Maximizing expected generalization for learning complex query concepts6976016Abstract A method of learning user query concept for searching visual images encoded in computer readable storage media comprising: providing a multiplicity of sample images encoded in a computer readable medium; providing a multiplicity of sample expressions that correspond to sample images and in which terms of the sample expressions represent features of corresponding sample images; defining a user query concept sample space bounded by a boundary k-CNF expression and by a boundary k-DNF expression refining the user query concept sample space by, soliciting user feedback as to which of the multiple presented sample images are close to the user's query concept; removing from the boundary k-CNF expression disjunctive terms based upon the solicited user feedback; and removing from the boundary k-DNF expression respective conjunctive terms based upon the solicited user feedback. Claims 1. A method of learning a user query concept for searching visual images encoded in computer readable storage media comprising: Description BACKGROUND OF THE INVENTION DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Introduction To learn users' query concepts, the present invention provides a query-concept learner process and a computer software based apparatus that "learns" a concept through an intelligent sampling process. The query-concept learner process fulfills two primary goals. By "learns," it is meant that the query-concept learner process evaluates user feedback as to the relevance of samples presented to the user in order to select from a database samples that are very likely to match, or at least come very close to matching, a user's current query concept. One, the concept-learner's hypothesis space must not be too restrictive, so it can model most practical query concepts. Two, the concept-learner should grasp a concept quickly and with a small number of labeled instances, since most users do not wait around to provide a great deal of feedback. To fulfill these design goals, the present invention uses a query-concept learner process that we refer to as, the Maximizing Expected Generalization Algorithm (MEGA). MEGA models query concepts in k-CNF [8], which can model almost all practical query concepts. k-CNF is more expressive than k-DNF, and it has both polynomial sample complexity and time complexity [9, 13]. To ensure that target concepts can be learned quickly and with a small number of samples, MEGA employs two sub-processes: (1) a sample selection (S-step); and (2) a feature reduction (F-step) process. In its S-step, MEGA judiciously selects samples that aimed at collecting maximum information from users to remove irrelevant features in its subsequent F-step. In its F-step, MEGA seeks to remove irrelevant terms from the query-concept (i.e., a k-CNF), and at the same time, refines the sampling boundary (i.e., a k-DNF) so that most informative samples can be selected in its subsequent S-step. MEGA is a recursive. The two-step process (S-step followed by F-step) repeats, each time with a smaller sample space and a smaller set of features, until the user query concept has been identified adequately. Unlike traditional query refinement methods, which uses only the S-step or only the F-step (Section 5 highlights related work), MEGA uses these two steps in a complementary way to achieve fast convergence to target concepts. In a present embodiment, in order to evaluate a user query concept efficiently, the MEGA query-concept learner process uses a multi-resolution/hierarchical learning method. Features are divided into subgroups of different resolutions. As explained more fully below, the query-concept learner process exploits the multi-resolution/hierarchical structure of the resolution hierarchy to reduce learning space and time complexity. It is believed that when features are divided carefully into G groups, MEGA can achieve a speedup of O(Gk-1) with little precision loss. Overview of Operation of the User Query-Concept Learner Process Referring to the illustrative drawing of FIG. X, there is shown a generalized flow diagram which illustrates the overall flow of a user query-concept learner process in accordance with a present embodiment of the invention. Typically, a user initiates the process by providing hints about his or her current query-concept. The objective is to use these hints to bootstrap the overall learner process by providing an initial set of positive samples that match the user's query-concept and an initial set of negative samples that do not match the user's query-concept. This software-based initialization process may involve a transfer of hints from a user computer to a software-based initialization process running on another computer that evaluates the hints in order to generate an initial set of samples. The user indicates which ,if any, samples meet the user's query-concept. Once the process has been initialized, a software-based sample selection process selects samples for presentation to the user. The sample images are selected from a query-concept sample space demarcated by a QCS, modeled as a k-CNF, and a CCS, modeled as a k-DNF. As explained in the sections below, sample images correspond to expressions that represent the features of the images. The expressions are stored in an expression database. The sample selection process evaluates these expressions in view of the QCS and the CCS in order to determine which sample images to present to the user. The sample images are carefully selected in order to garner the maximum information from the user about the user's query concept. As explained below, a sample generally should be selected that is sufficiently close to the QCS so that the user is likely to label the sample as positive. Conversely, the sample generally should be selected that is sufficiently different from the QCS so that a positive labeling of the sample can serve as an indicator of what features are irrelevant to the user's query-concept. A software-based delivery process delivers the selected sample images to the user for viewing and feedback. The user views the sample images on his or her visual display device, such as a computer display screen, and labels the sample images so as to indicate which sample images match the user's query-concept (positive label) and which do not (negative label). Note that the user's labeling may be implicit. For instance, in one embodiment, samples that are not explicitly labeled as positive are implicitly presumed to have been labeled as negative. In other embodiments, the user may be required to explicitly label samples as positive and negative, and no implication is drawn from a failure to label. Next, the user's labels are communicated to a software-based process which receives the label information and forwards the label information to a software-based process that retrieves from the expression database, expressions that correspond to the labeled samples. A software-based comparison process compares the expressions for the positive labeled samples with the k-CNF to determine whether there are disjunctive terms of the k-CNF that are candidates for removal based upon differences between the k-CNF and the positive labeled samples. A software-based comparison process compares the negative labeled samples with the k-DNF to determine whether there are conjunctive terms of the k-DNF that are candidates for removal based upon differences between the k-DNF and the negative labeled samples. A software-based adjustment process adjusts the k-CNF by removal of disjunctive terms that meet a prescribed measure of difference from the positive labeled samples. A software-based adjustment process adjusts the k-DNF by removal of conjunctive terms that meet a prescribed measure of difference from the negative labeled samples. Finally, a software-based 'finished-yet process?'0 determines whether the QCS and the CCS have converged or collapsed such that the overall query-concept learner process is finished. If the overall process is not finished then the 'finished-yet?' process returns control to the software-based sample selection process. The overall process, therefore, runs recursively until the adjustment of the QCS, through changes in the k-CNF, and the adjustment of the CCS, through changes in the k-DNF, result in a collapsing or convergence of these two spaces, either of which extinguishes the query concept sample space from which samples are selected. 1.1 A Simple Motivating Example The following is a relatively simple hypothetical example that illustrates the need for a query-concept learner process and associated computer program based apparatus in accordance with the invention. This simple example is used throughout this specification to explain various aspects of our process and to contrast the process with others. This hypothetical example has a relatively simple feature set, and therefore, is useful for explaining in more simple terms certain aspects of the learner process. Although the learner process is being introduced through a simple example, it will be appreciated that the learner process is applicable to resolve query concepts involving complex feature sets. More specifically, in Section 4, the MEGA query-concept learner is shown to work well to learn complex query concepts for a high dimensional image dataset. Suppose Jane plans to apply to a graduate school. Before filling out the forms and paying the application fees, she would like to estimate her chances of being admitted. Since she does not know the admission criteria, she decides to learn the admission concept by induction. She calls up a few friends who applied last year and obtains the information shown in Table 1.
