7092740
Representing Conditional Independence Using Decision Trees
While the representation of decision trees is fully expressive theoretically, it has been observed that traditional decision trees has the replication problem. This problem makes decision trees to be large and learnable only when sufficient training data are available. In this paper, we present a new representation model, conditional independence trees (CITrees), to tackle the replication problem from probability perspective. We propose a novel algorithm for learning CITrees. Our experiments show that CITrees outperform naive Bayes (Langley, Iba, & Thomas 1992), C4.5 (Quinlan 1993), TAN (Friedman, Geiger, & Goldszmidt 1997), and AODE (Webb, Boughton, & Wang 2005) significantly in classification accuracy.
139220
Representational Upper Bounds of Bayesian Networks
One of the fundamental issues of Bayesian networks is their representational power, re-ecting what kind of functions they can or cannot represent. In this paper, we rst prove an upper bound on the representational power of Augmented Naive Bayes. We then extend the result to general Bayesian networks. Roughly speaking, if a function contains an m-XOR, there exists no Bayesian networks with node having at most m ? 1 parents to represent it.
1779699
Hidden Naive Bayes
The conditional independence assumption of naive Bayes essentially ignores attribute dependencies and is often violated. On the other hand, although a Bayesian network can represent arbitrary attribute dependencies, learning an optimal Bayesian network from data is intractable. The main reason is that learning the optimal structure of a Bayesian network is extremely time consuming. Thus, a Bayesian model without structure learning is desirable. In this paper, we propose a novel model, called hidden naive Bayes (HNB). In an HNB, a hidden parent is created for each attribute which combines the influences from all other attributes. We present an approach to creating hidden parents using the average of weighted one-dependence estimators. HNB inherits the structural simplicity of naive Bayes and can be easily learned without structure learning. We propose an algorithm for learning HNB based on conditional mutual information. We experimentally test HNB in terms of classification accuracy, using the 36 UCI data sets recommended by Weka (Witten & Frank 2000), and compare it to naive Bayes (Langley, Iba, & Thomas 1992), C4.5 (Quinlan 1993), SBC (Langley & Sage 1994), NBTree (Kohavi 1996), CL-TAN (Friedman, Geiger, & Goldszmidt 1997), and AODE (Webb, Boughton, & Wang 2005). The experimental results show that HNB outperforms naive Bayes, C4.5, SBC, NBTree, and CL-TAN, and is competitive with AODE.
2843129
Full Bayesian network classifiers
The structure of a Bayesian network (BN) encodes variable independence. Learning the structure of a BN, however, is typically of high computational complexity. In this paper, we explore and represent variable independence in learning conditional probability tables (CPTs), instead of in learning structure. A full Bayesian network is used as the structure and a decision tree is learned for each CPT. The resulting model is called full Bayesian network classifiers (FBCs). In learning an FBC, learning the decision trees for CPTs captures essentially both variable independence and context-specific independence. We present a novel, efficient decision tree learning, which is also effective in the context of FBC learning. In our experiments, the FBC learning algorithm demonstrates better performance in both classification and ranking compared with other state-of-the-art learning algorithms. In addition, its reduced effort on structure learning makes its time complexity quite low as well.
2128098
A Fast Decision Tree Learning Algorithm
There is growing interest in scaling up the widely-used decision-tree learning algorithms to very large data sets. Although numerous diverse techniques have been proposed, a fast tree-growing algorithm without substantial decrease in accuracy and substantial increase in space complexity is essential. In this paper, we present a novel, fast decision-tree learning algorithm that is based on a conditional independence assumption. The new algorithm has a time complexity of O(m ċ n), where m is the size of the training data and n is the number of attributes. This is a significant asymptotic improvement over the time complexity O(m ċ n2) of the standard decision-tree learning algorithm C4.5, with an additional space increase of only O(n). Experiments show that our algorithm performs competitively with C4.5 in accuracy on a large number of UCI benchmark data sets, and performs even better and significantly faster than C4.5 on a large number of text classification data sets. The time complexity of our algorithm is as low as naive Bayes'. Indeed, it is as fast as naive Bayes but outperforms naive Bayes in accuracy according to our experiments. Our algorithm is a core tree-growing algorithm that can be combined with other scaling-up techniques to achieve further speedup.
