Categories are critical for intelligent behavior. Our in-teractions with exemplars influence what we learn about categories (Chin-Parker & Ross, 2004; Medin, Lynch, Coley, & Atran, 1997). Markman and Ross (2003) pro-posed a transfer-appropriate processing framework for understanding this interaction–learning relationship. They reviewed how inference learning (e.g., an item is presented with its category label and most of its features, and the learner infers a missing feature) helps promote the learning of a prototype structure of a category. How-ever, categories are also learned when there is no helpful teacher providing labels for items or feedback about learn-ers’ categorizations. The goal of this article is to examine how inferences might help promote category learning in such an unsupervised instance and to explore the incre-mental nature of this category learning.

In one type of unsupervised learning task—category construction—participants partition a novel set of items. People overwhelmingly prefer to focus on a single dimen-sion and ignore the overall similarity of the items (Ahn & Medin, 1992; Medin, Wattenmaker, & Hampson, 1987; Milton & Wills, 2004; Regehr & Brooks, 1993), although many real-world categories are inductively rich, sharing many features, which is known as family resemblance (FR; Rosch & Mervis, 1975). Lassaline and Murphy (1996) argued that the lack of FR sorting is due to the lack of any interaction that requires people to learn about the category structure, such as attending to the relations

between features. Consistent with this idea, participants who asked about the pairing of the features1 were more likely to sort those items into FR categories (cf. Kaplan & Murphy, 1999; Spalding & Murphy, 1996; see Murphy, 2002, for a discussion). In contrast, questions about the frequency of individual features led to no differences in sorting when compared with a control group not asked any questions. This result suggests that one way in which people may learn FR categories in an unsupervised setting is by making inductive inferences about feature relations of category members.

We use this finding to examine two important issues in unsupervised category learning. First, what is learned from pairing inferences that allows people to learn the FR structure? Sorting provides a measure of those aspects of a representation that are most important for partitioning items, but does not provide information about what else might have been learned. Many category-learning theo-ries predict categorizations on the basis of dimensional weighting of relevant dimensions. Experiment 1 asks whether the pairing inferences lead to such differential weighting and whether it is restricted to people who do FR sorts, as we predicted. Experiment 2 asks whether the influ-ence of the inferences is specific to the pairings asked about, as might be more consistent with a transfer-appropriate pro-cessing framework. Second: Do pairing inferences lead to learning the FR structure, or is the process more incre-mental, as knowledge of the FR structure is built up over different interactions? For example, sorting is often used to assess the representation, but it is also an interaction: Viewing and sorting the items may lead to learning more about the category structure. Both experiments include measures before and after sorting, to allow an examina-tion of incremental learning. One possibility to be tested is whether pairing inferences lead to learning something specific to this interaction, such as the pairs asked about,

251 Copyright 2006 Psychonomic Society, Inc.

This research was supported by a National Science Foundation Gradu-ate Fellowship to the first author and by National Science Foundation Grant SBR 97-20304 to the second author. We thank Gregory L. Murphy and three anonymous reviewers for helpful comments. Correspondence should be addressed to M. Diaz, Department of Psychology, University of Illinois, 603 East Daniel Street, Champaign, IL 61820 (e-mail: mikediaz@uiuc.edu).

Sorting out categories: Incremental learning of category structure

MICHAEL DIAZ and BRIAN H. ROSSUniversity of Illinois at Urbana-Champaign, Urbana, Illinois

Two experiments examine how inferences might promote unsupervised and incremental category learning. Many categories have members related through overall similarity (e.g., a family resemblance structure) rather than by a defining feature. However, when people are asked to sort category mem-bers in a category construction task, they often do so by partitioning on a single feature. Starting from an earlier result showing that pairwise inferences increase family resemblance sorting (Lassaline & Murphy, 1996), we examine how these inferences lead to learning the family resemblance structure. Results show that the category structure is learned incrementally. The pairwise inferences influence participants’ weightings of feature pairs that were specifically asked about, which in turn affects their sorting. The sorting then allows further learning of the categorical structure. Thus, the inferences do not directly lead learners to the family resemblance structure, but they do provide a foundation to build on as the participants make additional judgments.