If we look at the GRE scores in the table, we see that students with either high or low GRE scores were admitted, also both kinds were rejected. Hence, we may conclude that the GRE is irrelevant in the admission process. Likewise, one's publication record does not affect admission acceptance, nor does having a high GPA. It may appear that the admission decision is entirely random. However, the graduate school actually uses a combination of reasonable criteria: it requires a high GPA and either a high GRE or publications. In other words, Admission: GPA=high Two obvious questions arise: "Are all the samples in Table 1 equally useful for learning the target concept?" and, "Are all features in the table relevant to the learning task?"
The following sections show how and why a query-concept learner process in accordance with the present invention can quickly learn a target concept like the example of admission criteria whereas other methods may not. It will also be shown that a concept learner in accordance with a present embodiment can tolerate noise, i.e., it works well even when a target concept is not in k-CNF and even when training data contain some errors. In addition, it will be shown that a multi-resolution/hierarchical learning approach in accordance with one embodiment of the invention can drastically reduce learning time and make the new query-concept learner effective when it "learns" a concept in very high dimensional spaces. 1.2 Definitions and Notations A query-concept learner in accordance with a present embodiment of the invention models query concepts in k-CNF and uses k-DNF to guide the sampling process. Definition 1: k-CNF: For constant k, the representation class k-CNF consists of Boolean formulae of the form c1 Definition 2: k-DNF: For constant k, the representation class k-DNF consists of Boolean formulae of the form d1 In a retrieval system in accordance with a present embodiment of the invention, queries are Boolean expressions consisting of predicates connected by the Boolean operators A k-CNF possesses the following three characteristics: 1: The terms (or literals) are combined by the 2: The predicates in a term are combined by the 3: A term can have at most k predicates. Suppose we have three predicates Px To find objects that are similar to a k-CNF concept, similarity between objects and the concept is measured. Similarity is first measured at the predicate level and then at the object level. At the predicate level, we let Fx Suppose a dataset contains N objects, denoted as Oi, where i=1 . . . N. Suppose each object can be depicted by M attributes, each of which is denoted by xk, where k=1 . . . M. At the object level, standard fuzzy rules, as defined by Zadeh [4, 21], can be used to aggregate individual predicates' similarity scores. An M-tree aggregation function that maps [0, 1]M to [0, 1] can be used to combine M similarity scores into one aggregated score. The rules are as follows: Conjunctive rule: Px Disjunctive rule: Px To assist the reader, Table 2 summarizes the parameters that have been introduced and that will be discussed in this document.
2 The MEGA User Query-Concept Learner Process This section describes how a user query-concept learner process in accordance with a present embodiment of the invention operates. Section 3 discusses how a process in accordance with a present embodiment deals with very large database issues such as high dimensional data and very large datasets. The query-concept learning process includes the following parts:
In order to more efficiently initiate the process of learning a query concept, a user may engage in a preliminary initialization process aimed at identifying an efficacious, sensible, and reasonable starting point for the concept learner process. The objective of this initialization process is to garner a collection of sample images to be presented to the user to elicit a user's initial input as to which of the initial sample images matches a user's current query concept. It will be appreciated that there may be a very large database of sample images available for presentation to the user. The question addressed by the initialization process is, "Where to start the concept learner process?" As explained below, the concept learner process according to the present invention proceeds based upon the user's indication of which images match, or at least are close to, the user's current query concept and which do not match, or at least are not close to the user's current query concept. The initialization process aims to identify an initial set of sample images that are likely to elicit a response from the user that identifies at least some of the initial sample images as matching or at least being close to the user's query concept and that identifies other of the initial sample images as not matching or at least not being close to the user's query concept. Thus, the initialization process aims to start the concept learner process with at least some sample images that match the user's query concept and some that do not match the user's query concept. As part of the initialization process, the user is requested to provide some indication of what he or she is looking for. This request, for example, may be made by asking the user to participate in a key word search or by requesting the user to choose from a number of different categories. The manner in which this initial indication is elicited from the user is not important provided that it does not frustrate the user by taking too long or being too difficult and provided that it results in an initial set of samples in which some are likely to match the user's current query concept and some are not. It is possible that in some cases, more than one initial set of samples will be presented to the user before there are both initial samples that match the user's query concept and samples that do not match. It will be appreciated that the initialization step is not critical to the practice of the invention. It is possible to launch immediately into the concept learner process without first identifying some samples that do and some samples that do not match the user's current query concept. However, it is believed that the initialization process will accelerate the concept learner process by providing a more effective starting point. More specifically, a user who cannot specify his/her query concept precisely can initially give the concept learner process some hints to start the learning process. For instance, a search for a document or for an image can start with a key word search or by selecting one or a few categories. It is believed that this bootstrapping initialization process is more practical than that of most traditional multimedia search engines, which make the unrealistic assumption that users can provide "perfect" examples (i.e., samples) to perform a query. A present embodiment of bootstrapping initialization process aims to present a set of samples to the user. The user then labels as positive a set of objects that match the user's query concept. Samples that do not match the user's query concept and that are not labeled as positive are considered to be a negative-labeled set. This initialization process, therefore, bootstraps the concept learner process by providing an initial positive-labeled set and an initial negative-labeled set. 2.2 Refinement Valiant's learning algorithm [19] is used as the starting point to refine a k-CNF concept. We extend the algorithm to:
More specifically, the query-concept learner process initializes a query concept space (QCS) as a k-CNF and a candidate concept space (CCS) as a k-DNF. The QCS starts as the most specific concept and the CCS as the most general concept. The target concept that query-concept learner process learns is more general than the initial QCS and more specific than the initial CCS. The query-concept learner process seeks to learn the QCS, while at the same time refining the CCS to delimit the boundary of the sampling space. (The shaded area in FIG. 1 shows the sampling space between the QCS and the CCS). the logical flow of the MEGA query-concept learner process is set forth below in general terms.
