| phenomenon | unlabelled data carrying information about the label distribution - when it does, and the fact that nobody can tell in advance whether it does— “As mentioned earlier, unlabelled data is only useful if it carries information useful for label prediction that is not contained in the labelled data alone or cannot be easily extracted from it.” |
| claim-type | critique— “What is more, it is impossible to guarantee that the introduction of unlabelled data will not degrade performance.” |
| method — evidence | — “the authors found that no algorithm uniformly outperformed the others. Substantial performance improvements over the baselines were observed on some data sets, while performance was found to be degraded on others. Relative performance also varied with the amount of unlabelled data.” |
| object of study — evidence | — “Semi-supervised classification methods attempt to utilize unlabelled data points to construct a learner whose performance exceeds the performance of learners obtained when using only the labelled data.” |
| research question — evidence | — “Not only is it difficult to precisely define the conditions under which any particular semi-supervised learning algorithm may work, it is also rarely straightforward to evaluate to what extent these conditions are satisfied.” |
| contribution — evidence | — “From our perspective, the smoothness, low-density, and manifold assumptions boil down to different definitions of the similarity between points: the smoothness assumption states that points that are close to each other in input space are similar; the low-density assumption states that points in the same high-density area are similar; and the… |
| transfer | from graph theory (matching): the matching problem - find a subset of edges sharing no vertices - is taken from graph theory and used to pair unlabelled samples in a semi-supervised learner— “Their approach is inspired by matching, a concept from graph theory where one tries to find a subset of edges in a graph such that the edges do not share any vertices.” | transfers[0] |
| mechanism | THE CATEGORY IS DECIDED BY A CHOICE THE PRACTITIONER USUALLY DOES NOT KNOW THEY ARE MAKING: `The concept of similarity we choose, often implicitly, dictates what constitutes a cluster`— “The concept of similarity we choose, often implicitly, dictates what constitutes a cluster.” | mechanisms[0] |
| mechanism | and the field's three named assumptions differ only in what they mean by `close` - smoothness says near in input space, low-density says in the same dense region, manifold says on the same low-dimensional surface— “From our perspective, the smoothness, low-density, and manifold assumptions boil down to different definitions of the similarity between points: the smoothness assumption states that points that are close to each other in input space are similar; the low-density assumption states that points in the same high-density area are similar; and the… | mechanisms[1] |
| mechanism | so all three are instances of the cluster assumption, which is itself the necessary condition for the whole enterprise: that p(x) carries information about p(y|x)— “Consequently, the semi-supervised learning assumptions can be seen as more specific instances of the cluster assumption: that similar points tend to belong to the same group.” | mechanisms[2] |
| mechanism | A TAXONOMY PAPER THAT DIAGNOSES WHAT IS WRONG WITH TAXONOMIES: `Existing categorizations ... are typically relatively flat, thereby failing to capture similarities between different groups of methods. Furthermore, the categorizations are often fine-tuned towards existing work, making them less suited for the inclusion of new approaches.` Two named failure modes - too shallow to show kinship, and overfitted to the papers that existed when it was drawn.— “Existing categorizations of semi-supervised learning methods generally use a subset of these properties and are typically relatively flat, thereby failing to capture similarities between different groups of methods. Furthermore, the categorizations are often fine-tuned towards existing work, making them less suited for the inclusion of new… | mechanisms[3] |
| mechanism | AND THE PROPOSED REPAIR IS STATED AS A DESIGN GOAL, NOT A RESULT: `we propose a new way to represent the spectrum ... we ATTEMPT to group them in a clear, FUTURE-PROOF way`. `attempt` and `future-proof` in one sentence - the second is a property no survey can demonstrate about itself at publication.— “In this survey, we propose a new way to represent the spectrum of semi-supervised classification algorithms. We attempt to group them in a clear, future-proof way, allowing researchers and practitioners alike to gain insight into the way semi-supervised learning methods relate to each other, to existing supervised learning methods, and to… | mechanisms[4] |
