2000 IterativeClassification

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Subject Headings: Iterative Supervised Classification Algorithm, Local Collective Classification Algorithm.


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Relational data offer a unique opportunity for improving the classification accuracy of statistical models. If two objects are related, inferring something about one object can aid inferences about the other. We present an iterative classification procedure that exploits this characteristic of relational data. This approach uses simple Bayesian classifiers in an iterative fashion, dynamically updating the attributes of some objects as inferences are made about related objects. Inferences made with high confidence in initial iterations are fed back into the data and are used to inform subsequent inferences about related objects. We evaluate the performance of this approach on a binary classification task. Experiments indicate that iterative classification significantly increases accuracy when compared to a single-pass approach.

1. Introduction

The structure of relational data presents a unique opportunity to use knowledge about one object to inform inferences about related objects. The goal of this work is to explore how conventional techniques for constructing and using classification models can be used in new ways to exploit this opportunity. Specifically, we investigate using simple Bayesian classifiers in an iterative fashion to improve classification accuracy by exploiting relational information in the data.

The hypothesis underlying this approach is that if two objects are related, inferring something about one object can assist inferences about the other. We call this approach iterative classification. Inferences made with high confidence in initial iterations are fed back into the data to strengthen inferences about related objects in subsequent iterations. Experimental evidence shows that iterative classification leads to a significant increase in classification accuracy when compared with a single-pass approach. This suggests that there are distinctive characteristics of relational data that can be used to improve classification accuracy.

Simple Bayesian classifiers (SBCs) take traditional attribute-value data as input. In order to use SBCs with relational data, we flatten the data first by calculating intrinsic and relational attributes about individual objects. However, we maintain a relational representation of the data and flatten dynamically only when needed by the classifier. Retaining the relational representation makes it possible to extract data, perform a series of calculations and then feed the results back into the relational structure for use in future calculations. The ability to perform iterative calculations in this manner is one of the benefits of maintaining a relational data representation. For example, some measures of centrality in social network analysis (Wasserman and Faust 1994) can only be calculated in such an iterative fashion. Kleinberg’s Hubs and Authorities algorithm for Web searching (1998) also uses iterative calculations in this manner.

2. Relational Classification

Relational data sets present a special opportunity for improving classification. The opportunity exists if, when two objects are related, inferring something about one object can help you infer something about the other. For example, if two people jointly own a business, and one of them is identified as a money launderer, then it may be more likely that the other is also involved in money laundering. The ability to exploit associations among objects in this manner has applications in many fields with relational data, including epidemiology, fraud detection, ecological analysis and sociology.

A relational classification technique, which uses information implicit in relationships, should classify more accurately than techniques that only examine objects in isolation. Relational classification techniques could be particularly useful in domains with abundant information about the relationships among objects but only limited information about the intrinsic properties of those objects. For example, relational classification might be applied to identify potential money-laundering operations based on bank deposits and business connections (Jensen 1997). In such a situation, the existence of an employee making large cash deposits for more than one business gives little information as to the legitimacy of those businesses. Many service and retail companies have high volumes of cash sales and it’s not uncommon for a person to be employed by more than one company. However, if one of the businesses is discovered to be a front company for money laundering, then the related businesses are more likely to be front companies as well. In this case, the relationship provided by a common depositor is more useful in the context of knowledge about the related companies.

There are multiple ways to approach classification in a relational context. One approach ignores related objects and builds classifiers based only on the properties of an object in isolation. Another approach looks at the properties of both the object and its related objects in a static manner, by taking a snapshot of the relational context at some time prior to classification. A third approach uses properties of related objects and dynamically updates those properties as predictions about related objects change. Iterative classification uses the latter approach, applying SBCs in a dynamic way to fully leverage the structure of relational data.

For example, in a data set we describe below, a relational data structure represents companies, their subsidiaries, corporate stockholders, officers and board members. Companies are linked indirectly through stockholders and through people serving simultaneously on several boards (see figure 1). Such an interlocking structure allows the creation of both intrinsic and relational attributes. Intrinsic attributes record characteristics of objects in isolation — for example, company type or officer salary. Relational attributes summarize characteristics of one or more related objects — for example, a company’s number of subsidiaries or the maximum salary of any board member.

