In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our classification model is nonparametric, making no assumptions about the shape of the class distributions or the boundaries between them. The performance of the method is demonstrated on several data sets, both for metric learning and linear dimensionality reduction.

KNN score on the training set.

Inference in these "exponential family harrnoniums" is

We describe a way of using multiple different types of similarity relationship tolearn a low-dimensional embedding of a dataset. Our method chooses different, possibly overlapping representations of similarity by individually reweighting the dimensions of a common underlying latent space. When applied to a single similarity relation that is based on Euclidean distancesbetween the input data points, the method reduces to simple dimensionality reduction. If additional information is available about the dataset or about subsets of it, we can use this information to clean up or otherwise improve the embedding. We demonstrate the potential usefulnessof this form of semi-supervised dimensionality reduction on some simple examples.

In models that define probabilities via energies, maximum likelihood learning typically involves using Markov Chain Monte Carlo to sample from the model's distribution.

We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word "bank", to have versions close to the images of both "river" and "finance" without forcing the images of outdoor concepts to be located close to those of corporate concepts.

We propose a model for natural images in which the probability of an image is proportional to the product of the probabilities of some filter outputs. We encourage the system to find sparse features by using a Studentt distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the system learns a topographic map in which the orientation, spatial frequency and location of the filters change smoothly across the map. Even though maximum likelihood learning is intractable in our model, the product form allows a relatively efficient learning procedure that works well even for highly overcomplete sets of filters. Once the model has been learned it can be used as a prior to derive the "iterated Wiener filter" for the purpose of denoising images.

We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word "bank", to have versions close to the images of both "river" and "finance" without forcing the images of outdoor concepts to be located close to those of corporate concepts.

We propose a model for natural images in which the probability of an image isproportional to the product of the probabilities of some filter outputs. Weencourage the system to find sparse features by using a Studentt distribution to model each filter output.

Boosting algorithms and successful applications thereof abound for classification andregression learning problems, but not for unsupervised learning. We propose a sequential approach to adding features to a random fieldmodel by training them to improve classification performance between the data and an equal-sized sample of "negative examples" generated fromthe model's current estimate of the data density.