| mechanism | THE FIELD'S OWN NAME FOR KNOWINGLY USING THE WRONG WORD: `in a slight abuse of notation`, used twice in this paper for two different acts - once to call lists `sets`, once to reassign X and x to random variables. Mathematics has a standard phrase for declaring a deliberate terminological error and continuing, and this survey uses it in a footnote and in body text without further comment.— “We note that the collections of data points referred to here are technically lists. However, following common usage, in this survey, we refer to them as ‘sets’ and, in a slight abuse of notation, apply standard set-theoretic concepts to them” | mechanisms[5] |
| critiques | the presentation of smoothness, low-density and manifold as separate assumptions, when they are one assumption under three definitions of similarity— “From our perspective, the smoothness, low-density, and manifold assumptions boil down to different definitions of the similarity between points: the smoothness assumption states that points that are close to each other in input space are similar; the low-density assumption states that points in the same high-density area are similar; and the… | claim_relations[0] |
| critiques | the semi-supervised literature's record of when its methods fail, whose prevalence is described as likely under-reported— “What is more, it is impossible to guarantee that the introduction of unlabelled data will not degrade performance.” | claim_relations[1] |
| supports | Oliver et al.'s finding that degradation appeared only under a class mismatch between the labelled and unlabelled sets— “Performance degradations were observed only when there was a mismatch between the classes present in the labelled data and the classes present in the unlabelled data.” | claim_relations[2] |
| sense | `similar` - THE LOAD-BEARING WORD OF THE WHOLE FIELD AND IT IS A CHOICE. Smoothness, low-density and manifold are three definitions of it, and the survey's contribution is showing they are the same assumption differently parameterised. WHICH ONE YOU PICKED IS USUALLY IMPLICIT— “The concept of similarity we choose, often implicitly, dictates what constitutes a cluster.” | senses[0] |
| sense | the cluster assumption - AS RE-READ HERE: not one assumption among several but the genus of which the other three are species, and equivalent to the necessary condition that p(x) carries information about p(y|x)— “Consequently, the semi-supervised learning assumptions can be seen as more specific instances of the cluster assumption: that similar points tend to belong to the same group.” | senses[1] |
| sense | `semi-supervised learning works` - AS THE SURVEY IS FORCED TO QUALIFY IT: it can help, it can do nothing, and it can DEGRADE performance, with no way to know which in advance. The literature's record of the third case is described as UNDER-REPORTED— “What is more, it is impossible to guarantee that the introduction of unlabelled data will not degrade performance.” | senses[2] |
| sense | `sets` - A DECLARED TYPE ERROR, KEPT ON PURPOSE: `the collections of data points referred to here are technically lists. However, following common usage, in this survey, we refer to them as ‘sets’ and, in a slight abuse of notation, apply standard set-theoretic concepts to them.` The authors know the word is wrong, say so in a footnote, and use it anyway because the field does.— “We note that the collections of data points referred to here are technically lists. However, following common usage, in this survey, we refer to them as ‘sets’ and, in a slight abuse of notation, apply standard set-theoretic concepts to them” | senses[3] |
| sense | `abuse of notation` IS USED TWICE IN THIS PAPER FOR TWO DIFFERENT ACTS. The second is symbol reuse: `we use X and x to denote random variables and their realizations, respectively, rather than data points` - the same symbols carry a new meaning from that point on.— “In the following, with a slight abuse of notation, we use X and x to denote random variables and their realizations, respectively, rather than data points” | senses[4] |
| sense | `inductive` / `transductive` - the split is defined by WHAT THE METHOD RETURNS, not by how it works: `the former attempt to find a classification model, whereas the latter are solely concerned with obtaining label predictions for the given unlabelled data points`.— “At the highest level, it distinguishes between inductive and transductive methods, which give rise to distinct optimization procedures: the former attempt to find a classification model, whereas the latter are solely concerned with obtaining label predictions for the given unlabelled data points” | senses[5] |
| sense | 'margin' - ONE TERM, TWO DIFFERENT KINDS OF OBJECT, AND THE SURVEY RECORDS BOTH WITHOUT CHOOSING: 'the _margin_, which is defined as the distance between the decision boundary and the data points closest to it. The term is also commonly used to describe the area extruding from the decision boundary in which no data points lie.' A SCALAR AND A REGION. Not two readings of one quantity - two different types, so 'maximise the margin' and 'lies within the margin' are grammatical with different referents, and only one of them can be a number. This record already carries the survey's declared type error over 'sets', kept on purpose, and its two senses of 'abuse of notation'; this is the same survey's third type-level observation, and the only one it does not flag as its own.— “The objective of an SVM is to find a decision boundary that maximizes the margin, which is defined as the distance between the decision boundary and the data points closest to it. The term is also commonly used to describe the area extruding from the decision boundary in which no data points lie.” | senses[6] |
