17434758
An Empirical Study of the Noise Impact on Cost-Sensitive Learning
In this paper, we perform an empirical study of the impact of noise on cost-sensitive (CS) learning, through observations on how a CS learner reacts to the mislabeled training examples in terms of misclassification cost and classification accuracy. Our empirical results and theoretical analysis indicate that mislabeled training examples can raise serious concerns for cost-sensitive classification, especially when misclassifying some classes becomes extremely expensive. Compared to general inductive learning, the problem of noise handling and data cleansing is more crucial, and should be carefully investigated to ensure the success of CS learning.
11232317
Cost-constrained data acquisition for intelligent data preparation
Real-world data is noisy and can often suffer from corruptions or incomplete values that may impact the models created from the data. To build accurate predictive models, data acquisition is usually adopted to prepare the data and complete missing values. However, due to the significant cost of doing so and the inherent correlations in the data set, acquiring correct information for all instances is prohibitive and unnecessary. An interesting and important problem that arises here is to select what kinds of instances to complete so the model built from the processed data can receive the "maximum" performance improvement. This problem is complicated by the reality that the costs associated with the attributes are different, and fixing the missing values of some attributes is inherently more expensive than others. Therefore, the problem becomes that given a fixed budget, what kinds of instances should be selected for preparation, so that the learner built from the processed data set can maximize its performance? In this paper, we propose a solution for this problem, and the essential idea is to combine attribute costs and the relevance of each attribute to the target concept, so that the data acquisition can pay more attention to those attributes that are cheap in price but informative for classification. To this end, we will first introduce a unique economical factor (EF) that seamlessly integrates the cost and the importance (in terms of classification) of each attribute. Then, we will propose a cost-constrained data acquisition model, where active learning, missing value prediction, and impact-sensitive instance ranking are combined for effective data acquisition. Experimental results and comparative studies from real-world data sets demonstrate the effectiveness of our method.
5621999
Accelerated Kernel Feature Analysis
A fast algorithm, Accelerated Kernel Feature Analysis (AKFA), that discovers salient features evidenced in a sample of n unclassified patterns, is presented. Like earlier kernel-based feature selection algorithms, AKFA implicitly embeds each pattern into a Hilbert space, H, induced by a Mercer kernel. An \ell-dimensional linear subspace of H is iteratively constructed by maximizing a variance condition for the nonlinearly transformed sample. This linear subspace can then be used to define more efficient data representations and pattern classifiers. AKFA requires O(\elln2) operations, as compared to 0(n^3) for Sch¨olkof, Smola, and M¨uller’s Kernel Principal Component Analysis (KPCA), and O(\ell^2 n^2) for Smola, Mangasarian, and Sch¨olkopf’s Sparse Kernel Feature Analysis (SKFA). Numerical experiments show that AKFA can generate more concise feature representations than both KPCA and SKFA, and demonstrate that AKFA obtains similar classification performance as KPCA for a face recognition problem.
1977839
Effective classification of noisy data streams with attribute-oriented dynamic classifier selection
Recently, mining from data streams has become an important and challenging task for many real-world applications such as credit card fraud protection and sensor networking. One popular solution is to separate stream data into chunks, learn a base classifier from each chunk, and then integrate all base classifiers for effective classification. In this paper, we propose a new dynamic classifier selection (DCS) mechanism to integrate base classifiers for effective mining from data streams. The proposed algorithm dynamically selects a single “best” classifier to classify each test instance at run time. Our scheme uses statistical information from attribute values, and uses each attribute to partition the evaluation set into disjoint subsets, followed by a procedure that evaluates the classification accuracy of each base classifier on these subsets. Given a test instance, its attribute values determine the subsets that the similar instances in the evaluation set have constructed, and the classifier with the highest classification accuracy on those subsets is selected to classify the test instance. Experimental results and comparative studies demonstrate the efficiency and efficacy of our method. Such a DCS scheme appears to be promising in mining data streams with dramatic concept drifting or with a significant amount of noise, where the base classifiers are likely conflictive or have low confidence.
