Multi-instance learning deals with problems that treat bags of instances as training examples. In single-instance learning problems, dimensionality reduction is an essential step for high-dimensional data analysis and has been studied for years. The curse of dimensionality also exists in multiinstance learning tasks, yet this difficult task has not been studied before. Direct application of existing single-instance dimensionality reduction objectives to multi-instance learning tasks may not work well since it ignores the characteristic of multi-instance learning that the labels of bags are known while the labels of instances are unknown. In this paper, we propose an effective model and develop an efficient algorithm to solve the multi-instance dimensionality reduction problem. We formulate the objective as an optimization problem by considering orthonormality and sparsity constraints in the projection matrix for dimensionality reduction, and then solve it by the gradient descent along the tangent space of the orthonormal matrices. We also propose an approximation for improving the efficiency. Experimental results validate the effectiveness of the proposed method.

In this paper, we present a constrained co-clustering approach for clustering textual documents. Our approach combines the benefits of information-theoretic co-clustering and constrained clustering. We use a two-sided hidden Markov random field (HMRF) to model both the document and word constraints. We also develop an alternating expectation maximization (EM) algorithm to optimize the constrained co-clustering model. We have conducted two sets of experiments on a benchmark data set: (1) using human-provided category labels to derive document and word constraints for semi-supervised document clustering, and (2) using automatically extracted named entities to derive document constraints for unsupervised document clustering. Compared to several representative constrained clustering and co-clustering approaches, our approach is shown to be more effective for high-dimensional, sparse text data.

Matrix factorization is a fundamental technique in machine learning that is applicable to collaborative filtering, information retrieval and many other areas. In collaborative filtering and many other tasks, the objective is to fill in missing elements of a sparse data matrix. One of the biggest challenges in this case is filling in a column or row of the matrix with very few observations. In this paper we introduce a Bayesian matrix factorization model that performs regression against side information known about the data in addition to the observations. The side information helps by adding observed entries to the factored matrices. We also introduce a nonparametric mixture model for the prior of the rows and columns of the factored matrices that gives a different regularization for each latent class. Besides providing a richer prior, the posterior distribution of mixture assignments reveals the latent classes. Using Gibbs sampling for inference, we apply our model to the Netflix Prize problem of predicting movie ratings given an incomplete user-movie ratings matrix. Incorporating rating information with gathered metadata information, our Bayesian approach outperforms other matrix factorization techniques even when using fewer dimensions.

Multi-instance learning, as other machine learning tasks, also suffers from the curse of dimensionality. Although dimensionality reduction methods have been investigated for many years, multi-instance dimensionality reduction methods remain untouched. On the other hand, most algorithms in multi- instance framework treat instances in each bag as independently and identically distributed samples, which fails to utilize the structure information conveyed by instances in a bag. In this paper, we propose a multi-instance dimensionality reduction method, which treats instances in each bag as non-i.i.d. samples. We regard every bag as a whole entity and define a bag margin objective function. By maximizing the margin of positive and negative bags, we learn a subspace to obtain more salient representation of original data. Experiments demonstrate the effectiveness of the proposed method.

This paper presents the Topic-Aspect Model (TAM), a Bayesian mixture model which jointly discovers topics and aspects. We broadly define an aspect of a document as a characteristic that spans the document, such as an underlying theme or perspective. Unlike previous models which cluster words by topic or aspect, our model can generate token assignments in both of these dimensions, rather than assuming words come from only one of two orthogonal models. We present two applications of the model. First, we model a corpus of computational linguistics abstracts, and find that the scientific topics identified in the data tend to include both a computational aspect and a linguistic aspect. For example, the computational aspect of GRAMMAR emphasizes parsing, whereas the linguistic aspect focuses on formal languages. Secondly, we show that the model can capture different viewpoints on a variety of topics in a corpus of editorials about the Israeli-Palestinian conflict. We show both qualitative and quantitative improvements in TAM over two other state-of-the-art topic models.