Psychonomic Bulletin & Review2006, 13 (2), 251-256

252 DIAZ AND ROSS

which can then be built upon for a more complete learning of the FR structure.

EXPERIMENT 1

Although dimensional weighting is a main source of category learning in many theories, it is not clear from a transfer-appropriate processing view whether or not pair-ing inferences influence sorting through differential weighting of relevant dimensions. This experiment asks whether these inferences lead to such weighting and whether this weighting is predictive of FR sorts. We used the category structure from Lassaline and Murphy (1996; see Table 1) consisting of five FR-relevant dimensions (i.e., predictive of the FR category structure), Dimensions A through E, and three FR-irrelevant dimensions, Dimen-sions F, G, and H.

A similarity comparison triad task assessed how par-ticipants weighted dimensions. An original item was pre-sented with two new items, and participants chose the new item most similar to the original. One choice matched on FR-relevant dimensions and the other choice matched equally well on FR-irrelevant dimensions. If participants’ representations more heavily weight the FR dimensions, they will select the FR-relevant choice. To assess incre-mental learning, we gave the task both after the pairing or frequency questions (presort) and after the sorting

(postsort). The main issues were (1) whether the pairing group weighted the FR-relevant dimensions more heavily, (2) whether all the pairing learners showed this differen-tial weighting (or only those who later did FR sorts), and (3) whether the sorting influenced the later weighting.

MethodDesign. The between-subjects manipulation was instructions,

either frequency or pairing. The presort and postsort similarity com-parison tests were given to all of the participants.

Participants. Thirty-one University of Illinois students partici-pated in small groups for course credit, with 18 in the pairing condi-tion and 13 in the frequency condition.

Materials. The items were 20 feature lists of vehicles, as in Table 1. Each item was printed on an index card that contained three features from FR-relevant dimensions and two from FR-irrelevant dimensions. The corresponding features for Dimensions A through H were: green or white, nonradial or radial tires, uses gas or diesel, automatic or manual transmission, cloth or vinyl seat covers, con-vertible or nonconvertible, two or four doors, and bumper or window stickers. Dimension G (an FR-irrelevant dimension) was the only dimension present in every item, and it therefore could be used for a unidimensional sort. The pairing and frequency question booklets consisted of the questions as ordered in Table 2, each on a separate page.

The 20 similarity comparison test items, 1 per page, contrasted an original study item, printed in the bottom center, with two novel comparison items, printed in the top left and top right. Both of the novel items overlapped with the original on the same number of dimensions (three or four). However, one novel item had the same features on the FR-relevant dimensions and different features on the FR-irrelevant dimensions, whereas the other novel item had the reverse. For example, consider Item 1 in Table 1, with features A1, B1, C1, F1, and G1. The novel items for this similarity comparison contained features on four of these dimensions, A, B, F, and G, as well as one additional dimension, D. One novel item had features A1, B1, D1, F0, and G0, and hence it matched on two FR-relevant features (A1 and B1). The other novel item had features A0, B0, D0, F1, and G1, and hence matched on two FR-irrelevant features (F1 and G1; note that Dimension G was present in every item). Thus, every comparison had one novel item from the same FR category as the original item (matching features on FR-relevant dimensions) and one novel item from the other FR category (mismatching fea-tures on the FR-relevant dimensions). If the FR-relevant features are more heavily weighted, then the novel items with FR-relevant feature overlap will be chosen more often.

The novel items overlapped with the original item on four dimen-sions (5 comparisons) or three dimensions (10 comparisons). The three-dimensional overlap comparisons consisted of half with one feature matching the original and half with two features matching. The remaining 5 comparisons were filler items, sharing one or two features with the original item, but mismatching each other on all five features.

Procedure. The procedure included the questions and sort-ing from Lassaline and Murphy (1996), as well as two similarity comparison tests: questions (pairing or frequency), similarity com-parisons; sorting, similarity comparisons. The participants in both groups looked through the 20 items and then answered their respec-tive questions (see Table 2). They were asked to look at all the cards, write the answer down on the question page, and wait until every participant had answered that question. The correct answer was then given, after which they proceeded to the next question.