| sense | `pseudo-labelled data` - A NAME WHOSE PREFIX CARRIES THE ONLY WARNING. `previously unlabelled data that is augmented with predictions from earlier iterations of the learners. The latter is commonly referred to as _pseudo-labelled data_.` `pseudo-` is doing all the epistemic work: the data is treated exactly like labelled data by the algorithm, and only the name records that the labels are the model's own guesses. Drop the prefix in a citation and the caution is gone with it.— “previously unlabelled data that is augmented with predictions from earlier iterations of the learners. The latter is commonly referred to as pseudo-labelled data.” | senses[7] |
| sense | Semi-supervised learning - a machine-learning branch that performs tasks using both labelled and unlabelled data— “Semi-supervised learning is the branch of machine learning concerned with using labelled as well as unlabelled data to perform certain learning tasks” | senses[8] |
| sense | Wrapper methods - pseudo-label unlabelled data externally while the supervised learner remains unaware of label provenance— “Such methods are known as wrapper methods: the unlabelled data is pseudo-labelled by a wrapper procedure, and a purely supervised learning algorithm, unaware of the distinction between originally labelled and pseudo-labelled data, constructs the final inductive classifier” | senses[9] |
| sense | Unsupervised preprocessing methods - use unlabelled data for features, clustering, or initial parameters but give the classifier only original labels— “Secondly, we consider unsupervised preprocessing methods, which either extract useful features from the unlabelled data, pre-cluster the data, or determine the initial parameters of a supervised learning procedure in an unsupervised manner. Like wrapper methods, they can be used with any supervised classifier. However, unlike wrapper methods… | senses[10] |
| sense | Intrinsically semi-supervised - no intermediate step and no supervised base learner— “These methods, which we call intrinsically semi-supervised, do not rely on any intermediate steps or supervised base learners” | senses[11] |
| sense | Co-training - self-training extended to multiple classifiers that learn from one another's most confident predictions— “Secondly, we consider co-training, an extension of self-training to multiple classifiers that are iteratively re-trained on each other’s most confident predictions” | senses[12] |
| sense | Pseudo-labelled boosting methods - sequential ensembles whose classifiers use labels plus earlier classifiers' confident unlabelled predictions— “Lastly, we consider pseudo-labelled boosting methods. Like traditional boosting methods, they build a classifier ensemble by constructing individual classifiers sequentially, where each individual classifier is trained on both labelled data and the most confident predictions of the previous classifiers on unlabelled data” | senses[13] |
| sense | Inference - the final transductive graph-based phase, where the graph assigns labels to unlabelled data points— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference. In the first step, the set of objects, X, is used to construct a graph where each node represents a data point and pairwise similar data points are connected by an edge. In the second step, these edges are weighted to… | senses[14] |
| sense | Training in wrapper methods - fitting classifiers on labelled and possibly prior pseudo-labelled data— “The procedure usually consists of two alternating steps of training and pseudo-labelling. In the training step, one or more supervised classifiers are trained on the labelled data and, possibly, pseudo-labelled data from previous iterations. In the pseudo-labelling step, the resulting classifiers are used to infer labels for the previously… | senses[15] |
| sense | Pseudo-labelling in wrapper methods - turning confident predictions for unlabelled objects into labels for the next iteration— “The procedure usually consists of two alternating steps of training and pseudo-labelling. In the training step, one or more supervised classifiers are trained on the labelled data and, possibly, pseudo-labelled data from previous iterations. In the pseudo-labelling step, the resulting classifiers are used to infer labels for the previously… | senses[16] |
