If it ain't broke, don't fix it: Sparse metric repair

Gilbert, Anna C.; Jain, Lalit

doi:10.1109/allerton.2017.8262793

Cited by 16 publications

(33 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First we estimate distances between the data points, we then correct these distances so that they adhere to a metric, finally we run a suitable dimension reduction algorithm. We use the Increase Only Metric Repair (IOMR) algorithm in Gilbert and Jain [7] to repair the inaccurate distance matrices. As we can see in Figure 1, all of the dimension reduction algorithms depend on the local distances and not on the actual data points themselves.…”

Section: Our Approach and Contributionsmentioning

confidence: 99%

“…Gilbert and Jain in [7] defined the sparse metric repair problem. They define Sym n (R ≥0 ) to be the set of positive real symmetric matrices.…”

Section: Metric Repairmentioning

confidence: 99%

“…(1) where · p is the vector 0 is the pseudonorm that counts the number of non-zero entries. In [7], they define three variants of the corresponding to three different: S = R ≤0 decrease only metric repair (DOMR), S = R ≥0 increase only metric repair (IOMR), and S = R, which is simply called metric repair or MR. In general, for any given set S we shall refer to problem as MR(S) For the rest of paper we will focus on the increase only case and use the following algorithm from [7]:…”

Section: Metric Repairmentioning

confidence: 99%

“…As it was noted in the [7], one could relax Equation (1) to a convex optimization problem by minimizing P 1 instead of P 0 . Gilbert and Jain used various different convex optimization methods, and while these methods produce satisfactory results, they were extremely slow.…”

Section: Metric Repairmentioning

confidence: 99%

“…Because the distances do not satisfy a metric, the points all collapse to one location and cannot be distinguished in the figure. In the lower right figure (d), we first repair the corrupted distance matrix, using a metric repair algorithm from [7], and then embed the data using ISOMAP. The resulting embedding is much closer to the original embedding, with some minor distortion.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Unsupervised Metric Learning in Presence of Missing Data

Gilbert

Sonthalia

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Self Cite

View full text Add to dashboard Cite

For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a highdimensional space and, because of this high-dimensional structure, most algorithms inefficient. The typical solution is to reduce the dimension of the input data using a standard dimension reduction algorithms such as ISOMAP, LAPLACIAN EIGENMAPS or LLES. This approach, however, does not always work in practice as these algorithms require that we have somewhat ideal data. Unfortunately, most data sets either have missing entries or unacceptably noisy values. That is, real data are far from ideal and we cannot use these algorithms directly.In this paper, we focus on the case when we have missing data. Some techniques, such as matrix completion, can be used to fill in missing data but these methods do not capture the non-linear structure of the manifold. Here, we present a new algorithm MR-MISSING that extends these previous algorithms and can be used to compute low dimensional representation on data sets with missing entries. We demonstrate the effectiveness of our algorithm by running three different experiments. We visually verify the effectiveness of our algorithm on synthetic manifolds, we numerically compare our projections against those computed by first filling in data using nlPCA and mDRUR on the MNIST data set, and we also show that we can do classification on MNIST with missing data. We also provide a theoretical guarantee for MR-MISSING under some simplifying assumptions.

show abstract

Section: Our Approach and Contributionsmentioning

confidence: 99%

“…Gilbert and Jain in [7] defined the sparse metric repair problem. They define Sym n (R ≥0 ) to be the set of positive real symmetric matrices.…”

Section: Metric Repairmentioning

confidence: 99%

Section: Metric Repairmentioning

confidence: 99%

Section: Metric Repairmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Unsupervised Metric Learning in Presence of Missing Data

Gilbert

Sonthalia

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Self Cite

View full text Add to dashboard Cite

show abstract

Multi‐scale affinities with missing data: Estimation and applications

Zhang

Mishne

Chabrière

2021

Statistical Analysis

View full text Add to dashboard Cite

Many machine learning algorithms depend on weights that quantify row and column similarities of a data matrix. The choice of weights can dramatically impact the effectiveness of the algorithm. Nonetheless, the problem of choosing weights has arguably not been given enough study. When a data matrix is completely observed, Gaussian kernel affinities can be used to quantify the local similarity between pairs of rows and pairs of columns. Computing weights in the presence of missing data, however, becomes challenging. In this paper, we propose a new method to construct row and column affinities even when data are missing by building off a co-clustering technique. This method takes advantage of solving the optimization problem for multiple pairs of cost parameters and filling in the missing values with increasingly smooth estimates. It exploits the coupled similarity structure among both the rows and columns of a data matrix.We show these affinities can be used to perform tasks such as data imputation, clustering, and matrix completion on graphs.

show abstract