Inferring Categories to Accelerate the Learning of New Classes
Robert Goeddel

Abstract— On-the-fly learning systems are necessary for the
deployment of general purpose robots. New training examples
for such systems are often supplied by mentor interactions.
Due to the cost of acquiring such examples, it is desirable to
reduce the number of necessary interactions. Transfer learning
has been shown to improve classification results for classes with
small numbers of training examples by pooling knowledge from
related classes. Standard practice in these works is to assume
that the relationship between the transfer target and related
classes is already known.
In this work, we explore how previously learned categories, or
related groupings of classes, can be used to transfer knowledge
to novel classes without explicitly known relationships to them.
We demonstrate an algorithm for determining the category
membership of a novel class, focusing on the difficult case when
few training examples are available. We show that classifiers
trained via this method outperform classifiers optimized to learn
the novel class individually when evaluated on both synthetic
and real-world datasets.

I. I NTRODUCTION
To deploy general purpose robots into the world, it is necessary to develop algorithms that can learn on the fly. Such
algorithms allow systems to deal with the ever-increasing
quantity of novel experiences a robot might encounter. In
this paper, we present a method for discovering and exploiting categorical relationships between new and previously
discovered classes. This allows us to learn classifiers for
new objects with fewer training examples by transferring
knowledge from previous examples. In particular, we focus
on small-data domains, where training data is either sparse
or expensive to acquire (e.g. a system driven by mentor
interactions).
Transfer learning aims to re-use examples of previously
encountered classes to improve classification performance
for another related class [1]. In this case, a class refers
to a distribution of objects that may be described by the
same label (e.g. “red”). Some classes actually subsume sets
of lower level classes, establishing a hierarchy (e.g. cats
and dogs are both animals or running and walking are both
forms of human locomotion). In this work, we refer to higher
level classes such as animal as categories. Exploiting these
semantic relationships between classes in the same category
can lead to transfer of knowledge between domains [2].
An example domain in which a robotic system interacts
with colored blocks of various shapes is illustrated in Fig. 1.
We expect that, given prior knowledge of the characteristics
of these blocks, the robotic system should be able to exploit
this knowledge when a new class of block is first observed.
The authors are with the Department of Computer Science
and Engineering, The University of Michigan, Ann Arbor, MI

{rgoeddel,ebolson}@umich.edu

Edwin Olson

Fig. 1: A robot operating in a blocks-world domain. The system
should be able to leverage prior experiences to accelerate the
recognition of new blocks.

For example, having seen the colors red, green, and blue, we
hypothesize that knowing “purple” is also a color will allow
the system to learn to identify purple from fewer examples.
In transfer learning problems, it is commonly assumed
that correspondence between the novel class and previously
learned classes is known a priori. In the case of learning
novel classes, though, the relationship to previously seen
things may be unknown. Therefore, not only do we wish to
use previous experiences to bootstrap the process of learning
to classify novel classes, but also to deduce which experiences are most relevant to this task. In this paper, we show
how to assign new classes to high-level categories for the purpose of improving classification performance. We construct
a method for identifying category membership automatically
and use this to perform transfer learning, demonstrating that
this reduces the number of training examples necessary to
train a serviceable classifier. Our contributions are:
• A method for discovering relationships between novel
classes and known categories of classes.
• Evaluation of our method on synthetic and real-world
data showing performance gains over classifiers trained
to specialize on a specific class.
• Empirical characterization of the advantages of our
method for few training examples as well as the possible
failure modes of the algorithm.
II. R ELATED W ORK
Transfer learning is the process of reusing knowledge from
one domain in another. While the transfer domains may
be tightly coupled (e.g. using previous knowledge of the
category color to help learn the concept “purple”), some
applications are less intuitive (e.g. learning action sequences
for heterogeneous sets of robots) [3].