Relational attributes fall into two categories which we will call static relational and dynamic relational. Any intrinsic attribute has the potential to be predicted by an SBC model; from the same company data we could predict any of the intrinsic attributes mentioned above. Static relational attributes use known intrinsic attributes of related objects and as such they can be computed without the need for inference. The values of static relational attributes remain constant over the course of classification. Dynamic relational attributes use inferred intrinsic attributes of related objects so they require that at least some related objects be classified before the attribute can be computed. The values of dynamic relational attributes may change as classification progresses and additional inferences are made about related objects. For example, if we were predicting company type, then static relational attributes might record the number of board members who have the title CEO or the average salary of officers. Dynamic relational attributes might record the most prevalent type of corporate stockholder or the maximum number of subsidiaries that share the same type. Both of these latter attributes are dynamic and relational because they reference the company type of related objects, the very thing we are trying to infer about the primary object. For notational simplicity, the remainder of this paper will refer to intrinsic and static relational attributes as static attributes, and dynamic relational attributes as dynamic attributes.

  • Figure 1: Corporate data ontology

In a relational corporate data set, knowing the type of one company might help us infer the type of another company to which it is related, and vice versa. For instance, we may find that individuals tend to serve on boards of companies with the same type, so if a person is on the board of both company X and company Y, and company X is a bank, then company Y is more likely to also be a bank. Or we may find that companies tend to own stock in companies with the same type, so if a company owns both company X and company Y, and company X is a bank, then company Y is more likely to be a bank. In situations of this type, the relations among objects assist the inferences.

In iterative classification, a model is built using a variety of static and dynamic attributes. When training the model, the class labels of all objects are known and consequently the values of all dynamic attributes are also known.

The trained classifier) is then applied to previously unseen examples for which the class labels are unknown. Initially, because class labels of related objects are unknown, values of all dynamic attributes are also unknown. However, their values can be estimated as classification progresses. At the onset, the classifier makes predictions for all objects based only on the values of static attributes. Classifications made with high probability are accepted as valid and are written into the data as known class labels. SBCs are useful for iterative classification because each prediction has an associated probability estimate that can be used to guide iterative classification.

After some percentage of the most certain classifications are “accepted” the classifier starts the next iteration, recalculating dynamic attributes in light of this new information and proceeding with classification once again. At each iteration, additional dynamic attributes are filled in and a greater percentage of classifications are accepted.

Iterative Classification Algorithm

1. Build model on fully labeled training set
2. Applyto test set of N instances. For each iteration i : 1 to m
  a. Calculate values for dynamic relational attributes
  b. Use model to predict class labels
  c. Sort inferences by probability
  d. Accept k class labels, where k = N (i / m )
3. Output final inferences made by model on test set

Related Work

Previous work of the WebKB project investigated classification in a relational context (Craven et al. 1998). WebKB used both SBCs and FOIL, a greedy covering algorithm for learning function-free Horn clauses, to label web pages automatically. Relationships among pages, as encoded by their hyperlinks, are used along with intrinsic attributes to improve classification accuracy.

“Co-training” is an iterative approach to learning models (Blum and Mitchell 1998, Mitchell 1999) that was applied to the WebKB labeling task. Experiments show that a large number of unlabeled instances can be used to boost the performance of a learning algorithm when only a small set of labeled instances is available. Multiple classifiers are learned on independent sets of attributes, from a common set of training examples. Each classifier is run and its most confidently predicted positive and negative instances are added to the training set. The classifiers are relearned with the larger, augmented training set, and the process is repeated. By using the same training data, the classifiers each profit from the predictions of other classifiers. Co-training is tested in a relational context; however, it can be applied to attributevalue data as well. This method uses iteration for learning models instead of using iteration in the application of learned models, as does iterative classification.

Slattery (2000) has investigated using relational information in the test set to classify web pages more accurately. FOIL-HUBS is an extension of FOIL inspired by the Hubs & Authorities algorithm (Kleinberg 1998). FOIL-HUBS identifies the existence of hubs for each target class (e.g., student-hubs point to many student pages) and hub weights contribute to the probability that pages pointed to by the hubs are of a particular class. FOIL-HUBS employs an iterative classification scheme to predict class labels and estimate hub weights, which is similar to our own algorithm for iterative classification, but it is limited to domains where hub nodes exist. In contrast, our work represents an initial attempt to provide a uniform framework for the calculation and use of a wider range of dynamic attributes, albeit within a simpler model representation (SBCs as opposed to function-free Horn clauses).

Freidman et al. (1998) have investigated the use of a relational framework to make sophisticated probabilistic inferences. They have shown how to learn probabilistic relational models (PRMs) from relational databases. PRMs extend the applicability of Bayesian networks techniques (Heckerman 1995), and allow the properties of an object to depend probabilistically on both intrinsic and relational attributes. As currently applied, PRMs do not use initial inferences to inform later inferences about related objects. However, PRMs could be used in the same way that SBCs are used for iterative classification in the work reported here.

