Domain adaptation (DA) algorithms address the problem of distribution shift between training and testing data. Recent approaches transform data into a shared subspace by minimizing the shift between their marginal distributions. We propose a method to learn a common subspace that will leverage the class conditional distributions of training samples along with reducing the marginal distribution shift. To learn the subspace, we employ a supervised technique based on non-parametric mutual information by inducing soft label assignment for the unlabeled test data. The approach presents an iterative linear transformation for subspace learning by repeatedly updating test data predictions via soft-labeling and consequently improving the subspace with maximization of mutual information. A set of comprehensive experiments on benchmark datasets is conducted to prove the efficacy of our novel framework over state-of-the-art approaches.

Domain adaptation (DA) algorithms utilize a label-rich old dataset (domain) to build a machine learning model (classification, detection etc.) in a label-scarce new dataset with different data distribution. Recent approaches transform cross-domain data into a shared subspace by minimizing the shift between their marginal distributions. In this paper, we propose a novel iterative method to learn a common subspace based on non-parametric quadratic mutual information (QMI) between data and corresponding class labels. We extend a prior work of discriminative subspace learning based on maximization of QMI and integrate instance weighting into the QMI formulation. We propose an adaptive weighting model to identify relevant samples that share underlying similarity across domains and ignore irrelevant ones. Due to difficulty of applying cross-validation, an alternative strategy is integrated with the proposed algorithm to setup model parameters. A set of comprehensive experiments on benchmark datasets is conducted to prove the efficacy of our proposed framework over state-of-the-art approaches.

This paper introduces an extension to consensus clustering that allows a feedback of the results of the consensus to the original clustering processes. The original clustering processes may use this information to update their partitioning of the data. An exponential weighting approach, called lambda consensus, is presented as a method to merged the consensus information into graph based and vector space based clustering algorithms. Successful consensus clustering is highly dependent on the quality and diversity of the partitions in the ensemble. The feedback signal allows the clustering processes to adapt their algorithms to attempt to improve quality and diversity of the set of partitions in the ensemble. Communication requirements are on the same order as consensus clustering as only the consensus labels are returned to the clustering processes. The method is evaluated on real world data sets.

This paper introduces an algorithm for determining data clusters called TILO/PRC (Topologically Intrinsic Lexicographic Ordering/Pinch Ratio Clustering). The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise. The TILO portion of the algorithm progressively improves a linear ordering of the points in a data set until the ordering satisfies a topological condition called strongly irreducible. The PRC algorithm then divides the data set based on this ordering and a heuristic metric called the pinch ratio. We demonstrate the effectiveness of TILO/PRC for finding clusters in a wide variety of real and synthetic data sets and compare the results to existing clustering methods. Moreover, because the output of TILO depends on the initial ordering, we consider the effects of different random orderings on the final clusters defined by PRC, and show that choosing an initial ordering based on a different clustering algorithm can improve the final clusters. These results verify that both the theoretical foundations of TILO and the heuristic notion of pinch ratio are reasonable.

Nearest neighbor classification assumes locally constant class conditional probabilities. This assumption becomes invalid in high dimensions due to the curse-of-dimensionality. Severe bias can be introduced under these conditions when using the nearest neighbor rule. We propose an adaptive nearest neighbor classification method to try to minimize bias. We use quasiconformal transformed kernels to compute neighborhoods over which the class probabilities tend to be more homogeneous. As a result, better classification performance can be expected. The efficacy of our method is validated and compared against other competing techniques using a variety of data sets.

Relevance feedback is an attractive approach to developing flexible metrics for content-based retrieval in image and video databases. Large image databases require an index structure in order to reduce nearest neighbor computation. However, flexible metrics can alter an input space in a highly nonlinear fashion, thereby rendering the index structure useless. Few systems have been developed that address the apparent flexible metric/indexing dilemma. This paper proposes kernel indexing to try to address this dilemma. The key observation is that kernel metrics may be nonlinear and highly dynamic in the input space but remain Euclidean in induced feature space. It is this linear invariance in feature space that enables us to learn arbitrary relevance functions without changing the index in feature space. As a result, kernel indexing supports efficient relevance feedback retrieval in large image databases. Experimental results using a large set of image data are very promising.

