### abstract ###
In this paper, we propose the MIML ( Multi-Instance Multi-Label learning )
 framework where an example is described by multiple instances and associated with
 multiple class labels
Compared to traditional learning frameworks, the MIML
 framework is more convenient and natural for representing complicated objects which
 have multiple semantic meanings
To learn from MIML examples, we propose the
 \textsc{MimlBoost} and \textsc{MimlSvm} algorithms based on a simple degeneration
 strategy, and experiments show that solving problems involving complicated objects with
 multiple semantic meanings in the MIML framework can lead to good performance
Considering that the degeneration process may lose information, we propose the
 \textsc{D-MimlSvm} algorithm which tackles MIML problems directly in a regularization
 framework
Moreover, we show that even when we do not have access to the real objects
 and thus cannot capture more information from real objects by using the MIML
 representation, MIML is still useful
We propose the \textsc{InsDif} and
 \textsc{SubCod} algorithms \textsc{InsDif} works by transforming single-instances into
 the MIML representation for learning, while \textsc{SubCod} works by transforming
 single-label examples into the MIML representation for learning
Experiments show that
 in some tasks they are able to achieve better performance than learning the
 single-instances or single-label examples directly
### introduction ###
In  traditional supervised learning , an object is represented by an instance,
 i e , a feature vector, and associated with a class label
Formally, let  SYMBOL 
 denote the instance space (or feature space) and  SYMBOL  the set of class labels
The task is to learn a function  SYMBOL  from a given data set
  SYMBOL , where  SYMBOL  is an instance and  SYMBOL  is the known label of  SYMBOL
Although this formalization is prevailing and successful, there are many real-world
 problems which do not fit in this framework well
In particular, each object in this
 framework belongs to only one concept and therefore the corresponding instance is
 associated with a single class label
However, many real-world objects are complicated,
 which may belong to multiple concepts simultaneously
For example, an image can belong
 to several classes simultaneously, eg ,  grasslands ,  lions ,
  Africa , etc ; a text document can be classified to several categories if it is
 viewed from different aspects, eg ,  scientific novel ,  Jules Verne's
 writing  or even  books on traveling ; a web page can be recognized as
  news page ,  sports page ,  soccer page , etc
In a specific real
 task, maybe only one of the multiple concepts is the right semantic meaning
For
 example, in image retrieval when a user is interested in an image with lions, s/he may
 be only interested in the concept  lions  instead of the other concepts
  grasslands  and  Africa  associated with that image
The difficulty here
 is caused by those objects that involve multiple concepts
To choose the right semantic meaning for such objects for a specific scenario is the fundamental difficulty of many tasks
In contrast to starting from a large universe of all possible concepts involved in the task, it may be helpful to get the subset of concepts associated with the concerned object at first, and then make a choice in the small subset later
However, getting the subset of concepts, that is, assigning proper class labels to such objects, is still a challenging task
We notice that as an alternative to representing an object by a single instance, in
 many cases it is possible to represent a complicated object using a set of instances
For example, multiple patches can be extracted from an image where each patch is
 described by an instance, and thus the image can be represented by a set of instances;
 multiple sections can be extracted from a document where each section is described by
 an instance, and thus the document can be represented by a set of instances; multiple
 links can be extracted from a web page where each link is described by an instance, and
 thus the web page can be represented by a set of instances
Using multiple instances to
 represent those complicated objects may be helpful because some inherent patterns which
 are closely related to some labels may become explicit and clearer
In this paper, we propose the MIML ( Multi-Instance Multi-Label learning )
 framework, where an example is described by multiple instances and associated with
 multiple class labels
Compared to traditional learning frameworks, the MIML framework is more convenient
 and natural for representing complicated objects
To exploit the advantages of the MIML
 representation, new learning algorithms are needed
We propose the \textsc{MimlBoost}
 algorithm and the \textsc{MimlSvm} algorithm based on a simple degeneration strategy,
 and experiments show that solving problems involving complicated objects with multiple
 semantic meanings under the MIML framework can lead to good performance
Considering
 that the degeneration process may lose information, we also propose the
 \textsc{D-MimlSvm} (i e , Direct \textsc{MimlSvm}) algorithm which tackles MIML
 problems directly in a regularization framework
Experiments show that this ``direct''
 algorithm outperforms the ``indirect'' \textsc{MimlSvm} algorithm
In some practical tasks we do not have access to the real objects themselves such as
 the real images and the real web pages; instead, we are given observational data where
 each real object has already been represented by a single instance
Thus, in such cases
 we cannot capture more information from the real objects using the MIML representation
Even in this situation, however, MIML is still useful
We propose the \textsc{InsDif}
 (i e , INStance DIFferentiation) algorithm which transforms single-instances into MIML
 examples for learning
This algorithm is able to achieve a better performance than
 learning the single-instances directly in some tasks
This is not strange because for
 an object associated with multiple class labels, if it is described by only a single
 instance, the information corresponding to these labels are mixed and thus difficult
 for learning; if we can transform the single-instance into a set of instances in some
 proper ways, the mixed information might be detached to some extent and thus less
 difficult for learning
MIML can also be helpful for learning single-label objects
We propose the
 \textsc{SubCod} (i e , SUB-COncept Discovery) algorithm which works by discovering
 sub-concepts of the target concept at first and then transforming the data into MIML
 examples for learning
This algorithm is able to achieve a better performance than
 learning the single-label examples directly in some tasks
This is also not strange
 because for a label corresponding to a high-level complicated concept, it may be quite
 difficult to learn this concept directly since many different lower-level concepts are
 mixed; if we can transform the single-label into a set of labels corresponding to some
 sub-concepts, which are relatively clearer and easier for learning, we can learn these
 labels at first and then derive the high-level complicated label based on them with a
 less difficulty
The rest of this paper is organized as follows
In Section~, we review
 some related work
In Section~, we propose the MIML framework
In
 Section~ we propose the \textsc{MimlBoost} and \textsc{MimlSvm}
 algorithms, and apply them to tasks where the objects are represented as MIML examples
In Section~ we present the \textsc{D-MimlSvm} algorithm and compare it
 with the ``indirect'' \textsc{MimlSvm} algorithm
In Sections~ and
 , we study the usefulness of MIML when we do not have access to real
 objects
Concretely, in Section~, we propose the \textsc{InsDif}
 algorithm and show that using MIML can be better than learning single-instances
 directly; in Section~ we propose the \textsc{SubCod} algorithm and
 show that using MIML can be better than learning single-label examples directly
Finally, we conclude the paper in Section~