| control | the published empirical comparisons are surveyed rather than a single one cited - eight data sets in one study, several neural methods on two image problems in another — failed— “the authors found that no algorithm uniformly outperformed the others. Substantial performance improvements over the baselines were observed on some data sets, while performance was found to be degraded on others. Relative performance also varied with the amount of unlabelled data.” — rules out a field-level claim resting on the studies that happened to work; the answer reported is that NO ALGORITHM UNIFORMLY OUTPERFORMED THE OTHERS and relative performance varied with the amount of unlabelled data— “the authors found that no algorithm uniformly outperformed the others. Substantial performance improvements over the baselines were observed on some data sets, while performance was found to be degraded on others. Relative performance also varied with the amount of unlabelled data.” | controls[0] |
| control | where degradation was observed, the condition producing it is isolated - a mismatch between the classes in the labelled and the unlabelled data — held— “Performance degradations were observed only when there was a mismatch between the classes present in the labelled data and the classes present in the unlabelled data.” — rules out degradation being treated as unexplained noise; here it has a named cause that a practitioner can check for— “Performance degradations were observed only when there was a mismatch between the classes present in the labelled data and the classes present in the unlabelled data.” | controls[1] |
| control | whether the conditions for a given method to work can be evaluated on a given dataset — failed— “In other words: if the data points (both unlabelled and labelled) cannot be meaningfully clustered, it is impossible for a semi-supervised learning method to improve on a supervised learning method.” — rules out nothing - it is 'rarely straightforward to evaluate to what extent these conditions are satisfied', which is why the necessary condition is not a test— “Not only is it difficult to precisely define the conditions under which any particular semi-supervised learning algorithm may work, it is also rarely straightforward to evaluate to what extent these conditions are satisfied.” | controls[2] |
| weight | the presentation of smoothness, low-density and manifold as separate assumptions, when they are one assumption under three definitions of similarity — 0.9— “From our perspective, the smoothness, low-density, and manifold assumptions boil down to different definitions of the similarity between points: the smoothness assumption states that points that are close to each other in input space are similar; the low-density assumption states that points in the same high-density area are similar; and the… | claim_relations[0] |
| weight | the semi-supervised literature's record of when its methods fail, whose prevalence is described as likely under-reported — 0.9— “What is more, it is impossible to guarantee that the introduction of unlabelled data will not degrade performance.” | claim_relations[1] |
| weight | Oliver et al.'s finding that degradation appeared only under a class mismatch between the labelled and unlabelled sets — 0.8— “Performance degradations were observed only when there was a mismatch between the classes present in the labelled data and the classes present in the unlabelled data.” | claim_relations[2] |
| audit | smoothness —is-a→ cluster assumption — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but endpoint by anaphora: 'the semi-supervised learning assumptions' = the smoothness, low-density and manifold assumptions of the previous sentence; is-a is loose.— “Consequently, the semi-supervised learning assumptions can be seen as more specific instances of the cluster assumption: that similar points tend to belong to the same group.” | concept_edges[0] |
| audit | manifold —is-a→ cluster assumption — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span introduces the cluster assumption as an additional assumption beside manifolds; is-a is loose.— “Consequently, if we are able to determine which manifolds exist and which data points lie on which manifold, the class assignments of unlabelled data points can be inferred from the labelled data points on the same manifold. 2.2 Connection to clustering In semi-supervised learning research, an additional assumption that is often included is… | concept_edges[1] |
| note | self-training —same-as→ self-learning — Given parenthetically and without preference, in a sentence that cites a survey whose own title uses a THIRD name - 'Self-labeled techniques for semi-supervised learning…'. Three names for one method inside one sentence, and the paper treats the multiplicity as unremarkable.— “Self-training methods (sometimes also called “self-learning” methods) are the most basic of pseudo-labelling approaches” | concept_edges[2] |
| relation | self-training —same-as→ self-learning — one method, two names, offered parenthetically and without preference— “Self-training methods (sometimes also called “self-learning” methods) are the most basic of pseudo-labelling approaches”— “Self-training methods (sometimes also called “self-learning” methods)” | concept_edges[2] |
| weight | self-training —same-as→ self-learning — 0.9— “Self-training methods (sometimes also called “self-learning” methods) are the most basic of pseudo-labelling approaches” | concept_edges[2] |
