**4. The effect of partial exemplar experience on multi-modal categorization**

An unexplored issue in human categorization is whether concepts can be learned when less than complete information is available. Partial information, of course, arises in most common situations - occlusion, as in ordinary perception when one object partially covers another, thereby obscuring the object, or circumstance, as when an object can be seen but not touched or touched but not seen. In the present study, we investigated the learning of concepts when an object could be viewed but not touched or the reverse. An added manipulation was the criticality of the missing information. In one condition, texture was critical to the separation of the two categories to be learned; in another, the length of the stimulus was critical. The dimensions were the length, width, and texture of the objects to be classified (the stimuli were simple elliptical shapes, with texture variations on the backside of the stimulus). When length was critical, it needed to be combined with width or texture of the same object to unambiguously classify it into category A or B. That is, length (when critical to classification) could not be used by itself; it had to be combined with either width or texture to classify the stimulus with 100% accuracy. Figure 7 shows the overall structure of the two categories in the length critical condition (not shown is the length x texture figure, which was similarly structured as length x width). Note that texture and width was not informative for classification in this condition, since the integration of these two dimensions resulted in ambiguous classification. When texture was critical, it needed to be combined with length or width for unambiguous classification (essentially the same figure but substitute texture for length). In the control condition, all three dimensions were always available for inspection, i.e., the subject was free to view and touch (the backside) of each stimulus (which varied in texture) during learning, and either length or texture was critical to classification. In all, there were 20 stimuli, 10 in each category. In the partial condition, the subject was provided partial information only on each stimulus, being able to view but not touch half the stimuli; the remaining half could be touched but not viewed. In the 'length critical' condition, the categories could be separated if length was integrated with width or texture; in the 'texture critical' condition, the categories could be separated only if texture was integrated with either length or width.

We hypothesized that the modality of the crucial dimension should have no effect in learning if all dimensions are presented simultaneously. Ernst (2007) showed that normally non-related experiences of vision and touch, namely luminance and resistance to pressure, can be integrated by showing that participants who experienced the two dimensions as being correlated had a lower threshold to discriminate stimuli than stimuli with noncorrelated dimensions. Therefore, we predicted that there should be no difference in learning categorization performance between participants in the length and texture crucial dimension conditions if they have full experience with the learning stimuli. If there is a difference we would assume participants in the texture crucial dimension condition would perform worse in categorization tests across learning and transfer than subjects who studied stimuli with length as the crucial dimension due to a potential difficulty resulting from forcing participants in the texture as the crucial dimension condition to integrate across modalities.

the case in Experiment 1, false recognition of the midpoint and prototype objects was lower

An unexplored issue in human categorization is whether concepts can be learned when less than complete information is available. Partial information, of course, arises in most common situations - occlusion, as in ordinary perception when one object partially covers another, thereby obscuring the object, or circumstance, as when an object can be seen but not touched or touched but not seen. In the present study, we investigated the learning of concepts when an object could be viewed but not touched or the reverse. An added manipulation was the criticality of the missing information. In one condition, texture was critical to the separation of the two categories to be learned; in another, the length of the stimulus was critical. The dimensions were the length, width, and texture of the objects to be classified (the stimuli were simple elliptical shapes, with texture variations on the backside of the stimulus). When length was critical, it needed to be combined with width or texture of the same object to unambiguously classify it into category A or B. That is, length (when critical to classification) could not be used by itself; it had to be combined with either width or texture to classify the stimulus with 100% accuracy. Figure 7 shows the overall structure of the two categories in the length critical condition (not shown is the length x texture figure, which was similarly structured as length x width). Note that texture and width was not informative for classification in this condition, since the integration of these two dimensions resulted in ambiguous classification. When texture was critical, it needed to be combined with length or width for unambiguous classification (essentially the same figure but substitute texture for length). In the control condition, all three dimensions were always available for inspection, i.e., the subject was free to view and touch (the backside) of each stimulus (which varied in texture) during learning, and either length or texture was critical to classification. In all, there were 20 stimuli, 10 in each category. In the partial condition, the subject was provided partial information only on each stimulus, being able to view but not touch half the stimuli; the remaining half could be touched but not viewed. In the 'length critical' condition, the categories could be separated if length was integrated with width or texture; in the 'texture critical' condition, the categories could be separated only if texture