A variety of transfer learning strategies may be adopted
depending on the available data [1]. For example, semisupervised learning is an increasingly popular topic and can
be applied to situations where labeled data is expensive, but
unlabeled data is abundant [4]. Models can be fit to the
unlabeled data that have predictive power with regards to
the labeled data. For example, Pan et al. present a method
for projecting unlabeled data from one domain and labeled
data from another into a shared feature space such that the
domains are better suited for transfer learning [5]. In general,
though, semi-supervised learning techniques are most useful
when it is known that the unlabeled data are instances of
the labeled data, which is typically not the case for large,
general purpose systems.
Another common application of transfer learning is to
perform multi-class feature selection. Feature selection can
greatly improve classification results when many irrelevant
features are present [6], [7]. In addition, previous works
have shown that pooling data from related classes for the
purpose of simultaneous learning can lead to classification
performance increases across classes [8]. The benefit is that
feature selection may be performed such that one keeps
features that are common across a set of related classes [9],
[10]. Evgeniou et al. show that they are able to reduce the
size of the feature space, reducing computation, and also that
joint learning outperforms learning independent classifiers
for each class.
This strategy can be particularly useful in the context of
machine vision, as even unrelated classes of objects often
share visual features [11]. Torralba et al. find that, not only do
jointly learned visual features allow for similar performance
to specialized classifiers while requiring fewer total features,
but these features also tend to be more general purpose. As
a result, the feature space only grows logarithmically with
the number of jointly learned classes as many features can
be reused.
A common theme for these techniques is that they rely on
a priori knowledge of which classes are related to the class
being bootstrapped. One strategy for discovering such relationships is to use WordNet or Wikipedia to learn semantic
relatedness [12], [13]. It has been shown that such relatedness
measures may be used to aid in visual classification [2], [14].
Unsupervised category discovery is also often employed
to find relations between subsets of data for organizational
or classification purposes [15], [16], [17]. These methods
are powerful as they can take advantage of latent relationships between classes of data. While human-recognizable
categories such as “animal” or “color” may be discovered,
it is also possible that these methods will discover unique
and unpredictable groupings of classes. The disadvantage to
such methods is that it is not obvious which category a novel
class belongs to.
In this work, we explore a variation of the transfer learning
problem where categorical relationships between our initial
classes are known, but where this information is not known
for novel classes. The goal, then, is to 1) identify the category
membership of novel classes and 2) use this to perform

transfer learning. We show that extending our categories
to cover new classes boosts early-stage learning for these
classes in addition to providing additional object metainformation.
III. M ETHODOLOGY
The input for our problem is an observed feature vector,
labeled with both class and category. In this work, we focus
on objects with single-category membership. As a mentor
provides new labeled training instances for previously unseen
classes, we attempt to match the novel class to an existing
category so that knowledge transfer may occur. The key
idea in our work is that classes within a single category are
related; specifically, the same features tend to be informative.
This idea suggests both 1) a way of transferring knowledge
and 2) a way of testing category membership.
Our proposed method may be outlined as follows:
1) Use known categories and the initial corpus of training
data to perform joint feature selection on each category
subject to the constraint that all classes within one a
category use the same features.
2) When an example of a novel/uncategorized class is encountered, hypothesize that the novel class is a member
of each known category in turn. For each category,
construct a one-vs-all classifier based on the category’s
joint features that distinguishes between the novel class
and other category members.
3) Evaluate each category-specific classifier using crossvalidation to score its performance.
4) If one or more of the categories provides sufficiently
improved performance over a standard one-vs-all classifier using all known features, propose that the novel
class is a member of the best performing category.
In the following sections, we will discuss how to jointly
select features for a category and how to evaluate the quality
of a category membership hypothesis. Additionally, we will
how to transfer knowledge from a category to a novel class.
A. Multi-Class Feature Selection
The first step is to jointly learn the appropriate features
to describe each of the known categories. Category-specific
features not only offer speed, but also boost classification
accuracy. As feature selection can be slow, they can be
initially calculated offline and then updated periodically as
relevant training examples are added. In this work, we will
not explore when periodic updating should happen, and
instead will focus strictly on pre-computed category features.
We use a greedy feature elimination algorithm to select
category features. Pseudocode for the algorithm is given
in Alg. 1. The method is supplied with a set of related
labels (the proposed category) as well as the relevant labeled
training examples. The category feature set is initialized to
contain every feature. Then features are greedily removed
from the set, one at a time, based on the average crossvalidation scores for all of the category classes. Features
are removed until 1) only one feature is left in the category
feature set or 2) the average cross-validation score decreases

Algorithm 1 Joint Feature Selection
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:

categoryF eatures ← all features
thresh ← user defined performance threshold
bestScore ← score(categoryF eatures)
while size(catF eatures) > 1 do
bestF eatures ← ∅
for f eature ∈ categoryF eatures do
if score(bestF eatures) <
score(categoryF eatures − f eature) then
bestF eatures ← categoryF eatures − f eature
if bestScore − thresh < score(bestF eatures) then
categoryF eatures ← bestF eatures
bestScore = max(bestScore, score(bestF eatures))
else
break
return categoryF eatures