After answering all the questions, the participants returned the cards and questions, and they were given the presort similarity com-parison booklets. They were told to circle the item at the top that was “most similar to the item at the bottom.” After completing this self-paced test, they returned the booklets and received the original

Table 1Abstract Structure of Items (From Lassaline & Murphy, 1996)

FR-RelevantDimensions

FR-IrrelevantDimensions

Item A B C D E F G H

Category 11 1 1 1 – – 1 1 –2 1 1 – 1 – 1 0 –3 1 – 1 1 – 0 1 –4 – 1 1 1 – 0 0 –5 1 1 – – 1 1 1 –6 1 – 1 – 1 1 0 –7 – 1 1 – 1 – 0 18 1 – – 1 1 – 1 09 – 1 – 1 1 – 1 1

10 – 1 – 1 1 – 0 0

Category 211 0 0 0 – – 1 1 –12 0 0 – 0 – 1 0 –13 0 – 0 0 – 0 1 –14 – 0 0 0 – 0 0 –15 0 0 – – 0 1 1 –16 0 – 0 – 0 1 0 –17 – 0 0 – 0 – 0 118 0 – – 0 0 – 1 019 – 0 – 0 0 – 1 120 – 0 – 0 0 – 0 0

Note—Participants were never told what category an item belonged to. Categories 1 and 2 are used here solely to indicate the FR structure of the items. The two possible features for each dimension are represented by 0 and 1. A dash indicates that no feature was presented for that dimen-sion. Table originally appeared in “Induction and Category Coherence,” by M. E. Lassaline and G. L. Murphy, 1996, Psychonomic Bulletin & Review, 3, p. 97. Copyright 1996 by the Psychonomic Society.

INCREMENTAL LEARNING 253

items to sort. They were instructed to spread these items face up on the table and to put together items that “go best or most naturally to-gether” until there were just two piles. The participants then received a new booklet for another similarity comparison test (postsort).

Results and DiscussionAs in Lassaline and Murphy (1996), all sorts were clas-

sified as FR (Table 1), one-dimensional (using dimension G), or other. We also calculated the deviation from FR, which is the minimum number of items that would have to be moved to form an FR sort, ranging from a score of 0 (for FR sort) to 10 (for unidimensional sort).

The sorting results closely replicated Lassaline and Mur-phy’s (1996) results (see Table 3). The pairing group was much more likely than the frequency group to form an FR sort (Fisher’s exact test, p � .01) and had a 3.43 lower FR deviation score [F(1,29) � 4.89, MSe � 18.18, p � .05].

Three comparisons are of interest. First, contrary to ex-pectations, the pairing group did not give significantly more weight to the FR-relevant dimensions presort (see top part of Table 4), compared with either the frequency group [t(29) � 0.94, n.s.] or chance [t(17) � 1.67, n.s.].

Second, the FR sorters in the pairing group did give more weight to the FR-relevant dimensions presort (see bot-tom part of Table 4). They tended to select the FR- relevant choice, .79 [t(8) � 5.56, p � .01], and did so more than the non-FR sorters in the pairing group [t(16) � 4.35, p � .01].2 This finding suggests that the lack of an overall pairing– frequency difference was due to a mixing of different pair-ing groups.

Third, sorting influenced the postsort similarity com-parisons in the pairing group. FR sorters’ .07 increase from presort to postsort differed from the .10 decrease of the rest of the pairing group [t(16) � 2.08, p � .054], with 6 of 9 FR sorters showing increased performance between tests compared with only 1 of 9 from the rest of the pair-ing group (Fisher’s exact test, p � .05). There was also a significant decrease in the frequency group [t(12) � 3.09, p � .01, with 9 of 13 showing a decrease and 2 showing no difference], suggesting greater weighting of the FR-irrelevant dimensions.