We hypothesized that the modality of the crucial dimension should have no effect in learning if all dimensions are presented simultaneously. Ernst (2007) showed that normally non-related experiences of vision and touch, namely luminance and resistance to pressure, can be integrated by showing that participants who experienced the two dimensions as being correlated had a lower threshold to discriminate stimuli than stimuli with noncorrelated dimensions. Therefore, we predicted that there should be no difference in learning categorization performance between participants in the length and texture crucial dimension conditions if they have full experience with the learning stimuli. If there is a difference we would assume participants in the texture crucial dimension condition would perform worse in categorization tests across learning and transfer than subjects who studied stimuli with length as the crucial dimension due to a potential difficulty resulting from forcing participants in the texture as the crucial dimension condition to integrate across

**4. The effect of partial exemplar experience on multi-modal categorization** 

than for the new objects closest to the category prototype.

was integrated with either length or width.

modalities.

Second, when texture is the crucial dimension there should be reliable differences in categorization performance across learning trials and transfer between subjects in the partial and complete experience conditions. The integration of the crucial dimension with its related dimensions should become more difficult, if not impossible, if the related dimensions are not simultaneously provided with the crucial dimension, as when texture is the crucial dimension, as opposed to if one of the related dimensions is provided simultaneously with the crucial dimension, as when length is the crucial dimension. As such, for participants with partial experience, those that studied categories with texture as the crucial dimension should have worse categorization performance in learning compared to participants whose crucial dimension was length.

Fig. 7. Categorical structure in the length-critical condition

These two predictions would result in little difference in categorization accuracy across learning trials between participants with full experience and length as their crucial dimension, participants with partial experience and length as their crucial dimension, and participants with full experience and texture as their crucial dimension, yet all three of those groups of participants would perform very differently across learning trials from participants with partial experience and texture as their crucial dimension.

#### **4.1 Method, procedure, and results**

Subjects received 6 learning trials, the results of which are shown in Figure 8. Overall, learning was as predicted – when length was the critical dimension and learning was partial, learning was unaffected, i.e., being deprived of texture (even though texture and length could also be used to discriminate the categories) did not degrade learning, since length could always be combined with width for categorical separation. Similarly, when texture was critical, it was readily learned in the complete condition but learning was severely retarded in the partial condition. That is partial experience inhibited access to diagnostic categorical information only when texture was the crucial dimension.

Haptic Concepts 17

in Experiment 1, in the visual or haptic modality, followed by similarity judgments in the

Participants were either exposed to no learning or the same learning procedure used previously. They were individually tested and randomly assigned to one of the 6 conditions. Followed learning or no learning, participants were asked to make similarity judgments to the 105 possible paired-objects on a Likert-scale ranging from 1 to 9, with 1 = minimal similarity and 9 = maximal similarity. These 105 paired objects were presented randomly. For the haptic judgments, the objects were presented sequentially, with each object presented first or second about the same number of times. Ratings were self-paced but restricted to a maximum duration of 15 sec. When objects were presented visually, a similar procedure was used in which first one object was presented for inspection followed by the

The learning data mirrored that found previously, with more rapid learning for visual than haptic presentation but with terminal levels reaching nearly 100% in all learning conditions. As a consequence, the multidimensional spaces derived from similarity ratings following

For each of the six conditions, the objects were multidimensionally scaled in dimensions 1-6. The three dimensional solutions were selected for further analysis because stress levels were low (none exceeded .05), of comparable value, and were the highest dimensionality that could be visually inspected. Three analyses were performed: (a) computation of the structural ratio (Homa, Rhodes, & Chambliss, 1979) for 15 objects as well as overall for each condition; (b) a comparison of the structural similarity among the six conditions; and (c) computation of each object to the centroid of its learning exemplars. The first measure tells us how structured each space was and whether the psychological structure mirrored objective structure. The second measure tells us whether the various scalings produced similar or different representations. The third measure assesses whether the prototype for