FIG. 2: Algorithm MEGA Step 2.a: This is the sample selection process. The sample process selects samples from the unlabeled pool U. The unlabeled pool contains samples that have not yet been labeled as matching or not matching the current user query-concept. This step passes QCS, CCS, and U to procedure Sample to generate Kα samples. In the present embodiment of the invention QCS is modeled as a k-DNF, and CCS is modeled as a k-DNF. Therefore, the k-CNF and k-DNF are passed to procedure sample. The procedure Sample is discussed in Section 2.3. Step 2.b: This process solicits user feedback. A user marks an object positive if the object fits his/her query concept. An unmarked object is considered as having been marked negative by the user. As the query-concept learner process proceeds in an attempt to learn a query concept, it will submit successive sets of sample images to the user. If the attempt is successful, then the sample images in each successive sample set are likely to be progressively closer to the user's query concept. As a result, the user will be forced to more carefully refine his or her choices from one sample image set to the next. Thus, by presenting sets of images that are progressively closer to the query concept, the query-concept learner process urges the user to be progressively more selective and exacting in labeling sample images, as matching or not matching the user's current query-concept. Step 2.c: This is the feature reduction process. It refines QCS and CCS. Step 2.c.1: This process refines QCS. For each disjunctive term in the k-CNF, which models the QCS, the feature reduction process examines each positive-labeled sample image and uses function ƒ to compute the probability that the disjunctive term should be eliminated. The feature reduction process then calls procedure Vote to tally the votes among the positive-labeled sample images and compares the vote with threshold Kd to decide whether that disjunctive term is to be removed. According to the procedure vote, if sufficient numbers of positive-labeled sample images contradict the QCS with respect to a disjunctive term (i.e., if the threshold is exceeded), the term is removed from the QCS. The procedure Vote, which decides how aggressive the feature reduction process is in eliminating terms, in Section 2.6. Step 2.c.2: This process refines CCS. Similar to Step 2.c.1, for each conjunctive term in the CCS, modeled a k-DNF, the feature reduction process examines each negative-labeled sample image, and uses function ƒ to compute the probability that the conjunctive term should be eliminated. The feature reduction process then calls procedure Vote to tally the votes among the negative-labeled sample images. Then it compares the vote with threshold Kc to decide whether that conjunctive term is to be removed from the k-DNF. According to the procedure vote, if sufficient numbers of negative-labeled instances satisfy the k-DNF with respect to a conjunctive term, the term is removed from the k-DNF. Step 2.d: This process performs bookkeeping by reducing the unlabeled pool. The refinement step terminates when the learning process converges to the target concept (Converged?=true) or the concept is collapsed (Collapsed?=true). (Converged? and Collapsed? are defined below.) In practice, the refinement stops when no unlabeled instance u can be found between the QCS and the CCS. 2.3 Sampling The query-concept learner process invokes procedure Sample to select the next Kα, unlabeled instances to ask for user feedback. From the college-admission example presented in Section 1, we learn that if we would like to minimize our work (i.e., call a minimum number of friends), we should choose our samples judiciously. But, what constitutes a good sample? We know that we learn nothing from a sample if
To make sure that a sample is useful, the query-concept learner process employs two strategies: The query-concept learner process employs an additional secondary strategy to facilitate the identification of useful samples: Samples must be selected from the query concept sample space, which is bounded by the CCS and the QCS. Samples with expressions that are outside the CCS are ineligible for selection. Thus, for example, a sample whose expression includes a prescribed number of features that are absent from the k-DNF is ineligible for selection as a sample. In a present embodiment, a sample is ineligible if its expression includes even one feature that is not represented by a conjunctive term in the k-DNF. Moreover, in order to be effective in eliciting useful user feedback, a the expression representing a sample should be close to but not identical to the k-CNF. The question of how close to the k-CNF a sample's expression should be is an important one. That difference should be carefully selected if the learner process is to achieve optimal performance in terms of rapid and accurate resolution of a query-concept. More specifically, it may appear that if we pick a sample that has more dissimilar disjunctions (compared to the QCS), we may have a better chance of eliminating more disjunctive terms. This is, however, not true. In once embodiment, a sample must be labeled by the user as positive to be useful for refining k-CNF which models the QCS. In other words, a user must indicate, either expressly or implicitly, that a given sample matches the user's query concept in order for that sample to be useful in refining the QCS. Unfortunately, a sample with more disjunctions that are dissimilar to the target concept is less likely to be labeled positive. Therefore, in choosing a sample, there is a trade off between those with more contradictory terms and those more likely to be labeled positive. 2.4 Estimation of Optimal Difference Between Sample and QCS One of the criteria for selecting a sample is the closeness of the sample to the QCS, which is modeled as a k-CNF. A measure of the closeness of a sample to the k-CNF is the number of terms in sample's expression that differ from corresponding disjunctive terms of the k-CNF. Thus, one aspect of optimizing a query-concept learner process is a determination of the optimum difference between a sample and a k-CNF as measured by the number of terms of the sample's expression that differ from corresponding disjunctive terms of the k-CNF. As explained in the following sections, this optimum number is determined through estimation. More specifically, let Ψ denote the number of disjunctions remaining in the k-CNF. The number of disjunctions that can be eliminated in the current round of sampling (denoted as P) is between zero and Ψ. We can write the probability of eliminating P terms as Pe(P). Pe(P) is a monotonically decreasing function of P. The query-concept learner process can be tuned for optimal performance by finding the P that can eliminate the maximum expected number of disjunctive terms, given a sample. The objective function can be written as To solve P*, we must know Pe(P), which can be estimated by the two methods described below: probabilistic estimation and empirical estimation. 