The Expectation-Maximization (EM) algorithm (Dempster, Laird, and Rubin 1977) is similar to in spirit to iterative classification, but it addresses a somewhat different problem. The EM algorithm uses a two-step iterative procedure to find the maximum-likelihood estimate of the parameters of an underlying distribution (a model) from a data set containing incomplete or missing data (Bilmes 1998). The first step of EM (the "expectation" step) finds the expected value of missing data values, given the current model. The second step of EM (the "maximization" step) finds the maximumlikelihood model, given the inferred data. After replacing the current model with the new model, the process repeats. In contrast to iterative classification, EM readjusts the model in the second step, rather than adjusting the values of attributes that serve as inputs to the model. Thus, it is a method of learning a model given attribute-value data, rather than a method of applying a learned model to relational data.

Kleinberg (1998) developed an iterative algorithm, called Hubs & Authorities, for Web searching based on the network structure of hyperlinked pages on the Web. The algorithm uses a graph structure, with nodes corresponding to web pages and directed links indicating the presence of hyperlinks between pages. Given the task of identifying authoritative pages, two mutually reinforcing attributes are defined: hub weight and authority weight. The weights are calculated in an iterative fashion by feeding the values of one attribute into the calculations of the other. The iterative nature of this algorithm is similar to our approach in that it maintains and updates attribute values throughout the procedure. However, the algorithm assumes the values of both attributes are known for each instance and starts by assigning equal weights to all pages. It does not use a predictive model to assign weight values.


Conclusions and Future Work

A number of conclusions can be drawn from this work about the potential of iterative classification. We have shown that there is an opportunity to use relations in data to increase classification accuracy, and that an iterative approach exploiting this opportunity can produce a significant improvement in accuracy for a binary classification task in the corporate data set. We have outlined several necessary conditions for successful application of iterative classification. For iterative classification to improve on a static approach, a data set should exhibit the following characteristics: insufficient predictive power from static attributes and useful dynamic attributes, rich relational structure, and islands of certain knowledge from which to jump start the iterative process. Expansion and formal verification of these ideas is an important area for further investigation. In addition to presenting opportunities for discovery, relational data also offer several challenges. Devising a sampling procedure that does not bias statistical estimates of relational attributes is a difficult task. As the relational data structure becomes more complex, our opportunities for improving classification increase, but so do the challenges of sampling. Future work would be aided by the use of naturally disjoint data sets with similar distributions such as the university web sites used by Slattery (2000).

Formulating useful dynamic attributes is also challenging. It is difficult to define the value of a dynamic attribute when some, but not all of the related class labels have been inferred. Because the classifier is trained on full knowledge, dynamic attribute values expressing partial knowledge can bias or mislead the predictions of the classifier. A few incorrect inferences could have a “snowball effect,” with the dynamic attributes cascading the mistakes throughout the test set. For this reason it is important to use dynamic attributes whose values are either known with complete certainty or not at all. Threshold attributes are a good example of this type of “robust” attribute, where the value is known as soon as a particular value threshold is exceeded. Both dynamic attributes used in this experiment are examples of threshold attributes. Future work includes both establishing the effects of threshold attributes on iterative classification, and determining other types of robust attributes.

Attributes that combine probabilistic evidence of all related class labels are a potential alternative to threshold attributes. Instead of accepting the top percentage of predictions, or those exceeding a threshold, the algorithm would accept all predictions. The values of these probabilistic attributes are then determined by a combination of the probabilities associated with the inferred class labels of related objects. As the certainty of predictions change over the course of iterations, the attribute values could be dynamically updated. This is an area that requires additional exploration.

A potential pitfall of the specific variety of iterative classification explored here is that SBCs often produce biased probability estimates. SBCs are known to produce optimal class predictions in a wide variety of domains; however, SBC probability estimates are biased except under conditions of attribute independence. Future work includes exploring iterative classification with other methods that produce more accurate probability estimates such as Bayesian networks or PRMs (Freidman et al. 1999). We will also investigate the use of a threshold for accepting predictions instead of accepting a percentage determined by the number of iterations.

Another direction for future work involves extending the iterative procedure for prediction of multiple object types by simply combining the results of multiple classifiers. Each classifier would make use of the dynamic attributes filled in through the efforts of the other classifiers. In this sense the classifiers would collaborate with each other to improve accuracies for both classification tasks. Caruana (1997) has investigated the collaboration of multiple models for learning under the hypothesis that multiple, related learning tasks share the same representation, and learning one helps with learning another. A relational approach would be similar but would involve the collaborative application of models instead.


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 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
2000 IterativeClassificationJennifer Neville
David Jensen
Iterative Classification in Relational DataProceedings of the AAAI-2000 Workshop on Statistical Relational Learninghttps://www.aaai.org/Papers/Workshops/2000/WS-00-06/WS00-06-007.pdf2000