below a threshold. Higher threshold values lead to the
elimination of more features. For our tests, the threshold
parameter is set to 0.01, which means that we are willing to
tolerate no more than a percentage point drop in classification
accuracy. The algorithm is run independently for each known
category, resulting in categories learning specialized sets of
features.
Accuracy, a common performance metric, is the ratio of
true positives and true negatives to all results. An issue
with this accuracy metric is that it is greatly affected by
the distribution of the data. It measures the probability
with which we expect to give a correct response in our
classification task.
TP + TN
accuracy =
(1)
TP + FP + TN + FP
If 99% of training examples are negative, then a classifier that
always reports “negative” will do very well according to the
accuracy metric even though it never correctly recognizes
a positive example. Our training sets, by nature, are imbalanced since we are learning a new class based on an existing
large corpus of training data, making standard accuracy a
poor evaluation metric.
To avoid issues arising from imbalanced data, one can use
the balanced accuracy metric [18]. Balanced accuracy is the
mean of sensitivity and specificity. It gives equal weight to
both the true positive and true negative rates regardless of the
distribution of data. This alleviates the problem of a single,
more prevalent class dominating the feature selection process
during joint selection. We use this metric in this paper.
balancedAccuracy =

1
TP
TN
+
2 FN + TP
FP + TN

(2)

B. Transferring Category Knowledge to Novel Classes
We hypothesize that, since category members are well
distinguished by our jointly-learned category features, novel
classes also belonging to that category will be distinguishable
from existing category members. Conversely, novel classes

(a) Colored shapes separated
by color features

(b) Colored shapes separated
by shape features

(c) Purple as distinguished
by color features

(d) Purple as distinguished
by shape features

Fig. 2: A toy example of placing “purple” into the feature spaces
for the categories color and shape. When placed in the correct
category, color, purple training examples are tightly clustered,
making it easily distinguishable from other colors. When placed
into an incorrect category such as shape, purple training examples are scattered throughout the feature space, making purple
difficult to separate from other classes.

not belonging to a category will be poorly separable, and thus
difficult to distinguish, from the other category members as
the features selected are irrelevant to the novel class. The
categories “color” and “shape,” pictured in Fig. 2, provide
an illustrative example. As Figs. 2(a) and (b) show, we expect
that features selected for color and shape will result in very
different clusterings of identical objects. We exploit this
expectation by observing the accuracy with which a novel
class (in the example, purple), is classified. From this, we
determine whether it is likely that purple is either a shape or
a color. This allows us to construct a procedure for testing
the category membership of novel classes.
When provided with a new example of a novel class, test
the hypothesis that the class is a member of one of the
existing categories. For each known category, train a onevs-all classifier to identify the novel class using the subset
of jointly-selected features for that category. Hypothesized
novel class membership in each category is scored by computing the balanced accuracy for the associated classifier
via cross-validation. If the novel class is well separable
from other category members, then the cross-validation score
should be high, indicating potential category membership.
IV. E VALUATION
In this section, we define an experimental procedure
for evaluating learning strategies. We present experimental
results for both synthetic and real-world data and examine
strengths and possible failure modes of our method.

2) Single Class: Select features to optimize the crossvalidation score for a one-vs-all classifier distinguishing
between the novel class and all other classes.
3) Category Transfer: Select the category-based classifier
with the set of jointly-learned features that gives the
highest cross-validation score for a one-vs-all classifier
distinguishing between the novel class and all other
classes.

Fig. 3: An example of synthetic data from a category defined by
two features and with four member classes. The axes correspond
to feature values, with points representing randomly generated
object instances. The colors of the points correspond to the
ground truth class of the data point.

A. Classification Methods
Our first method of classification is the nearest-neighbor
classifier. Nearest-neighbor classifiers are appealing as they
are easy to implement and because they are non-parametric.
The nearest-neighbor classifier is a special case of the kNN, which returns a classification based on the votes of the
k closest training examples to the query point. We find that
values of k > 1 offered little to no benefit in this domain,
and in fact, can be detrimental to the goal of learning from
very few examples. This is because higher values of k require
more positive examples to return a positive classification. In
our domain, these examples may not yet exist, delaying our
ability to correctly classify a new class of object. Thus, we
only present results for the nearest-neighbor in this paper,
i.e. k = 1.
Our second method of classification is the support vector machine (SVM) [19]. SVMs are popular in learning
communities due to their classification efficiency and predictive power [20]. SVMs create decision boundaries for
classification by maximizing the margin (separation) between
the positive and negative examples of training data. One
downside to SVMs is that training can be expensive. We
use the LibSVM implementation of SVMs with a Gaussian
kernel and parameters tuned by a grid search through the
recommended ranges of values [21].
B. Experimental Procedure
In this section, we define a testing procedure in which
nearest-neighbor or SVM classification may be used interchangeably. We compare three different strategies for
learning novel classes.
1) Baseline: Train a one-vs-all classifier to discriminate
between the novel class and all other classes using all
available features.