2.5 Probabilistic Estimation We first consider how to estimate P* using a probability model. As we have seen in the college-admission example, if a sample contradicts more disjunctive terms, it is more likely to be labeled negative (i.e., less likely to be labeled positive). For example, a sample that contradicts predicate P1, is labeled negative only if P1 is in the user's query concept. A sample that contradicts both predicates P1 and P2 is labeled negative if either P1 or P2 is in the user's query concept. Formally, let random variable Φi be 1 if Pi is in the concept and 0 otherwise. For simplicity, let us assume that the Φi's are iid (independent and identically distributed), and the probability of Φi being 1 is p (0<p<1). The probability of a sample contradicting P disjunctive terms is marked positive only when none of these P terms appears in the user's query concept. This probability is (1-p)P. If we substitute Pe,(P) by (1-p)P on the right-hand side of Equation 1, we get max E(P)=P(1-p)P. If we take the derivative of E(P), we can find the optimal P value, denoted by P*: ##EQU1## Of course, it may be too strong an assumption that the probability p of all disjunctions is iid. However, we do not need a precise estimation here for the following two reasons: 1. Precise estimation may not be feasible and can be computationally intensive. 2. An approximate estimation is sufficient for bootstrapping. Once the system is up and running for a while and collects enough data, it can empirically estimate Pe(P) using its past experience. We discuss this process next. 2.6 Empirical Estimation The probability of eliminating P terms, Pe(P), can be estimated based on its past experience of the learner process. For each sample the learner process presents, a record can be created which sets forth how many disjunctions the sample contradicts with respect to the query concept and whether the sample is labeled positive. Once a sufficient amount of data has been collected, we can estimate Pe(P) empirically. We then pick the P* that can eliminate the maximum expected number of disjunctive terms. Again, a reasonable approach to estimate Pe(P) is to use probabilistic estimation when the learner process first starts and then to switch to empirical estimation when the sufficient data has been collected. The transition from probabilistic estimation to empirical estimation takes place gradually and only after numerous users have employed the query-concept learner process. This transition does not occur during the course of a single user session. Moreover, an abrupt transition from one estimation approach to the other could be problematic, since the two estimates of Pe(P) may differ substantially. This could lead to a sudden change in behavior of the sampling component of the active learner. To remedy this problem, we employ a Bayesian smoothing approach. Essentially the probabilistic estimation is the prior guess at the distribution over P and the empirical approach is the guess based purely on the data that has been gathered so far. The Bayesian approach combines both of these guesses in a principled manner. Before we start, we imagine that we have seen a number of samples of P. After refinement iteration, we gather new samples for P; then we add them to our current samples and adjust Pe(P). For example, before we start, we assume that we have already seen samples with P=1 being labeled positive three out of five times and samples with P=2 being labeled positive seven out of 20 times. In other words, we have successfully eliminated P=1 term three times out of five, and we have successfully eliminated P=2 terms 7 times out of 20. Thus initially Pe(P=1)=⅗=0.6 and P(P=2)= 7/20=0.35. Now suppose we do a query and in which we observe a sample with, P=2 being labeled positive. Then our new distribution is P(P=1)=⅗ and P(P=2)= 8/21. We continue in this manner. At first, the prior assumption has quite an effect on our guess about the distribution. The more imaginary samples we have in our prior assumption, the larger its effect. For instance, if we assume that P=1 being labeled positive 30 out of 50 times and that P=2 being labeled positive 70 out of 200 times, it takes more real samples to change Pe(P). With time, the more real samples we get, the less the effect of the prior assumption becomes, until eventually it has virtually no effect, and the observed data dominate the expression. This procedure gives us a smooth transition between the "probabilistic" and the "empirical" methods. User Feedback in the Refinement of the QCS and CCS. A user's indications of which sample images meet the user's current query-concept and which sample images do not meet the user's current query-concept are used as a basis for refinement of the QCS and the CCS, and therefore, as a basis for refinement of the query concept sample space which is bounded by the QCS and the CCS. One function in the refinement process is to evaluate whether or not a disjunctive term should be removed from the QCS which is modeled as a k-CNF. Another function in the refinement process is to evaluate whether a conjunctive term should be removed from the CCS which is modeled as a k-DNF. With regard to removal of a disjunctive term from the k-CNF, the way in which the function is achieved is to ascertain the level of difference, with respect to the term in question, between the k-CNF and the expressions for the one or more sample images indicated as matching the user's query-concept. Similarly, with regard to removal of a conjunctive term from the k-DNF, the way in which the function proceeds is to ascertain the level of difference, with respect to the term in question, between the k-DNF and the expressions for the one or more sample images indicated as not matching the user's query-concept. The specific approach to the employment of user feedback to refine the QCS and the CCS is a Procedure Vote described below. 2.7 Procedure Vote A Procedure Vote employed in a present embodiment functions to refine the QCS and CCS while also accounting for model bias and user errors. More specifically, in the previous example, we assume that all samples are noise-free. This assumption may not be realistic. There can be two sources of noise:
Procedure Vote The Procedure Vote process can be explained in the following general terms. Input: y, Pt Output: Pt Begin Sort Pt Return the γth highest Pt End Thus. the Procedure Vote controls the strictness of voting using γ. The larger the value of γ is, the more strict the voting is and therefore the harder it is to eliminate a term. When the noise level is high, we have less confidence in the correctness of user feedback. Thus, we want to be more cautious about eliminating a term. Being more cautious means increasing γ. Increasing γ, however, makes the learning process converge more slowly. To learn a concept when noise is present, one has to buy accuracy with time. Procedure Vote Example The parameter γ is the required number of votes to exceed a threshold, either Kc (k-CNF) or Kd (k-DNF). The value γ is a positive integer. The values Kc and Kd are values between zero and one. Suppose that we have three positive labeled instances y1, y2 and y3. Assume that c1 is a disjunctive term meaning that high-saturated red is true. Suppose that the QCS has a value of 1 on c1. Suppose that c1, c2, and c3 have values on c1 of 0.1, 0.2, and 0.3, respectively. The distance (i.e., the probability to remove) of y1 from the QCS with respect to c1 is 0.9. The distance of y2 from the QCS with respect to c1 is 0.8. The distance of y3 from the QCS with respect to c1 is 0.7. Now suppose Kc=0.85. Based on the above hypothetical, then if γ=1, then c1 is removed from the QCS because at least one sample image, y1, differs from the QCS with respect to c1 by an amount greater than the threshold Kc. However, if γ=2, then c1 is not removed from the QCS because there are not two sample images that differ from the QCS with respect to c1 by an amount greater than the threshold Kc. As explained above the differences from QCS of y1, y2 and y3 with respect to c1 are 0.9, 0.8 and 0.7, respectively. Only one of these exceeds the threshold of Kc=0.85. Therefore, if γ=2, then c1 is not removed from the QCS. The Procedure Vote operates in an analogous fashion to determine wheter or not to remove conjunctive terms from a CCS based upon γ and Kd. 3 EXAMPLE Below we show a toy example problem that illustrates the usefulness of the MEGA query-concept learner process. We will use this simple example to explain various aspects of our sampling approach and to contrast our approach with others. This example models an college admission concept that consists of a small number of Boolean predicates. (MEGA also works with fuzzy predicates.) Suppose Jane plans to apply to a graduate school. Before filling out the forms and paying the application fees, she would like to estimate her chances of being admitted. Since she does not know the admission criteria, she decides to learn the admission concept by induction. She randomly calls up a few friends who applied last year and obtains the information shown in Table 1.
There are three predicates in this problem, as shown in the table. The three predicates are:
The first question arises: "Are all the random samples in Table 1 equally useful for learning the target concept?" Apparently not, for several reasons. First, it seems that Pica's record may not be useful since she was unlikely to be admitted (i.e., her record is unlikely to be labeled positive). Second, both Emily and Mary have the same record, so one of these two records can be redundant. Third, Lulu's record is perfect and hence does not provide additional insight for learning the admission criteria. This example indicates that choosing samples randomly may not produce useful information for learning a target concept. Now, let us explain how MEGA's sampling method works more effectively than the random scheme. Suppose CCS and QCS are modeled as 2-CNF and 2-DNF, respectively. Their initial expressions can be written as follows: Suppose ψ* is one. Jane starts by calling his friends whose "profile" fails by exactly one disjunctive term. Jane calls three people and two tell her that they were admitted (i.e., they are the positive-labeled instances) as shown in Table 2. Based on the feedback, Jane use the positive labeled instances (Joe and Emily) to generalize the QCS concept to QCS=(GPA=high)
true) In the second round, Jane attempts to call friends to see if any of the remaining terms can be removed. He calls Kevin, whose profile is listed in the table. Since this sample is labeled negative, the QCS is not changed. But the CCS is reduced to (GRE=high Simplifying and rewriting both QCS and CCS gives us the following identical expression: The concept converges and the refinement terminates at this point. We have learned the admission criterion—a high GPA and either a high GRE or publications□ 4 Multi-resolution/Hierarchical Learning The MEGA scheme described so far does not yet concern its scalability with respect to M (the number of features for depicting an object). In this section, we describe MEGA's multi-resolution/hierarchical learning algorithm that tackles the dimensionality-curse problem. The number of disjunctions in a k-CNF (and, likewise, the conjunctives in a k-DNF) can be written as ##EQU2## When M is large, a moderate k can result in a large number of disjunctive terms in a k-CNF, which causes high space and time complexity for learning. For instance, an image database that we have built [1] characterizes each image with 144 features (M=144). The initial number of disjunctions in a 3-CNF is half a million and in a 4-CNF is eighteen million. To reduce the number of terms in a k-CNF, we divide a learning task into G sub-tasks, each of which learns a subset of the features. Dividing a feature space into G subspaces reduces both space and time complexity by a factor of O(Gk-1). For instance, setting G=12 in our image database reduces both space and time complexity for learning a 3-CNF by 140 times (the number of terms is reduced to 3,576), and for learning a 4-CNF by 1,850 times (the number of terms is reduced to 9,516). The savings is enormous in both space and learning time. (The wall-dock time is less than a second for one learning iteration for a 4-CNF concept on a Pentium-III processor.) This divide-and-conquer approach may trade precision for speed, since some terms that involve features from more than one feature subset can no longer be included in a concept. The loss of precision can be reduced by organizing a feature space in a multi-resolution fashion. The term feature resolution and a weak form of feature resolution that we call feature correlation are defined as follows: Definition 5: Feature resolution: Feature. Pi is said to have higher resolution than feature Pi if the presence of Pi implies the presence of Pj (or the absence of Pj implies the absence of Pi). Let Pi ε Pj denote that Pi has higher resolution than Pj. We say that Pi ε Pj if and only if the conditional probability P(Pj|Pi)=1. Definition 6: Feature correlation: A feature Pi is said to have high correlation with feature Pj if the presence of Pi implies the presence of Pj and vice versa with high probability. We say that Pi-Pj if and only if the conditional probability P(Pj|Pi)|P(Pj)=P(Pi|Pj)|P(Pi)≧δ. MEGA takes advantage of feature resolution and correlation in two ways—inter-group multi-resolution and intra-group multi-resolution—for achieving fast and accurate learning. Due to the space limitation, we limit our description of the heuristics of MEGA's multi-resolution learning algorithm to the following.
