text: In the past decades, feature-learning-based 3D shape retrieval approaches have been received widespread attention in the computer graphic community. These approaches usually explored the hand-crafted distance metric or conventional distance metric learning methods to compute the similarity of the single feature. The single feature always contains onefold geometric information, which cannot characterize the 3D shapes well. Therefore, the multiple features should be used for the retrieval task to overcome the limitation of single feature and further improve the performance. However, most conventional distance metric learning methods fail to integrate the complementary information from multiple features to construct the distance metric. To address these issue, a novel multi-feature distance metric learning method for non-rigid 3D shape retrieval is presented in this study, which can make full use of the complimentary geometric information from multiple shape features by utilizing the KL-divergences. Minimizing KL-divergence between different metric of features and a common metric is a consistency constraints, which can lead the consistency shared latent feature space of the multiple features. We apply the proposed method to 3D model retrieval, and test our method on well known benchmark database. The results show that our method substantially outperforms the state-of-the-art non-rigid 3D shape retrieval methods.
  @cite_18: Along with the arrival of multimedia time, multimedia data has replaced textual data to transfer information in various fields. As an important form of multimedia data, images have been widely utilized by many applications, such as face recognition and image classification. Therefore, how to accurately annotate each image from a large set of images is of vital importance but challenging. To perform these tasks well, it is crucial to extract suitable features to character the visual contents of images and learn an appropriate distance metric to measure similarities between all images. Unfortunately, existing feature operators, such as histogram of gradient, local binary pattern, and color histogram, care more about the visual character of images and lack the ability to distinguish semantic information. Similarities between those features cannot reflect the real category correlations due to the well-known semantic gap. In order to solve this problem, this paper proposes a regularized distance metric framework called semantic discriminative metric learning (SDML). SDML combines geometric mean with normalized divergences and separates images from different classes simultaneously. The learned distance metric can treat all images from different classes equally. And distinctions between similar classes with entirely different semantic contents are emphasized by SDML. This procedure ensures the consistency between dissimilarities and semantic distinctions and avoids inaccuracy similarities incurred by unbalanced locations of samples. Various experiments on benchmark image datasets show the excellent performance of the novel method.
  @cite_33: The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner.
  @cite_7: 
  @cite_21: Abstract Principal component analysis of a data matrix extracts the dominant patterns in the matrix in terms of a complementary set of score and loading plots. It is the responsibility of the data analyst to formulate the scientific issue at hand in terms of PC projections, PLS regressions, etc. Ask yourself, or the investigator, why the data matrix was collected, and for what purpose the experiments and measurements were made. Specify before the analysis what kinds of patterns you would expect and what you would find exciting. The results of the analysis depend on the scaling of the matrix, which therefore must be specified. Variance scaling, where each variable is scaled to unit variance, can be recommended for general use, provided that almost constant variables are left unscaled. Combining different types of variables warrants blockscaling. In the initial analysis, look for outliers and strong groupings in the plots, indicating that the data matrix perhaps should be “polished” or whether disjoint modeling is the proper course. For plotting purposes, two or three principal components are usually sufficient, but for modeling purposes the number of significant components should be properly determined, e.g. by cross-validation. Use the resulting principal components to guide your continued investigation or chemical experimentation, not as an end in itself.
  @cite_6: 
  @cite_44: In this letter we discuss a least squares version for support vector machine (SVM) classifiers. Due to equality type constraints in the formulation, the solution follows from solving a set of linear equations, instead of quadratic programming for classical SVM‘s. The approach is illustrated on a two-spiral benchmark classification problem.
  @cite_5: 
  @cite_31: Distance metric learning (DML) is an important technique to improve similarity search in content-based image retrieval. Despite being studied extensively, most existing DML approaches typically adopt a single-modal learning framework that learns the distance metric on either a single feature type or a combined feature space where multiple types of features are simply concatenated. Such single-modal DML methods suffer from some critical limitations: (i) some type of features may significantly dominate the others in the DML task due to diverse feature representations; and (ii) learning a distance metric on the combined high-dimensional feature space can be extremely time-consuming using the naive feature concatenation approach. To address these limitations, in this paper, we investigate a novel scheme of online multi-modal distance metric learning (OMDML), which explores a unified two-level online learning scheme: (i) it learns to optimize a distance metric on each individual feature space; and (ii) then it learns to find the optimal combination of diverse types of features. To further reduce the expensive cost of DML on high-dimensional feature space, we propose a low-rank OMDML algorithm which not only significantly reduces the computational cost but also retains highly competing or even better learning accuracy. We conduct extensive experiments to evaluate the performance of the proposed algorithms for multi-modal image retrieval, in which encouraging results validate the effectiveness of the proposed technique.
summary: Appropriate similarities between samples can improve the performances of the retrieval system. During the past decade, several well-known distance metric learning methods are proposed for various fields @cite_5 @cite_33 @cite_44 @cite_21 @cite_6 @cite_18 , such as ITML @cite_5 , LMNN @cite_33 , SVMs @cite_44 , PCA @cite_21 , LDA @cite_6 , etc. These algorithms have been used for many computer vision and computer graphic tasks, such as classification, retrieval, correspondence, etc. These algorithms solve the problem that most features lie in a complex high-dimensional spaces where Euclidean metric is ineffective. However, most distance metric learning methods fail to integrate compatible and complementary information from multiple features to construct a distance metric. In order to explore more useful information for various applications, many researchers invest many methods to combine multi-view setting to distance metric learning algorithm. Kan @cite_7 proposed a multi-view discriminant analysis as an extension of LDA, which has achieved excellent performances facing with multi-view features. Wu @cite_31 proposed an online multi-modal distance metric learning which has been successfully applied in image retrieval.