SVM parameters are optimized individually for each
method. For the generic classifier with no feature selection, a
grid search through the parameter space is performed based
on all of the available training data. For both of the feature
selection-based methods, we find that SVM performance is
improved most by optimizing the parameters for classification solely on relevant category examples.
Using the above strategies, we perform 100 test trials. For
each trial, we generate a training set consisting of an equal
number of examples of each class. We select a random class
to withdraw from the training set and consider this our “novel
class.” To observe how each classification strategy performs,
we introduce instances of the novel class one at a time and
evaluate each against a test set.
Our expectation is that the baseline should exhibit the
worst classification performance as it is most likely to
suffer from problems due to high-dimensionality. Performing
feature selection for the novel class alone should provide
improvement over the baseline as it will eliminate features irrelevant to distinguishing examples of the class. Our method
should outperform both as correctly placing a class in a
category allows us to utilize previous observations when
choosing our features. We expect the largest gains to be made
early, before the single class feature selection has enough
training examples to learn a suitable feature mask.
C. Synthetic Data
All synthetic features are normalized values between 0 and
1. While normalization is not strictly necessary, it facilitates
the use of classifiers such as nearest-neighbor, where larger
feature values can give disproportionate weight to those
features. Classifiers such as SVMs have also been shown
to be sensitive to feature normalization [22]. Alternatively,
normalization factors may be learned online. However, in our
domain, where data is likely to be sparse, this can be difficult
as insufficient data may have been seen to accurately scale
feature values.
Categories are defined by a unique, non-overlapping subsets of features. Classes belonging to a category are defined
by unique ranges of values that each category-specific feature
may assume. We generate these ranges such that each class
occupies 1) an equal volume of the category hyperspace and
2) is perfectly separable from the other classes. Random
examples are generated by selecting a set of class memberships (one for each category) for each training example
and by populating the relevant features with values sampled
uniformly at random from the class-defined ranges. Example
synthetic data can be seen in Fig. 3.

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Fig. 4: Mean nearest-neighbor classification results for varying amounts of category data. Error bars indicate one standard deviation. Cat.
Xfer denotes our category transfer method. Regardless of the number of training examples provided for each existing class, our method
is able to train higher accuracy classifiers than methods not employing knowledge of categories.

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Fig. 5: Mean SVM classification results for varying amounts of category data. Error bars indicate one standard deviation. Cat. Xfer denotes
our category transfer method. Though baseline learning performance improves for SVM compared to nearest-neighbor classification,
our method is still able to improve classification accuracy, particularly when we have very few training examples of the novel class.

In our presented synthetic results, we use 3 categories,
each with 8 classes. The feature vectors for training examples
in those classes are separable using three dimensions. We find
these results to be representative of other synthetic category
structures tested. All results are based on a set of 10,000
synthetic data points.
D. Real-world Data
Additional testing is performed on two real world datasets.
The first is Munroe’s XKCD Color Survey, from which we
take a set of 196,000 labeled color data points identifying 27
distinct colors [23]. From this, we remove two colors with
insufficiently large amounts of training examples (1 and 2
examples, respectively) and select test and training sets from
what remains.
We also examine results for a small data set collected
in the blocks domain pictured in Fig. 1. We collected
observations of colored blocks using a Microsoft Kinect. A
total of 105 blocks were automatically segmented from the
scene and hand-labeled for color, shape, and size. We create
a test set by randomly selecting 30% of the training examples
for each class and then train our classifiers on the remainder.
This domain is intended to emphasize learning from very
small amounts of data, as all labels must be solicited from
a human mentor and are thus costly to obtain.
E. Synthetic Data Experimental Results
Nearest-neighbor classifier results for 10, 20, and 50
instances of each known class can be seen in Fig. 4.

The baseline algorithm improves as more data is acquired,
but improvement is slow and quickly plateaus. This indicates
that the method is unable to filter out the important information given by relevant features from the rest of the feature
space.
Single class feature selection is better able to filter out
irrelevant features, but the quality of features selected varies
wildly for the first several training examples. This is likely
due to overfitting the selected features to such small amounts
of data. Data from individual trials backs up this hypothesis,
as the features selected vary (sometimes dramatically) as new
training data is added. These fluctuations in feature selection
manifest themselves as large fluctuations in accuracy during
testing, leading to the high variance seen in the single class
results.
Classifiers trained via category transfer provide larger and
more consistent improvements in accuracy. This is because,
during joint feature selection, we are able to pool data
from many classes to learn a general set of features that
works well for all category members. Most importantly, even
for very little training data, category knowledge provides a
substantial boost in performance over the baseline, achieving
over half its gains within seeing the first 5 training instances
of a novel class. In short, these results demonstrate that
our approach significantly reduces the number of training
examples required in order to learn a serviceable classifier.
Results for the same tests run with SVMs can be seen in
Fig. 5. The average performance of the SVM baseline and
category transfer methods exhibit similar trends to those seen

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Fig. 6: Mean nearest-neighbor classification results on the XKCD Color Survey for increasing amounts of distractor features. Category
transfer proves to be most robust to extraneous features.