| note | inductive —distinct-from→ transductive — The top-level split of the taxonomy, and the differentiating property is the OUTPUT TYPE - a model versus a label vector.— “At the highest level, it distinguishes between inductive and transductive methods, which give rise to distinct optimization procedures: the former attempt to find a classification model, whereas the latter are solely concerned with obtaining label predictions for the given unlabelled data points” | concept_edges[3] |
| relation | inductive —distinct-from→ transductive — the taxonomy's top-level split, and the differentiating property is the OUTPUT TYPE - a model versus a label vector— “At the highest level, it distinguishes between inductive and transductive methods, which give rise to distinct optimization procedures: the former attempt to find a classification model, whereas the latter are solely concerned with obtaining label predictions for the given unlabelled data points”— “it distinguishes between inductive and transductive methods” | concept_edges[3] |
| weight | inductive —distinct-from→ transductive — 0.95— “At the highest level, it distinguishes between inductive and transductive methods, which give rise to distinct optimization procedures: the former attempt to find a classification model, whereas the latter are solely concerned with obtaining label predictions for the given unlabelled data points” | concept_edges[3] |
| note | graph construction —part-of→ Transductive graph-based methods — 'consist of' is in the containment cue list, so this edge is cue-tested. Weight 0.9 rather than 1.0 - 'GENERALLY consist of' is the survey hedging across the family it is describing.— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference.” | concept_edges[4] |
| weight | graph construction —part-of→ Transductive graph-based methods — 0.9— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference.” | concept_edges[4] |
| note | graph weighting —part-of→ Transductive graph-based methods — Second of the three steps, same sentence, same hedge.— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference.” | concept_edges[5] |
| weight | graph weighting —part-of→ Transductive graph-based methods — 0.9— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference.” | concept_edges[5] |
| note | inference —part-of→ Transductive graph-based methods — The survey says these methods generally have the three steps, so the paper-level hedge is 0.9.— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference. In the first step, the set of objects, X, is used to construct a graph where each node represents a data point and pairwise similar data points are connected by an edge. In the second step, these edges are weighted to… | concept_edges[6] |
| weight | inference —part-of→ Transductive graph-based methods — 0.9— “Transductive graph-based methods generally consist of three steps: graph construction, graph weighting and inference. In the first step, the set of objects, X, is used to construct a graph where each node represents a data point and pairwise similar data points are connected by an edge. In the second step, these edges are weighted to… | concept_edges[6] |
| audit | pseudo-labelling —part-of→ wrapper methods — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'The procedure ... pseudo-labelling step'; 'wrapper methods' is named only in the preceding text.— “The procedure usually consists of two alternating steps of training and pseudo-labelling. In the training step, one or more supervised classifiers are trained on the labelled data and, possibly, pseudo-labelled data from previous iterations. In the pseudo-labelling step, the resulting classifiers are used to infer labels for the previously… | concept_edges[8] |
| note | pseudo-labelling —part-of→ wrapper methods — The procedure usually has these two alternating steps; weight 0.9 preserves that hedge.— “The procedure usually consists of two alternating steps of training and pseudo-labelling. In the training step, one or more supervised classifiers are trained on the labelled data and, possibly, pseudo-labelled data from previous iterations. In the pseudo-labelling step, the resulting classifiers are used to infer labels for the previously… | concept_edges[8] |
| weight | pseudo-labelling —part-of→ wrapper methods — 0.9— “The procedure usually consists of two alternating steps of training and pseudo-labelling. In the training step, one or more supervised classifiers are trained on the labelled data and, possibly, pseudo-labelled data from previous iterations. In the pseudo-labelling step, the resulting classifiers are used to infer labels for the previously… | concept_edges[8] |
| note | unsupervised preprocessing methods —distinct-from→ wrapper methods — The paper explicitly contrasts what the supervised classifier receives under the two method families.— “Secondly, we consider unsupervised preprocessing methods, which either extract useful features from the unlabelled data, pre-cluster the data, or determine the initial parameters of a supervised learning procedure in an unsupervised manner. Like wrapper methods, they can be used with any supervised classifier. However, unlike wrapper methods… | concept_edges[9] |