The structural ratio was calculated for each of the 15 objects in a given condition by calculating the mean distance of that item to members of the same category, relative to the mean distance to objects from the other two categories. The mean of these 15 ratios for a given condition defined the mean structural ratio and represented level of conceptual structure, with smaller values indicating greater structure and values approaching 1.00 indicating a random structure. Figure 9 shows the mean structural ratio for each of the six

The structural ratios (SRs) ranged from (poorest) the space determined from visual inspection of the objects following no learning (SR = .414) to haptic inspection following systematic learning (SR = .223). In general, the structural ratios decreased with degree of learning, with the weakest structure associated with no learning (SR = .381), greatest structure with systematic learning (SR = .297), and intermediate structure with random learning (SR = .332). Overall, the haptic conceptual spaces were more structured than were the visual spaces (.301 vs. .381). To assess the similarity among the six conditions,

learning were based on comparable and near-errorless performance.

each category was positioned away from or near the centroid of each category

same modality as training.

second object of the rating pair.

**5.2 Results** 

conditions.

Fig. 8. Learning rate as a function of full and partial experience with length or texture as the crucial dimension.

## **5. Multidimensional scaling of a haptic vs. visual space**

Insight into the patterning of results was further explored by multidimensional scaling of the objects. A total of six different scalings was performed, determined by haptic or visual inspection and following either no learning, random learning, or systematic learning. In each condition, the subject made similarity judgments to object pairs. We were especially interested in whether the space generated from visual judgments mirrored that when judgments were made haptically, and whether this space was further altered by prior learning. Since vision appeared to dominate haptic categories, and since more information appears to be available following visual examination, we expected that the haptic space would be structured more tightly than the visual space. This would be consistent with the hypothesis that the visual modality provides more, perhaps idiosyncratic, information than haptic exploration, and this additional information might be expected to increase stimulus discrimination and reduce overall categorical structure.

#### **5.1 Method**

Ninety Arizona State University undergraduates were drawn from the same subject pool as in previous experiments and randomly assigned to one of the six conditions. For two conditions, the similarity judgments were made either haptically or visually and followed no learning. For the remaining four conditions, learning was either systematic or random, as

Fig. 8. Learning rate as a function of full and partial experience with length or texture as the

Insight into the patterning of results was further explored by multidimensional scaling of the objects. A total of six different scalings was performed, determined by haptic or visual inspection and following either no learning, random learning, or systematic learning. In each condition, the subject made similarity judgments to object pairs. We were especially interested in whether the space generated from visual judgments mirrored that when judgments were made haptically, and whether this space was further altered by prior learning. Since vision appeared to dominate haptic categories, and since more information appears to be available following visual examination, we expected that the haptic space would be structured more tightly than the visual space. This would be consistent with the hypothesis that the visual modality provides more, perhaps idiosyncratic, information than haptic exploration, and this additional information might be expected to increase stimulus

Ninety Arizona State University undergraduates were drawn from the same subject pool as in previous experiments and randomly assigned to one of the six conditions. For two conditions, the similarity judgments were made either haptically or visually and followed no learning. For the remaining four conditions, learning was either systematic or random, as

**5. Multidimensional scaling of a haptic vs. visual space** 

discrimination and reduce overall categorical structure.

crucial dimension.

**5.1 Method** 

in Experiment 1, in the visual or haptic modality, followed by similarity judgments in the same modality as training.

Participants were either exposed to no learning or the same learning procedure used previously. They were individually tested and randomly assigned to one of the 6 conditions. Followed learning or no learning, participants were asked to make similarity judgments to the 105 possible paired-objects on a Likert-scale ranging from 1 to 9, with 1 = minimal similarity and 9 = maximal similarity. These 105 paired objects were presented randomly. For the haptic judgments, the objects were presented sequentially, with each object presented first or second about the same number of times. Ratings were self-paced but restricted to a maximum duration of 15 sec. When objects were presented visually, a similar procedure was used in which first one object was presented for inspection followed by the second object of the rating pair.
