An Information Retrieval Approach for Finding Dependent Subspaces of Multiple Views
Finding relationships between multiple views of data is essential both in exploratory analysis and as pre-processing for predictive tasks. A prominent approach is to apply variants of Canonical Correlation Analysis (CCA), a classical method seeking correlated components between views. The basic CCA is restricted to maximizing a simple dependency criterion, correlation, measured directly between data coordinates. We introduce a new method that finds dependent subspaces of views directly optimized for the data analysis task of neighbor retrieval between multiple views. We optimize mappings for each view such as linear transformations to maximize cross-view similarity between neighborhoods of data samples. The criterion arises directly from the well-defined retrieval task, detects nonlinear and local similarities, measures dependency of data relationships rather than only individual data coordinates, and is related to well understood measures of information retrieval quality. In experiments the proposed method outperforms alternatives in preserving cross-view neighborhood similarities, and yields insights into local dependencies between multiple views.
This paper proposes a multiview learning approach to finding dependent subspaces optimized for maximizing cross-view similarity between neighborhoods of data samples. The motivation comes from information retrieval tasks. Authors position their work as an alternative to CCA-based multiview learning; note, however, that CCA based techniques have very different purpose and are rather broadly applicable than the setting considered here. Main points: - I am not sure what authors mean by time complexity. It would appear that they simply report the computational cost of evaluating the objective in equation (7). Is there a sense of how many iterations of the L-BFGS method? Since that is going to be difficult given the nature of the optimization problem, one would appreciate some sense of how hard or easy it is in practice to optimize the objective in (7) and how that varies with various problem dimensions. Authors argue that scalability is not their first concern, which is understandable, but if they are going to make some remarks about the computational cost, it better be clarified that the reported cost is for some small part of their overall approach rather than “time complexity”. - Since authors position their approach as an alternative to CCA, they should remark about how CCA, even though a nonconvex optimization problem, can be solved exactly with computational cost that is linear in the data size and only quadratic with dimensionality even with a naive implementation. The method proposed in the paper does not seem to be tractable, at least not immediately. - The empirical results with synthetic data are a it confusing. First of all the data generation procedure is quite convoluted, I am not sure why we need to process each coordinate separately in different groups, and then permute and combine etc. A simple benchmark where we take different linear transformations of a shared representation and add independent noise would suffice to confirm that the proposed method does something reasonable. I am also baffled why CCA does not recover the true subspace - arguably it is the level of additive noise that would impact the recoverability - however the proposed method is nearly exact so the noise level is perhaps not so severe. It is also not clear if authors are using regularization with CCA - without regularization CCA can be have in a funny manner. This needs to be clarified.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
An Information Retrieval Approach for Finding Dependent Subspaces of Multiple Views
Finding relationships between multiple views of data is essential both in exploratory analysis and as pre-processing for predictive tasks. A prominent approach is to apply variants of Canonical Correlation Analysis (CCA), a classical method seeking correlated components between views. The basic CCA is restricted to maximizing a simple dependency criterion, correlation, measured directly between data coordinates. We introduce a new method that finds dependent subspaces of views directly optimized for the data analysis task of neighbor retrieval between multiple views. We optimize mappings for each view such as linear transformations to maximize cross-view similarity between neighborhoods of data samples. The criterion arises directly from the well-defined retrieval task, detects nonlinear and local similarities, measures dependency of data relationships rather than only individual data coordinates, and is related to well understood measures of information retrieval quality. In experiments the proposed method outperforms alternatives in preserving cross-view neighborhood similarities, and yields insights into local dependencies between multiple views.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper proposes a multiview learning approach to finding dependent subspaces optimized for maximizing cross-view similarity between neighborhoods of data samples. The motivation comes from information retrieval tasks. Authors position their work as an alternative to CCA-based multiview learning; note, however, that CCA based techniques have very different purpose and are rather broadly applicable than the setting considered here. Main points: - I am not sure what authors mean by time complexity. It would appear that they simply report the computational cost of evaluating the objective in equation (7). Is there a sense of how many iterations of the L-BFGS method? Since that is going to be difficult given the nature of the optimization problem, one would appreciate some sense of how hard or easy it is in practice to optimize the objective in (7) and how that varies with various problem dimensions. Authors argue that scalability is not their first concern, which is understandable, but if they are going to make some remarks about the computational cost, it better be clarified that the reported cost is for some small part of their overall approach rather than “time complexity”. - Since authors position their approach as an alternative to CCA, they should remark about how CCA, even though a nonconvex optimization problem, can be solved exactly with computational cost that is linear in the data size and only quadratic with dimensionality even with a naive implementation. The method proposed in the paper does not seem to be tractable, at least not immediately. - The empirical results with synthetic data are a it confusing. First of all the data generation procedure is quite convoluted, I am not sure why we need to process each coordinate separately in different groups, and then permute and combine etc. A simple benchmark where we take different linear transformations of a shared representation and add independent noise would suffice to confirm that the proposed method does something reasonable. I am also baffled why CCA does not recover the true subspace - arguably it is the level of additive noise that would impact the recoverability - however the proposed method is nearly exact so the noise level is perhaps not so severe. It is also not clear if authors are using regularization with CCA - without regularization CCA can be have in a funny manner. This needs to be clarified.
assistant
This paper proposes a multiview learning approach to finding dependent subspaces optimized for maximizing cross-view similarity between neighborhoods of data samples. The motivation comes from information retrieval tasks. Authors position their work as an alternative to CCA-based multiview learning; note, however, that CCA based techniques have very different purpose and are rather broadly applicable than the setting considered here. Main points: - I am not sure what authors mean by time complexity. It would appear that they simply report the computational cost of evaluating the objective in equation (7). Is there a sense of how many iterations of the L-BFGS method? Since that is going to be difficult given the nature of the optimization problem, one would appreciate some sense of how hard or easy it is in practice to optimize the objective in (7) and how that varies with various problem dimensions. Authors argue that scalability is not their first concern, which is understandable, but if they are going to make some remarks about the computational cost, it better be clarified that the reported cost is for some small part of their overall approach rather than “time complexity”. - Since authors position their approach as an alternative to CCA, they should remark about how CCA, even though a nonconvex optimization problem, can be solved exactly with computational cost that is linear in the data size and only quadratic with dimensionality even with a naive implementation. The method proposed in the paper does not seem to be tractable, at least not immediately. - The empirical results with synthetic data are a it confusing. First of all the data generation procedure is quite convoluted, I am not sure why we need to process each coordinate separately in different groups, and then permute and combine etc. A simple benchmark where we take different linear transformations of a shared representation and add independent noise would suffice to confirm that the proposed method does something reasonable. I am also baffled why CCA does not recover the true subspace - arguably it is the level of additive noise that would impact the recoverability - however the proposed method is nearly exact so the noise level is perhaps not so severe. It is also not clear if authors are using regularization with CCA - without regularization CCA can be have in a funny manner. This needs to be clarified.