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Fig. 7: Category transfer for identifying the “arch” shape with
jointly learned category feature masks (a) and with humanspecified feature masks (b). Categories insufficiently covered by
classes are prone to overfitting, and thus perform more poorly
than even the baseline.

for nearest-neighbor classification, though variance for both
methods is higher. Surprisingly, the single class optimization
method often performs worse than the baseline. This is
likely due to the fact that SVMs are better able to deal
with high-dimensionality than nearest-neighbor. Thus, while
single class optimization still suffers from overfitting the
feature space (and may even remove relevant features),
the baseline SVM merely discounts less important features
without completely discarding them.
Nearest-neighbor outperforms SVM on average for very
few novel training examples. For this reason, all real-world
data examples are compared with nearest-neighbor classification.
F. Real-world Experimental Results
As only one category is present in the XKCD Color
Survey, we alter the experimental procedure to obscure
the relevant features. For a given color example, a feature
vector is initialized containing red, green, and blue color
channel values in the range [0, 1]. Then, the feature vector is
“polluted” with extra features, values for which are sampled
from the Gaussian distribution N (0.5, 0.05) and clamped
between 0 and 1. For few examples, these features are hard to
distinguish from the actual distributions of the relevant color
features. For each experimental trial, 10 random examples
of each color are chosen as training data. We then vary the
number of distractor features added until the system fails.
It is expected that category transfer will not only increase

performance the most, but also be best able to filter out the
noisy features.
Experimental results for nearest-neighbor classification on
the XKCD Color Survey can be seen in Fig. 6. Our results
show that by employing category knowledge, our approach
improves classification accuracy. As expected, as the number
of extraneous features increases, category transfer performance is largely unaffected, while both the baseline and
single class feature selection methods rapidly degrade in
classification accuracy. Category transfer finally begins to
fail around 30 extraneous features, at which point 90% of
the features are noisy. Preliminary investigation indicates that
the point of failure follows a roughly linear relationship to
the amount category training data.
G. Real-world Failure Mode
The results for the Kinect blocks dataset for novel colors
unsurprisingly resemble the XKCD Color Survey results
(though both the baseline and single class methods improve
in average performance). The shape category presents an
interesting challenge, though. The feature space designed
for the color, shape, and size categories is dominated by
many shape features. However, variety in shape training
data is limited. Thus, joint feature learning is susceptible to
removing important shape features when learning the shape
category.
For example, the majority of the shape objects in the data
set are angular in nature (e.g. squares, triangles, rectangles).
One shape, however, the “arch”, is a rectangle with a semicircular portion cut from one side. An example of a green
arch can be seen in the lower left of Fig. 1. When the shape
category is learned without the arch present, feature selection
removes the features that would allow the classifier to distinguish an arch from a rectangle as they are not yet necessary.
As a result of this premature feature removal, when the
arch is introduced, category transfer actually performs worse
than the other methods, as can be seen in Fig. 7. When
category masks are hand-selected, category transfer once
again demonstrates performance gains over the competing
methods.
The implication of this result is that, while category
transfer can allow us to make better use of small amount of
prior training data, it is imperative that the prior category data
cover the relevant feature space well. Otherwise, category

transfer is susceptible to overfitting the category feature mask
to the data.
V. C ONCLUSION
In this work, we demonstrate how transfer learning can
be used to boost early classification performance, reducing
the number of interactions necessary for a robot to learn a
serviceable classifier, even when the novel class’s category
membership is unknown. We present a method for determining membership of a novel class in the absence of known
category relationships and demonstrate that this method
works for both synthetic and real-world data. We empirically
characterize the properties of the algorithm, showing that the
majority of gains are made within the first 5 observations of
a novel class and identifying the types of domains which will
benefit most from category transfer.
ACKNOWLEDGEMENTS
The authors would also like to thank Lauren Hinkle for
her useful insight during early stages of this research. This
work was supported by ONR Grant N00014-13-1-0217.
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