5 Example for Multi-resolution Learning Suppose we use four predicates (i.e., features) to characterize an images. Suppose these four predicates are vehicle, car, animal, and tiger. A predicate is true when the object represented by the predicate is present in the image. For instance, vehicle is true when the image contains a vehicle. A 2-CNF consisting of these four predicates can be written as the following: As the number of predicates increases, the number of terms in a k-CNF can be very large. This large number of terms not only incur a large amount of memory requirement but also long computational time to process them. To reduce the number of terms, we can divide predicates into subgroups. In general, when we divide a k-CNF into G groups, we can reduce both memory and computational complexity by G The saving is 100 folds. Dividing predicates into subgroups may lose some inter-group terms. Suppose we divide the four predicates into two groups: Group one consists of vehicle and car, and group two consists of animal and tiger. We then have the following two sets of 2-CNF: From group one, we have: vehicle and car and (vehicle or car). From group two, we have: animal and tiger and (animal or tiger). When we join these two 2-CNF with an "and" operator, we have: Comparing expression (2) to expression (1), we lose four inter-group disjunctions: (vehicle Losing terms may degrade the expressiveness of k-CNF. However, we can divide the predicates intelligently so that the effect of losing terms is much less significant. The effect of losing terms is null if we can divide predicates in a multi-resolution manner. Follow the example above. If we divide predicates into group one: (vehicle, animal); and group two: (car, tiger), then the losing terms (vehicle or car), (animal or tiger) do not affect the expressiveness of the k-CNF. This is because car has a higher resolution than vehicle, and (car or vehicle)=car. Likewise, (animal or tiger)=tiger. We still lose two terms: (vehicle 6 Example: Muli-resolution Processing Let us reuse the k-CNF in the above example. Suppose we have an image example which contains a cat on a tree, and the image is marked positive. We do not need to examine all terms. Instead, we can just first examine the lowest resolution temrs. In this case, since the vehicle predicate (low resolution one) is contracted, we do not even need to examine the car predicate that has a finer resolution than vehicle. The elimination of the vehicle predicate eliminates all its higher resolution counterparts, and hence car. The cat object satisfy the animal predicate. We need to examine the tiger predicate which has a finer resolution than animal. Since tiger is not present, the tiger predicate is eliminated. We have animal retained in the concept. What is the advantage of examining predicates from low to high resolutions? We do not have to allocate memory for the higher resolution predicates until the lower ones are satisfied. We can save space and time. 7 Example: Multiple Pre-cluster Sets of Sample Images Suppose we have N images. We pre-group these images into M clusters. Each cluster has about N/M images, and the images in each cluster are "similar" to one another. We can pick one image from each cluster to represent the cluster. In other words, we can have M images, one from each cluster, to represent the N images. Now, if we need to select samples, we do not have to select samples from the N-image pool. We can select images from the M-image pool. Every time when we eliminate one of these M images, we eliminate the cluster that the image represents. Let N=one billion and M=one thousand. The amount of processing speed can be improve by one million folds. Characterizing Images with Expressions Comprising Features Values Each sample image is characterized by a set of features. Individual features are represented by individual terms of an expression that represents the image. The individual terms are calculated based upon constituent components of an image. For instance, in a present embodiment of the invention, the pixel values that comprise an image are processed to derive values for the features that characterize the image. For each image there is an expression comprising a plurality of feature values. Each value represents a feature of the image. In a present embodiment, each feature is represented by a value between 0 and 1. Thus, each image corresponds to an expression comprised of terms that represent features of the image. The following Color Table and Texture Table represent the features that are evaluated for images in accordance with a present embodiment of the invention. The image is evaluated with respect to 11 recognized cultural colors (black, white, red, yellow, green, blue, brown, purple, pink, orange and gray) plus one miscellaneous color for a total of 12 colors. The image also is evaluated for vertical, diagonal and horizontal texture. Each image is evaluated for each of the twelve (12) colors, and each color is characterized by the nine (9) color features listed in the Color Table. Thus, one hundred and eight (108) color features are evaluated for each image. In addition, each image is evaluated for each of the thirty-six (36) texture features listed in the Texture Chart. Therefore, one hundred and forty-four (144) features are evaluated for each image, and each image is represented by its own 144 (feature) term expression.