| evidence status note | concept — THE TERM IS NOT IN THE QUOTE - the quote's former and latter terms are inductive and transductive methods, named in the sentence just before it ('between inductive and transductive methods'). That sentence is not quoted because reference-list text is spliced into its citation.— “The former, like supervised learning methods, yield a classification model that can be used to predict the label of previously unseen data points. The latter do not yield such a model, but instead directly provide predictions” | concepts[6] |
| evidence status note | concept — THE TERM IS NOT IN THE QUOTE - the quote's former and latter terms are inductive and transductive methods, named in the sentence just before it ('between inductive and transductive methods'). That sentence is not quoted because reference-list text is spliced into its citation.— “The former, like supervised learning methods, yield a classification model that can be used to predict the label of previously unseen data points. The latter do not yield such a model, but instead directly provide predictions” | concepts[7] |
| outcome | control — failed— “the authors found that no algorithm uniformly outperformed the others. Substantial performance improvements over the baselines were observed on some data sets, while performance was found to be degraded on others. Relative performance also varied with the amount of unlabelled data.” | controls[0] |
| outcome | control — held— “Performance degradations were observed only when there was a mismatch between the classes present in the labelled data and the classes present in the unlabelled data.” | controls[1] |
| outcome | control — failed— “Not only is it difficult to precisely define the conditions under which any particular semi-supervised learning algorithm may work, it is also rarely straightforward to evaluate to what extent these conditions are satisfied.”— “In other words: if the data points (both unlabelled and labelled) cannot be meaningfully clustered, it is impossible for a semi-supervised learning method to improve on a supervised learning method.” | controls[2] |
| no type for this | co-training → self-training — The paper says co-training extends self-training to multiple classifiers. Extension is not is-a, part-of, same-as, distinct-from, contrasted-with, operationalised-as, causes, or renamed-across-fields; the concept-edge schema has no extends type.— “Secondly, we consider co-training, an extension of self-training to multiple classifiers that are iteratively re-trained on each other’s most confident predictions” | unhoused_relations[0] |
| limitation | THE NECESSARY CONDITION CANNOT BE CHECKED. `if the data points ... cannot be meaningfully clustered, it is impossible for a semi-supervised learning method to improve on a supervised learning method` - and whether they can is exactly what cannot be established in advance— “In other words: if the data points (both unlabelled and labelled) cannot be meaningfully clustered, it is impossible for a semi-supervised learning method to improve on a supervised learning method.” | limitations[0] |
| limitation | stated twice over, at both levels: it is difficult to DEFINE the conditions under which an algorithm works, and `rarely straightforward to evaluate to what extent these conditions are satisfied`— “Not only is it difficult to precisely define the conditions under which any particular semi-supervised learning algorithm may work, it is also rarely straightforward to evaluate to what extent these conditions are satisfied.” | limitations[1] |
| limitation | IT IS IMPOSSIBLE TO GUARANTEE THAT UNLABELLED DATA WILL NOT DEGRADE PERFORMANCE - the method can do worse than ignoring the extra data, and no test tells you beforehand— “What is more, it is impossible to guarantee that the introduction of unlabelled data will not degrade performance.” | limitations[2] |
| limitation | and no method exists to choose the algorithm a priori, exactly as in supervised learning - so the practitioner picks the assumption and finds out afterwards— “As is the case for supervised learning algorithms, no method has yet been discovered to determine a priori what learning method is best-suited for any particular problem.” | limitations[3] |
| limitation | THE CENTRAL CLAIM ABOUT THE TAXONOMY IS UNFALSIFIABLE AT TIME OF WRITING: `allowing researchers and practitioners alike to gain insight into the way semi-supervised learning methods relate to each other`, built in a `future-proof way`. The paper's stated advantage over prior categorizations is that new methods will fit it - a claim only later work can test, and the same claim the superseded categorizations could have made.— “In this survey, we propose a new way to represent the spectrum of semi-supervised classification algorithms. We attempt to group them in a clear, future-proof way, allowing researchers and practitioners alike to gain insight into the way semi-supervised learning methods relate to each other, to existing supervised learning methods, and to… | limitations[4] |