In sum, only the FR sorters in the pairing group weighted the FR-relevant dimensions heavily before the sorting. In addition, the sorting influenced postsort weighting, lead-

Table 2Questions Asked in Each Group

(Corresponding Abstract Notation Given in Parentheses)

Question Correct Answer

Pairing If a vehicle has a Manual Transmission (D0), what kind of seat covers (E) does it have? Vinyl Seat Covers (E0) If a vehicle has a Green Paint Job (A1), what kind of fuel (C) does it use? Uses Gas (C1) If a vehicle has a Convertible Roof (F1), how many doors (G) does it have? Two or Four Doors (G1 or G0) If a vehicle Uses Gas (C1), what kind of tires (B) does it have? Non Radial Tires (B1) If a vehicle has Vinyl Seat Covers (E0), what color (A) is it? White (A0)

Frequency How many vehicles are White (A0)? 6 How many vehicles have a Manual Transmission (D0)? 6 How many vehicles are Green (A1)? 6 How many vehicles Use Diesel (C1)? 5 How many vehicles have a Convertible Roof (F1)? 8 How many vehicles have Two Doors (G1)? 10 How many vehicles have Vinyl Seat Covers (E0)? 6 How many vehicles have Non Radial Tires (B1)? 7

Table 3Proportions of Each Type of Sort and FR Deviation Scores for

Each Instructional Group (Pairing or Frequency)

Lassaline andMurphy (1996) Experiment 1 Experiment 2

Sort Pairing Frequency Pairing Frequency Pairing

FR .54 .17 .50 .00 .471-D .21 .50 .28 .62 .22Other .21 .33 .22 .38 .31

FR deviation 4.17 7.00 4.72 8.15 3.83

Note—FR, family resemblance; 1-D, one-dimensional.

254 DIAZ AND ROSS

ing to a small increase for FR sorters and a decrease for all other groups.

EXPERIMENT 2

Experiment 2 focused on what the FR sorters knew. Al-though these participants represented only about half of the pairing group, they offered the best clue to the learning of rich categorical structures. What did they know that enabled FR sorting, and what did they learn from this sorting?3

We consider two general views. First, from the perspec-tive of the early-structure view, the pairing questions lead some people to notice the FR structure. Perhaps, as they become familiar with the items and answer the pairing questions, they realize that feature pairs other than the ones specifically asked about occurred together as well, leading to learning of the FR structure. Second, from the perspective of the incremental-structure view, the pairing questions lead to much less learning, but enough to allow some participants to sort by FR and learn further category knowledge from that sorting. As one possibility, consis-tent with a strict interpretation of the transfer-appropriate processing view, imagine that they learned only the feature pairs queried (see Table 2). Even so, they could sort by FR if they put together items with either feature of these pairs and put items with the opposing features in the other cat-egory. For example, suppose a person remembered only the D0–E0 and E0–A0 questions. If all items with at least one of A0, D0, and E0 were put in one pile, and all items with A1, D1, and E1 were put in the other pile, it would be an FR sort. (Even just remembering E0–A0 would allow FR sorting of 18 of the items.) Although Experiment 1 showed differential weighting of FR-relevant dimensions, this result could be due to increased weighting of features associated with the specific pairs asked about.

To contrast these two views, we used presort and post-sort item-commonality comparison tests to examine what learners knew about the feature pairs. Each test had one alternative that preserved the FR-structure pairing be-tween the FR-relevant features and one alternative that violated one of these pairings. Half of the violations were of a feature combination that was asked about in the pair-ing questions, whereas the other violations were of a com-bination that was not asked about. Participants were asked to choose the alternative that had the most commonalities with the original items. If they were sensitive to the feature

combination being tested, they would choose the alterna-tive that preserved the feature combination.

There are two questions of interest concerning the FR sorters. First, did they learn only the asked-about feature pairs, or were they sensitive to the not-asked-about pairs as well? Second, did this pattern change after the sort? The early-structure view predicts presort sensitivity to both types of feature pairs with little change after the sort, whereas the incremental-structure view (along with transfer-appropriate processing) predicts greater presort sensitivity to asked-about pairs and less difference postsort.

MethodDesign. All of the participants received the pairing questions,

plus presort and postsort item-commonality comparisons. The fea-ture combinations tested either were asked about in the pairing ques-tions or were not asked about.

Participants. Thirty-six University of Illinois students partici-pated in small groups for course credit.

Materials. The study items were the same as those used in Ex-periment 1. To counterbalance the features used in the asked-about/not-asked-about tests, a second set of study items switched the fea-ture values between Dimensions A and B and between Dimensions C and D.