The computation of values for the image features such as those described above is well known to persons skilled in the art. Color set, histograms and texture feature extraction are described in, John R. Smith and Shih-Fu Chang, Tools and Techniques for Color Image Retrieval, IS&T/SPIE Proceedings, Vol. 2670, Storage & Retrieval for Image and Video Database IV, 1996, which is expressly incorporated herein by this reference. Color set and histograms as well as elongation and spreadness are described in, E. Chang, B. Li, and C. L. Towards Perception-Based Image Retrieval. IEEE, Content-Based Access of Image and Video Libraries, pages 101-105, June 2000, which is expressly incorporated herein by this reference. The computation of color moments is described in, Jan Flusser and Tomas Suk, On the Calculation of Image Moments, Research Report No. 1946, January 1999, Journal of Pattern Recognition Letters, which is expressly incorporated herein by this reference. Color moments are used to compute elongation and spreadness. There are mulitple resolutions of color features. The presence/absence of each color is at the coarse level of resolution. For instance, coarsest level colr evaluation determines whether or not the color red is present in the image. This determination can be made through the evaluation of a color histogram of the entire image. If the color red comprises less than some prescribed percentage of the overall color in the image, then the color red may be determined to be absent from the image. The average and variance of hue, saturation and intensity (HVS) are at a middle level of color resolution . Thus, for example, if the color red is determined to be present in the image, then a determination is made of the average and variance for each of the red hue, red saturation and red intensity. The color elongation and spreadness are at the finest level of color resolution. Color elongation can be characterized by multiple (7) image moments. Spreadness is a measure of the spatial variance of a color over the image. There are also multiple levels of resolution for texture features. Referring to the Texture Table, there is a an evaluation of the coarse, middle and fine level of feature resolution for each of vertical, diagonal and horizontal textures. In other words, an evaluation is made for each of the thrity-six (36) entries in the Texture Table. Thus, for example, referring to the horizontal-coarse (upper left) block in the Texture Table, an image is evaluated to determine feature values for an average coarse-horizontal energy feature, a coarse-horizontal energy varianc feature, coarse-horizontal elongation feature and a coarse-horizontal spreadness feature. Similarly, for example, referring to the medium-diagonal (center) block in the Texture Table, an image is evaluated to determine feature values for an average medium-diagonal energy feature, a medium-diagonal energy varianc feature, medium-diagonal elongation feature and a medium-diagonal spreadness feature. Multi-Resolution Processing of Color Features As explained in the above sections, the MEGA query-concept learner process can evaluate samples for refinement through term removal in a multi-resolution fashion. It will be appreciated that multi-resolution refinement is an optimization technique that is not essential to the invention. With respect to colors, multi-resolution evaluation can be described in general terms as follows. With respect to removal of disjunctive terms from the QCS, first, there is an evaluation of differences between positive labeled sample images and the QCS with respect to the eleven cultural colors and the one miscellaneous color. During this first phase, only features relating to the presence/absence of these twelve colors are evaluated. Next, there is an evaluation of the differences between positive labeled sample images and the QCS with respect to hue saturation and intensity (HVS). However, during this second phase, HVS features are evaluated relative to the QCS only for those basic coarse color features, out of the original twelve, that are found to be not different from the QCS. For example, if the red feature of a sample image is found to not match the red feature of the QCS, then in the second phase, there is no evaluation of the HVS for the color red. Finally, there is an evaluation of Elongation and Spreadness. However, during this third phase, Elongation and Spreadness features are evaluated relative to the QCS only for those cultural colors that are found to be not different from the QCS. The evaluation of conjunctive color terms of the CCS for removal proceeds in an analogous manner with respect to negative-labeled sample images. Multi-Resolution Processing of Texture Features With respect to textures, multi-resolution evaluation can be described in general terms as follows. It will be appreciated that multi-resolution refinement is an optimization technique that is not essential to the invention. With respect to removal of disjunctive terms from the QCS, first, there is an evaluation of differences between positive labeled sample images and the QCS with respect to the the coarse-horizontal, coarse-diagonal and coarse-vertical features. It will be noted that each of these three comprises a set of four features. During this first phase, only the twelve coarse texture feature are evaluated. Next, there is an evaluation of the differences between positive labeled sample images and the QCS with respect to the meium texture features, medium-horizontal, medium-diagonal and medium-vertical. However, during this second phase, medium texture features are evaluated relative to the QCS only for those basic coarse texture features that are found to be not different from the QCS. For instance, if a sample image's coarse-horizontal average energy is found to not match the corresponding feature in the QCS, then the medium-horizontal average energy is not evaluated. Finally, there is an evaluation of the differences between positive labeled sample images and the QCS with respect to the fine texture features, fine-horizontal, fine-diagonal and fine-vertical. However, during this third phase, fine texture features are evaluated relative to the QCS only for those medium texture features that are found to be not different from the QCS. For instance, if a sample image's medium-diagonal spreadness is found to not match the corresponding feature in the QCS, then the fine-diagonal spreadness is not evaluated. The evaluation of conjunctive texture terms of the CCS for removal proceeds in an analogous manner with respect to negative-labeled sample images. Relationship Between MEGA and SVMactive and SVMDex To make the query-concept learning even more efficient, a high-dimensional access method can be employed [12] to ensure that eliminating/replacing features incurs minimum additional search overhead. Commonly owned provisional patent application Ser. No. 60/292,820, filed May 22, 2001; and also claims the benefit of the filing date of commonly assigned provisional patent application, Ser. No. 60/281,053, filed Apr. 2, 2001, which is expressly incorporated herein by this reference, discloses such an access method. MEGA can speed up its sampling step by using the support vectors generated by SVMs. The commonly owned provisional patent applications which are expressly incorporated above, discloses the use of SVMs. It will be appreciated that SVMactive and SVMDex are not part of the MEGA query-concept learner process per se. However, is intended that the novel learner process disclosed in detail herein will be used in conjunction with SVM and SVMDex. 8 User Interface Examples The following provides an illustrative example of the user interface perspective of the novel query-concept learner process. We present examples in this section to show the learning steps of MEGA and SVMActive in two image query scenarios: image browsing and similarity search. Note that MEGA, and SVMActive are separate processes. In a proposed system, MEGA and SVMActive will be used together. The invention that is the focus of this patent application pertains to MEGA not SVMActive. Thus, SVMActive is not disclosed in detail herein. To learn more about SVMActive, refer to the cited ppapers by Edward Chang.