7586705
The Representational Power of Discrete Bayesian Networks
One of the most important fundamental properties of Bayesian networks is the representational power, reflecting what kind of functions they can or cannot represent. In this paper, we establish an association between the structural complexity of Bayesian networks and their representational power. We use the maximum number of nodes' parents as the measure for the structural complexity of Bayesian networks, and the maximum XOR contained in a target function as the measure for the function complexity. A representational upper bound is established and proved. Roughly speaking, discrete Bayesian networks with each node having at most k parents cannot represent any function containing (k+1)-XORs. Our theoretical results help us to gain a deeper understanding on the capacities and limitations of Bayesian networks.
2426049
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions
4541399
Discriminant analysis with tensor representation
In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a discriminant tensor criterion (DTC), whereby multiple interrelated lower-dimensional discriminative subspaces are derived for feature selection. Then, a novel approach called k-mode cluster-based discriminant analysis is presented to iteratively learn these subspaces by unfolding the tensor along different tensor dimensions. We call this algorithm discriminant analysis with tensor representation (DATER), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes; 2) for classification problems involving higher-order tensors, the DATER algorithm can avoid the curse of dimensionality dilemma and overcome the small sample size problem; and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based on higher order tensors has the potential to outperform the traditional subspace learning algorithms, especially in the small sample size cases.
11721850
Estimating LOC for information systems from their conceptual data models
Effort and cost estimation is crucial in software management. Estimation of software size plays a key role in the estimation. Line of Code (LOC) is still a commonly used software size measure. Despite the fact that software sizing is well recognized as an important problem for more than two decades, there is still much problem in existing methods. Conceptual data model is widely used in the requirements analysis for information systems. It is also not difficult to construct conceptual data models in the early stage of developing information systems. Much characteristic of an information system is actually reflected from its conceptual data model. We explore into the use of conceptual data model for estimating LOC. This paper proposes a novel method for estimating LOC for an information system from its conceptual data model through the use of multiple linear regression model. We have validated the method through collecting samples from both the industry and open-source systems.
10720283
Discriminant Analysis on Embedded Manifold
Previous manifold learning algorithms mainly focus on uncovering the low dimensional geometry structure from a set of samples that lie on or nearly on a manifold in an unsupervised manner. However, the representations from unsupervised learning are not always optimal in discriminating capability. In this paper, a novel algorithm is introduced to conduct discriminant analysis in term of the embedded manifold structure. We propose a novel clustering algorithm, called Intra-Cluster Balanced K-Means (ICBKM), which ensures that there are balanced samples for the classes in a cluster; and the local discriminative features for all clusters are simultaneously calculated by following the global Fisher criterion. Compared to the traditional linear/kernel discriminant analysis algorithms, ours has the following characteristics: 1) it is approximately a locally linear yet globally nonlinear discriminant analyzer; 2) it can be considered a special Kernel-DA with geometry-adaptive-kernel, in contrast to traditional KDA whose kernel is independent to the samples; and 3) its computation and memory cost are reduced a great deal compared to traditional KDA, especially for the cases with large number of samples. It does not need to store the original samples for computing the low dimensional representation for new data. The evaluation on toy problem shows that it is effective in deriving discriminative representations for the problem with nonlinear classification hyperplane. When applied to the face recognition problem, it is shown that, compared with LDA and traditional KDA on YALE and PIE databases, the proposed algorithm significantly outperforms LDA and
6600637
Localized Content-Based Image Retrieval
We define localized content-based image retrieval as a CBIR task where the user is only interested in a portion of the image, and the rest of the image is irrelevant. In this paper we present a localized CBIR system, ACCIO, that uses labeled images in conjunction with a multiple-instance learning algorithm to first identify the desired object and weight the features accordingly, and then to rank images in the database using a similarity measure that is based upon only the relevant portions of the image. A challenge for localized CBIR is how to represent the image to capture the content. We present and compare two novel image representations, which extend traditional segmentation-based and salient point-based techniques respectively, to capture content in a localized CBIR setting.