The 12 item-commonality comparisons consisted of descriptions of two vehicles printed on a sheet of paper. (Only items with exactly one asked-about pair of FR-relevant features were included.) Each comparison had two original items, but one had the value on one of the FR-relevant features switched to the other category. For half of the comparisons, this switched value broke an asked-about combina-tion, and for the remaining comparisons, it did not. For example, one of the item-commonality comparisons contrasted Item 3 (with fea-tures A1, C1, D1, F0, and G1) with Item 17 with one of its features changed (C0 to C1, so that it was B0, C1, E0, G0, and H1). Because the fourth pairing question (see Table 2) asked “If a vehicle has C1, what type of B does it have?” this change to Item 17 is breaking an asked-about combination (C1–B1). If people are sensitive to asked-about pairs, they will choose the original item (Item 3) over the changed item. A similar logic applies to the not-asked-about pairs.

Procedure. The procedure was similar to the procedure for the pairing group in Experiment 1, except that the presort and postsort tests were these item-commonality comparisons. For these tests, the participants were told that the items they had just studied had “a lot of commonalities with each other, similar to the way that vehicles from the same manufacturer have commonalities with each other. On each page of the booklet, circle which of the two vehicles you think shares more of these commonalities with the original study items.”

Results and DiscussionThe types of sorts and the FR deviation score were sim-

ilar to the findings in Experiment 1 and in Lassaline and Murphy (1996; see Table 3).

The item-commonality comparisons tested whether participants would notice violations of the FR-relevant feature combinations of the studied items. The mean pro-portion of responses consistent with the FR structure is presented in Table 5. We focus on the FR sorters, though the data are presented for the other participants in foot-notes, for completeness. The first question is whether the FR sorters were sensitive to only the asked-about pairs in the presort (consistent with the incremental-structure view) or to both types of pairs (consistent with the early-structure view). The results are quite clear. FR sorters

Table 4Proportions of Similarity Judgments Consistent

With Family Resemblance in Experiment 1

Pairing Frequency

Group Presort Postsort Presort Postsort

All .60 .59 .53 .37

FR .79 .87 – –1-D .40 .30 .52 .31Other .43 .33 .53 .45

Note—Because the similarity judgment was a two-alternative forced choice, proportions closer to zero are more consistent with the single feature G. FR, family resemblance; 1-D, one-dimensional.

INCREMENTAL LEARNING 255

were sensitive to violations of the asked-about combina-tions [t(16) � 6.24, p � .01; 15 of 17 responding above chance and the other 2 at chance], but were not sensitive to the not-asked-about combinations [t(16) � 0.50, n.s.; 7 above and 6 below chance, with 4 at chance].4

The second question was whether this difference for FR sorters changed after the sorting, as predicted by the incremental-structure view, and indeed it did. Postsort, FR sorters were now sensitive to the not-asked-about pairs [t(16) � 6.27, p � .01; 14 above chance, 1 below chance, and 2 at chance], with performance similar to performance for the asked-about pairs. The not-asked-about combina-tions showed a large increase from sorting [t(16) � 4.08, p � .01], with 14 of the 17 participants showing this in-crease. FR sorters were still sensitive to asked-about com-binations postsort [t(16) � 4.91, p � .01], showing little change from presort performance [t(16) � �0.39], with only 6 of 17 participants showing an increase.5

These results are strongly consistent with the incremental-structure view. The pairing questions led some people to learn the asked-about pairs and make FR sorts without knowledge of the other consistent-feature pairs. Generat-ing FR sorts allowed these people to recognize the other feature relationships consistent with the sort, the not-asked-about pairs.

GENERAL DISCUSSION

This research examined what might be learned from inductive inferences and how this learning might be built upon by later, category-based judgments. The main re-sults show a very specific effect of the pairwise inferences followed by incremental learning from the sorting. Some pairing participants learned the feature pairs they had been asked about, applied this knowledge in the sorting task to create the FR categories, and in doing so, learned more about the overall FR structure.