Nearest neighbor (NN) classification relies on the assumption that class conditional probabilities are locally constant. This assumption becomes false in high dimensions with finite samples due to the curse of dimensionality. The NN rule introduces severe bias under these conditions. We propose a locally adaptive neighborhood morphing classification method to try to minimize bias. We use local support vector machine learning to estimate an effective metric for producing neighborhoods that are elongated along less discriminant feature dimensions and constricted along most discriminant ones. As a result, the class conditional probabilities can be expected to be approximately constant in the modified neighborhoods, whereby better classification performance can be achieved. The efficacy of our method is validated and compared against other competing techniques using a number of datasets.

The paper presents a novel approach to ranking relevant images for retrieval. Distance in the feature space associated with a kernel is used to rank relevant images. An adaptive quasiconformal mapping based on relevance feedback is used to generate successive new kernels. The effect of the quasiconformal mapping is a change in the spatial resolution of the feature space. The spatial resolution around irrelevant samples is dilated, whereas the spatial resolution around relevant samples is contracted. This new space created by the quasiconformal kernel is used to measure the distance between the query and the images in the database. An interesting interpretation of the metric is found by looking at the Taylor series approximation to the original kernel. Then the squared distance in the feature space can be seen as a combination of a parzen window estimate of the squared Chi-squared distance and a weighted squared Euclidean distance. Experimental results using real-world data validate the efficacy of our method.

Nearest neighbor classification relies on the assumption that class conditional probabilities are locally constant. This assumption becomes false in high dimensions with finite samples due to the curse of dimensionality. The nearest neighbor rule introduces severe bias under these conditions. We propose a locally adaptive neighborhood morphing classification method to try to minimize bias. We use local support vector machine teaming to estimate an effective metric for producing neighborhoods that are elongated along less discriminant feature dimensions and constricted along most discriminant ones. As a result, the class conditional probabilities can be expected to be approximately constant in the modified neighborhoods, whereby better classification performance can be achieved. The efficacy of our method is validated and compared against other competing techniques using a number of data sets.

Probabilistic feature relevance learning (PFRL) is an effective technique for adaptively computing local feature relevance for content-based image retrieval. It however becomes less attractive in situations where all the input variables have the same local relevance, and yet retrieval performance might still be improved by simple query shifting. We propose a retrieval method that combines feature relevance learning and query shifting to try to achieve the best of both worlds. We use a linear discriminant analysis to compute the new query and exploit the local neighborhood structure centered at the new query by invoking PFRL. As a result, the modified neighborhoods at the new query tend to contain sample images that are more relevant to the input query. The efficacy of our method is validated using both synthetic and real world data.

Parallax displacement is used to determine a relative 3D conic projective structure. This value is invariant between any number of views in time if the conic is not moving with respect to the plane of the homography. It can be used to determine conic correspondence between three simultaneous views. The corresponding conics may then be used to determine the epipolar geometry. This method of determining conic correspondence works with unknown and even changing epipolar geometry. The relative 3D conic projective structure may be used to segment groups of conics which have consistent motion.

We define a distance measure between 3D polygonal arcs of equal length, and show that the minimum value of this distance measure is the smallest eigenvalue of a certain matrix. Using this, we develop a mismatch measure and a matching algorithm for 3D polygonal arcs of unequal lengths.

This paper presents mutual invariants of families of coplanar conics. These invariants are compared with the use for invariants of two conics and a case is presented where the proposed invariants have a greater discriminating power than the previously used invariants. The use of invariants is extended to any number of coplanar conics. A lambda-matrix is associated with each family of coplanar conics. The use of lambda-matrices is extended from the single-variable polynomial to multivariable polynomials. The Segre characteristic and other invariants of the lambda-matrix are used as invariants of the family of conics.

We show that the minimum value of a distance measure between 3-D polygonal arcs of equal length is the smallest eigenvalue of a certain matrix. Using this we develop a mismatch measure and a matching algorithm for 3-D polygonal arcs of unequal lengths.