15136742
Mining Complex Patterns across Sequences with Gap Requirements
The recurring appearance of sequential patterns, when confined by the predefined gap requirements, often implies strong temporal correlations or trends among pattern elements. In this paper, we study the problem of mining a set of gap constrained sequential patterns across multiple sequences. Given a set of sequences S1, S2,., SK constituting a single hypersequence S, we aim to find recurring patterns in S, say P, which may cross multiple sequences with all their matching characters in S bounded by the user specified gap constraints. Because of the combinatorial candidate explosion, traditional Apriori-based algorithms are computationally infeasible. Our research proposes a new mechanism to ensure pattern growing and pruning. When combining the pruning technique with our Gap Constrained Search (GCS) and map-based support prediction approaches, our method achieves a speed about 40 times faster than its other peers.
14899560
Dealing with Predictive-but-Unpredictable Attributes in Noisy Data Sources
Attribute noise can affect classification learning. Previous work in handling attribute noise has focused on those predictable attributes that can be predicted by the class and other attributes. However, attributes can often be predictive but unpredictable. Being predictive, they are essential to classification learning and it is important to handle their noise. Being unpredictable, they require strategies different from those of predictable attributes. This paper presents a study on identifying, cleansing and measuring noise for predictive-but-unpredictable attributes. New strategies are accordingly proposed. Both theoretical analysis and empirical evidence suggest that these strategies are more effective and more efficient than previous alternatives.
29079880
Graphs of Large Girth with Prescribed Partial Circular Colourings
Abstract.This paper completes the constructive proof of the following result: Suppose p/q≥2 is a rational number, A is a finite set and f1,f2,···,fn are mappings from A to {0,1,···,p−1}. Then for any integer g, there is a graph G=(V,E) of girth at least g with such that G has exactly n (p,q)-colourings (up to equivalence) g1,g2,···,gn, and each gi is an extension of fi. A probabilistic proof of this result was given in [8]. A constructive proof of the case p/q≥3 was given in [7].
12655450
The circular chromatic index of graphs of high girth
We show that for each @e>0 and each integer @D>=1, there exists a number g such that for any graph G of maximum degree @D and girth at least g, the circular chromatic index of G is at most @[email protected]
7791840
Pseudo-Hamiltonian-connected graphs
Abstract Given a graph G and a positive integer k , denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k . A graph G is called pseudo- k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo- k Hamiltonian-connected for some positive integer k . This paper proves that a graph G is pseudo-Hamiltonian-connected if and only if for every non-empty proper subset X of V(G) , |N(X)|>|X| . The proof of the characterization also provides a polynomial-time algorithm that decides whether or not a given graph is pseudo-Hamiltonian-connected. The characterization of pseudo-Hamiltonian-connected graphs also answers a question of Richard Nowakowski, which motivated this paper.
1052837
Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions
An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning problem is then formulated in terms of a Gaussian random field on this graph, where the mean of the field is characterized in terms of harmonic functions, and is efficiently obtained using matrix methods or belief propagation. The resulting learning algorithms have intimate connections with random walks, electric networks, and spectral graph theory. We discuss methods to incorporate class priors and the predictions of classifiers obtained by supervised learning. We also propose a method of parameter learning by entropy minimization, and show the algorithm's ability to perform feature selection. Promising experimental results are presented for synthetic data, digit classification, and text classification tasks.
14278266
Harmonic mixtures: combining mixture models and graph-based methods for inductive and scalable semi-supervised learning
Graph-based methods for semi-supervised learning have recently been shown to be promising for combining labeled and unlabeled data in classification problems. However, inference for graph-based methods often does not scale well to very large data sets, since it requires inversion of a large matrix or solution of a large linear program. Moreover, such approaches are inherently transductive, giving predictions for only those points in the unlabeled set, and not for an arbitrary test point. In this paper a new approach is presented that preserves the strengths of graph-based semi-supervised learning while overcoming the limitations of scalability and non-inductive inference, through a combination of generative mixture models and discriminative regularization using the graph Laplacian. Experimental results show that this approach preserves the accuracy of purely graph-based transductive methods when the data has "manifold structure," and at the same time achieves inductive learning with significantly reduced computational cost.