[FIG. 1: Wild Animal Query Screen #1.] 8.1 MEGA Query Steps In the following, we present an interActive query session using MEGA. This interActive query session involves seven screens that are illustrated in seven figures. The user's query concept in this example is "wild animals." Screen 1. Initial Screen. Our PBIR system presents the initial screen to the user as depicted in FIG. 1. The screen is split into two frames vertically. On the left-hand side of the screen is the learner frame; on the righthand side is the similarity search frame. Through the learner frame, PBIR learns what the user wants via an intelligent sampling process. The similarity search frame displays what the system thinks the user wants. (The user can set the number of images to be displayed in these frames.) Screen 2. Sampling and relevance feedback starts. Once the user clicks the "submit" button in the initial frame, the sampling and relevance feedback step commences to learn what the user wants. The PBIR system presents a number of samples in the learner frame, and the user highlights images that are relevant to his/her query concept by clicking on the relevant images. [FIG. 2: Wild Animal Query Screen #2.] [FIG. 3: Wild Animal Query Screen #3.] [FIG. 4: Wild Animal Query Screen #4.] [FIG. 5: Wild Animal Query Screen #5.] [FIG. 6: Wild Animal Query Screen #6.] [FIG. 7: Wild Animal Similarity Query (Screen #7).] As shown in FIG. 2, three images (the third image in rows one, two and four in the learner frame) are selected as relevant, and the rest of the unmarked images are considered irrelevant. The user indicates the end of his/her selection by clicking on the submit button in the learner screen. This action brings up the next screen. Screen 3. Sampling and relevance feedback continues. FIG. 3 shows the third screen. At this time, the similarity search frame still does not show any image, since the system has not been able to grasp the user's query concept at this point. The PBIR system again presents samples in the learner frame to solicit feedback. The user selects the second image in the third row as the only image relevant to the query concept. Screen 4. Sampling and relevance feedback continues. FIG. 4 shows the fourth screen. First, the similarity search frame displays what the PBIR system thinks will match the user's query concept at this time. As the figure indicates, the top nine returned images fit the concept of "wild animals." The user's query concept has been captured, though somewhat fuzzily. The user can ask the system to further refine the target concept by selecting relevant images in the learner frame. In this example, the fourth image in the second row and the third image in the fourth row are selected as relevant to the concept. After the user clicks on the submit button in the learner frame, the fifth screen is displayed. Screen 5. Sampling and relevance feedback continues. The similarity search frame in FIG. 5 shows that ten out of the top twelve images returned match the "wild animals" concept. The user selects four relevant images displayed in the learner frame. This leads to the final screen of this learning series. Screen 6. Sampling and relevance feedback ends. FIG. 6 shows that all returned images in the similarity search frames fit the query concept. Screen 7. Similarity search. At any time, the user can click on an image in the similarity search frame to request images that appear similar to the selected image. This step allows the user to zoom in onto a specific set of images that match some appearance criteria, such as color distribution, textures and shapes. As shown in FIG. 7, after clicking on one of the tiger images, the user will find similar tiger images returned in the similarity search frame. Notice that other wild animals are ranked lower than the matching tiger images, since the user has concentrated more on specific appearances than on general concepts. In summary, in this example we show that our PBIR system effeActively uses MEGA to learn a query concept. The images that match a concept do not have to appear similar in their low-level feature space. The learner is able to match high-level concepts to low-level features directly through an intelligent learning process. Our PBIR system can capture images that match a concept through MEGA or SVMActive, whereas the traditional image systems can do only appearance similarity searches. Again, as illustrated by this example, MEGA can capture the query concept of wild animal (wild animals can be elephants, tigers, bears, and etc), but a traditional similarity search engine can at best select only animals that appear similar. In Appendix, we attach the color screen dumps of the above "wild animals" query. In addition, we attach the five query examples for five concepts: architectures, fireworks, flowers, food, and people. These examples show that the PBIR system can fuzzily capture a concept usually in two to three feedback iterations and can comprehend a target concept very well in three to five iterations. 8.2 SVMActive Sample Results [FIG. 8: Flowers and Tigers Sample Query Results from SVMActive] Finally, FIG. 8 shows two sample results of using SVMActive one from a top-10 flowers query, and one from a top-10 tigers query. The returned images do not necessarily have the same lowlevel features or appearance. The returned flowers have colors of red, purple, white, and yellow, with or without leaves. The returned tiger images have tigers of different postures on different backgrounds. 8.3 Experiments In this section, we report our experimental results. The goals of our experiments were 1: To evaluate whether MEGA can learn k-CNF concepts accurately in the presence of a large number of irrelevant features. 2: To evaluate whether MEGA can converge to a target concept faster than traditional sampling schemes. 3: To evaluate whether MEGA is robust for noisy data or under situations in which the unknown target concept is not expressible in the provided hypothesis space. We assume all target concepts are in 3-CNF. To conduct our experiments, we used both synthesized data and real-world data.
We used precision and recall to measure performance. We tallied precision/recall for up to only 10 iterations, since we deemed it unrealistic to expect an interactive user to conduct more than 10 rounds of relevance feedback. We compared MEGA with the five sampling schemes: random, bounded random, nearest neighbor, query expansion, and aggressive. We used these sampling schemes for comparison because they are employed by some state-of-the-art systems described in Section 5. FIG. 4: Sampling Schemes FIG. 4 shows how some of these sampling algorithms work. The main features of the sampling schemes are given below.
We ran experiments on datasets of different distributions and repeated each experiment 10 times. The experimental results are presented in two groups. We first show the results of the experiments on the synthesized datasets. We then show the results on a 1,500-image dataset. 8.4 Query Concept Learning Applied to Synthesized Datasets We tested many target concepts on the two synthesized datasets. Due to space limitations, we present only three representative test cases, those that represent a disjunctive concept, a conjunctive of disjunctions, and a complex concept with more terms. The three tests are 1: P1 2: (P1 3: P1 We first assume that the dataset is free of user errors and set the sample size Kα to 20. In the remainder of this section, we report our initial results, and then we report the effects of model bias and user errors on MEGA (Sections 4.2.1 and 4.2.2). 8.4.1 Experimental Results FIG. 5: Precision vs. Recall (10 Features) FIG. 5 presents the precision/recall after three user iterations of the six sampling schemes learning the two concepts, (P1 Next, we were interested in learning the improvement on search accuracy with respect to the number of user iterations. This improvement trend can tell us how fast a scheme can learn a target concept. We present a set of tables and charts where we fix recall at 0.5 and examine the improvement in precision with respect to the number of iterations.
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