propose several algorithms for learning preference relations. These algorithms stem from well founded and robust class of regularized least-squares methods and have many attractive computational properties. In order to improve the performance of our methods, we introduce several non-linear kernel functions. Thus, contribution of this thesis is twofold: kernel functions for structured data that are used to take advantage of various non-vectorial data representations and the preference learning algorithms that are suitable for different tasks, namely efficient learning of preference relations, learning with large amount of training data, and semi-supervised preference learning. Proposed kernel-based algorithms and kernels are applied to the parse ranking task in natural language processing, document ranking in information retrieval, and remote homology detection in bioinformatics domain. Training of kernel-based ranking algorithms can be infeasible when the size of the training set is large. This problem is addressed by proposing a preference learning algorithm whose computation complexity scales linearly with the number of training data points. We also introduce sparse approximation of the algorithm that can be efficiently trained with large amount of data. For situations when small amount of labeled data but a large amount of unlabeled data is available, we propose a co-regularized preference learning algorithm. To conclude, the methods presented in this thesis address not only the problem of the efficient training of the algorithms but also fast regularization parameter selection, multiple output prediction, and cross-validation. Furthermore, proposed algorithms lead to notably better performance in many preference learning tasks considered.

Kernel-Based Ranking. Methods for Learning and Performance Estimation

Machine learning provides tools for automated construction of predictive models in data intensive areas of engineering and science. The family of regularized kernel methods have in the recent years become one of the mainstream approaches to machine learning, due to a number of advantages the methods share. The approach provides theoretically well-founded solutions to the problems of under- and overfitting, allows learning from structured data, and has been empirically demonstrated to yield high predictive performance on a wide range of application domains. Historically, the problems of classification and regression have gained the majority of attention in the field. In this thesis we focus on another type of learning problem, that of learning to rank. In learning to rank, the aim is from a set of past observations to learn a ranking function that can order new objects according to how well they match some underlying criterion of goodness. As an important special case of the setting, we can recover the bipartite ranking problem, corresponding to maximizing the area under the ROC curve (AUC) in binary classification. Ranking applications appear in a large variety of settings, examples encountered in this thesis include document retrieval in web search, recommender systems, information extraction and automated parsing of natural language. We consider the pairwise approach to learning to rank, where ranking models are learned by minimizing the expected probability of ranking any two randomly drawn test examples incorrectly. The development of computationally efficient kernel methods, based on this approach, has in the past proven to be challenging. Moreover, it is not clear what techniques for estimating the predictive performance of learned models are the most reliable in the ranking setting, and how the techniques can be implemented efficiently. The contributions of this thesis are as follows. First, we develop RankRLS, a computationally efficient kernel method for learning to rank, that is based on minimizing a regularized pairwise least-squares loss. In addition to training methods, we introduce a variety of algorithms for tasks such as model selection, multi-output learning, and cross-validation, based on computational shortcuts from matrix algebra. Second, we improve the fastest known training method for the linear version of the RankSVM algorithm, which is one of the most well established methods for learning to rank. Third, we study the combination of the empirical kernel map and reduced set approximation, which allows the large-scale training of kernel machines using linear solvers, and propose computationally efficient solutions to cross-validation when using the approach. Next, we explore the problem of reliable cross-validation when using AUC as a performance criterion, through an extensive simulation study. We demonstrate that the proposed leave-pair-out cross-validation approach leads to more reliable performance estimation than commonly used alternative approaches. Finally, we present a case study on applying machine learning to information extraction from biomedical literature, which combines several of the approaches considered in the thesis. The thesis is divided into two parts. Part I provides the background for the research work and summarizes the most central results, Part II consists of the five original research articles that are the main contribution of this thesis.

Reflexive Space. A Constructionist Model of the Russian Reflexive Marker

This study examines the structure of the Russian Reflexive Marker ( ся/-сь) and offers a usage-based model building on Construction Grammar and a probabilistic view of linguistic structure. Traditionally, reflexive verbs are accounted for relative to non-reflexive verbs. These accounts assume that linguistic structures emerge as pairs. Furthermore, these accounts assume directionality where the semantics and structure of a reflexive verb can be derived from the non-reflexive verb. However, this directionality does not necessarily hold diachronically. Additionally, the semantics and the patterns associated with a particular reflexive verb are not always shared with the non-reflexive verb. Thus, a model is proposed that can accommodate the traditional pairs as well as for the possible deviations without postulating different systems. A random sample of 2000 instances marked with the Reflexive Marker was extracted from the Russian National Corpus and the sample used in this study contains 819 unique reflexive verbs. This study moves away from the traditional pair account and introduces the concept of Neighbor Verb. A neighbor verb exists for a reflexive verb if they share the same phonological form excluding the Reflexive Marker. It is claimed here that the Reflexive Marker constitutes a system in Russian and the relation between the reflexive and neighbor verbs constitutes a cross-paradigmatic relation. Furthermore, the relation between the reflexive and the neighbor verb is argued to be of symbolic connectivity rather than directionality. Effectively, the relation holding between particular instantiations can vary. The theoretical basis of the present study builds on this assumption. Several new variables are examined in order to systematically model variability of this symbolic connectivity, specifically the degree and strength of connectivity between items. In usage-based models, the lexicon does not constitute an unstructured list of items. Instead, items are assumed to be interconnected in a network. This interconnectedness is defined as Neighborhood in this study. Additionally, each verb carves its own niche within the Neighborhood and this interconnectedness is modeled through rhyme verbs constituting the degree of connectivity of a particular verb in the lexicon. The second component of the degree of connectivity concerns the status of a particular verb relative to its rhyme verbs. The connectivity within the neighborhood of a particular verb varies and this variability is quantified by using the Levenshtein distance. The second property of the lexical network is the strength of connectivity between items. Frequency of use has been one of the primary variables in functional linguistics used to probe this. In addition, a new variable called Constructional Entropy is introduced in this study building on information theory. It is a quantification of the amount of information carried by a particular reflexive verb in one or more argument constructions. The results of the lexical connectivity indicate that the reflexive verbs have statistically greater neighborhood distances than the neighbor verbs. This distributional property can be used to motivate the traditional observation that the reflexive verbs tend to have idiosyncratic properties. A set of argument constructions, generalizations over usage patterns, are proposed for the reflexive verbs in this study. In addition to the variables associated with the lexical connectivity, a number of variables proposed in the literature are explored and used as predictors in the model. The second part of this study introduces the use of a machine learning algorithm called Random Forests. The performance of the model indicates that it is capable, up to a degree, of disambiguating the proposed argument construction types of the Russian Reflexive Marker. Additionally, a global ranking of the predictors used in the model is offered. Finally, most construction grammars assume that argument construction form a network structure. A new method is proposed that establishes generalization over the argument constructions referred to as Linking Construction. In sum, this study explores the structural properties of the Russian Reflexive Marker and a new model is set forth that can accommodate both the traditional pairs and potential deviations from it in a principled manner.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.