Non-metric distances are often more reasonable compared with metric ones in terms of consistency with human perceptions. However, existing locality-sensitive hashing (LSH) algorithms can only support data which are gauged with metrics. In this paper we propose a novel locality-sensitive hashing algorithm targeting such non-metric data. Data in original feature space are embedded into an implicit reproducing kernel Krein space and then hashed to obtain binary bits. Here we utilize the norm-keeping property of p-stable functions to ensure that two data's collision probability reflects their non-metric distance in original feature space. We investigate various concrete examples to validate the proposed algorithm. Extensive empirical evaluations well illustrate its effectiveness in terms of accuracy and retrieval speedup.

Dimensionality reduction plays an important role in many machine learning and pattern recognition tasks. In this paper, we present a novel dimensionality reduction algorithm called multilinear maximum distance embedding (M2DE), which includes three key components. To preserve the local geometry and discriminant information in the embedded space, M2DE utilizes a new objective function, which aims to maximize the distances between some particular pairs of data points, such as the distances between nearby points and the distances between data points from different classes. To make the mapping of new data points straightforward, and more importantly, to keep the natural tensor structure of high-order data, M2DE integrates multilinear techniques to learn the transformation matrices sequentially. To provide reasonable and stable embedding results, M2DE employs the L1-norm, which is more robust to outliers, to measure the dissimilarity between data points. Experiments on various datasets demonstrate that M2DE achieves good embedding results of high-order data for classification tasks.

Vectored data frequently occur in a variety of fields, which are easy to handle since they can be mathematically abstracted as points residing in a Euclidean space. An appropriate distance metric in the data space is quite demanding for a great number of applications. In this paper, we pose robust and tractable metric learning under pairwise constraints that are expressed as similarity judgements between data pairs. The major features of our approach include: 1) it maximizes the gap between the average squared distance among dissimilar pairs and the average squared distance among similar pairs; 2) it is capable of propagating similar constraints to all data pairs; and 3) it is easy to implement in contrast to the existing approaches using expensive optimization such as semidefinite programming. Our constrained metric learning approach has widespread applicability without being limited to particular backgrounds. Quantitative experiments are performed for classification and retrieval tasks, uncovering the effectiveness of the proposed approach.

Gaussian Mixture Model (GMM) is one of the most popular data clustering methods which can be viewed as a linear combination of different Gaussian components. In GMM, each cluster obeys Gaussian distribution and the task of clustering is to group observations into different components through estimating each cluster's own parameters. The Expectation-Maximization algorithm is always involved in such estimation problem. However, many previous studies have shown naturally occurring data may reside on or close to an underlying submanifold. In this paper, we consider the case where the probability distribution is supported on a submanifold of the ambient space. We take into account the smoothness of the conditional probability distribution along the geodesics of data manifold. That is, if two observations are close in intrinsic geometry, their distributions over different Gaussian components are similar. Simply speaking, we introduce a novel method based on manifold structure for data clustering, called Locally Consistent Gaussian Mixture Model (LCGMM). Specifically, we construct a nearest neighbor graph and adopt Kullback-Leibler Divergence as the distance measurement to regularize the objective function of GMM. Experiments on several data sets demonstrate the effectiveness of such regularization.

Non-negative matrix factorization (NMF), as a useful decomposition method for multivariate data, has been widely used in pattern recognition, information retrieval and computer vision. NMF is an effective algorithm to find the latent structure of the data and leads to a parts-based representation. However, NMF is essentially an unsupervised method and can not make use of label information. In this paper, we propose a novel semi-supervised matrix decomposition method, called Constrained Non-negative Matrix Factorization, which takes the label information as additional constraints. Specifically, we require that the data points sharing the same label have the same coordinate in the new representation space. This way, the learned representations can have more discriminating power. We demonstrate the effectiveness of this novel algorithm through a set of evaluations on real world applications.