This type of incremental learning may be important in many unsupervised learning situations. Imagine a simple case, with two FR structures but no labeling to separate them. It may be difficult for learners to notice the FR structures, given the large number of possible FR-relevant features and relations; and in the absence of a task involv-ing these items, they may not notice the FR. However, if a task requires the learners to make some inductive pre-dictions, they may learn rather specific knowledge—for

example, about pairwise feature relations. As they do so, these relations may provide them a tentative division of the items, perhaps increasing the accuracy of their predic-tions. This division may, by narrowing the set of items being considered and increasing the intercorrelations of the features (if the FR structures are accurately divided), lead to learning of other feature relations.

These results provide some constraints on recent views of incremental learning in unsupervised situations. For brevity, we omit discussions of background knowledge influences (see, e.g., Kaplan & Murphy, 1999) and su-pervised classification models (e.g., RULEX; Nosofsky, Palmeri, & McKinley, 1994) to focus on two models ap-plied to incremental category construction.

Ahn and Medin (1992) proposed a two-stage model of category construction. People choose the most salient di-mension and separate items based on that dimension. Any remaining items are then assigned on the basis of similar-ity to those groups. If the pairing questions biased people to separate on an FR-relevant dimension, then they would split 10–14 of the items (see Table 1), and the rest would be divided by the FR structure in the second stage. Thus, if pairing questions led to learning only the asked-about pairs, and this learning increased dimensional salience, this model would predict FR sorting. It would need addi-tional assumptions for allowing the not-asked-about pairs to be learned from the sorting.

In SUSTAIN (Love, Medin, & Gureckis, 2004), a general category-learning model, items are grouped into clusters. Attention becomes more focused, incrementally, on the dimensions that are consistently assigned to the same cluster. Eventually, if the structure allows it, one di-mension dominates, leading to a unidimensional sort. If SUSTAIN gave increased weight to the asked-about fea-ture pairs, it might then cluster items differently and sort into FR categories. This pairing-question influence could then lead SUSTAIN to distribute attention more broadly across the FR-relevant features, because exemplars in the same FR category would match on those features. That is, by creating these FR categories (and, thus, adjusting its feature weights), SUSTAIN might acquire a fuller under-standing of the FR category structure.

The present results provide some constraints about how transfer-appropriate processing and incremental learning work in a particular case. Those people who would later sort by FR first use knowledge of feature pairs asked about during the orienting task. As they sort, they begin to see the underlying category structure that includes the feature pairs not asked about, as well. For many rich, real-world categories, initial interactions are likely to give people only incomplete knowledge of a category. This partial knowledge, however, can help lead to a fuller understand-ing of the category structure.

REFERENCES

Ahn, W. K., & Medin, D. L. (1992). A two-stage model of category construction. Cognitive Science, 16, 81-121.

Chin-Parker, S., & Ross, B. H. (2004). Diagnosticity and prototyp-icality in category learning: A comparison of inference learning and

Table 5Proportions of Item-Commonality Comparisons Consistent With Family Resemblance by Type of Sort in Experiment 2

Asked About Not Asked About

Sort (n) Presort Postsort Presort Postsort

FR (17) .79 .76 .53 .831-D (8) .56 .56 .67 .48Other (11) .51 .43 .61 .62

Note—Asked-about comparisons broke a feature pair that was asked about in the pairing questions. Not-asked-about comparisons broke a feature pair that was not asked about in the pairing questions. FR, family resemblance; 1-D, one-dimensional.

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NOTES

1. Lassaline and Murphy (1996) called these induction questions, but pairing seems more descriptive.

2. We used all the non-FR sorters from the pairing groups, both to increase the number of observations and because the 1-D and Other sub-groups performed similarly.

3. They may also have learned from the other tests, but we do not ad-dress that possibility here.

4. Strangely, the non-FR sorters showed no evidence of having learned the asked-about pairs, .53, but showed an advantage for the not-asked-about pairs, .63 [t(18) � 0.96, n.s.; t(18) � 2.80, p � .01]; the latter difference partly comes about, though, because 2 participants had perfect scores.

5. The other pairing participants showed small, nonreliable decreases for both asked-about, .04, and not-asked-about pairs, .09 [t(18) � 0.62, n.s.; t(18) � 0.86, n.s.].

(Manuscript received November 16, 2004;revision accepted for publication July 18, 2005.)