{"id":"a6982c46-1f4b-42b5-97ae-87a0331c8bf3","arxiv_id":"2412.00553","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"MdMvFIF separates a multidimensional multivariate signal into spatial and temporal intrinsic mode functions by alternating space and time filtering.","lead":"This paper introduces a new algorithm, MdMvFIF, that breaks down data changing across both space and time into separate spatial and temporal components. It is tested on artificial signals and on global air temperature data, and could help analyze climate and imaging data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The algorithm's output is not well-defined: unspecified stopping thresholds and lack of convergence guarantees make the extracted IMFs threshold-dependent.","rationale":"The paper's strongest novel claim is that MdMvFIF is the first algorithm to treat time as a dimension separate from space and to allow independent frequency filtering. For that claim to be true, the algorithm must have a well-defined output: for a given input, the extracted IMFs should not depend on accidentally chosen thresholds or on the arbitrary order of spatial and temporal filtering. The manuscript leaves both the inner-loop stopping threshold and the outer-loop 'no oscillations left' condition unspecified (Section 2, Algorithm 1). The missing citation '[2, ?]' for the stopping rule is a concrete symptom that this ingredient is not supported. In the absence of a convergence theorem, the numerical examples are the only evidence; yet the examples report no quantitative errors and no comparisons with FA-MVEMD or Serial-EMD, which the paper claims to outperform. I therefore agree with the reader's weakest assumption. The concern is real but addressable: specifying the stopping rules, testing threshold sensitivity, and analysing the convergence of the (I - diag(DFT(w)))^k iteration would settle it. Because the synthetic experiments appear to align visually with ground truth, the appropriate verdict remains CONDITIONAL rather than REJECT.","tokens_in":8648,"tokens_out":9422,"duration_ms":98612,"concrete_test":"Run the released Matlab implementation on the two synthetic examples of Section 3 with the inner-loop relative-change threshold varied over 1e-2, 1e-4, 1e-6, 1e-8, with an explicit outer-loop oscillation test (e.g., residual has at most one extremum per spatial/temporal slice), and with the order swapped (time-first versus space-first). Report the number of IMFs and the L2 differences between reconstructed and ground-truth components. If the decomposition changes across thresholds or order beyond numerical round-off, the stopping rules are load-bearing and must be specified before the central claim can be accepted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that MdMvFIF extracts IMFs from spatiotemporal signals rests on the assumption that the alternating space/time inner loops converge to well-defined components independently of arbitrary stopping rules. In Section 2, the inner loops stop 'as soon as a prefixed threshold is reached' and the outer loop continues 'until there are no more oscillations left both in space and time', but no threshold value, no operational definition of 'oscillations left', and no convergence or error analysis are given. The reference for the stopping criterion is even incomplete ('[2, ?]'). Algorithm 1's output therefore depends on unspecified parameters and on the fixed space-then-time order. If different thresholds or reversed order produce materially different IMF counts or waveforms, the method is not a well-defined decomposition and the claim of extracting intrinsic components is not supported. The paper's figures show plausible reconstructions of the synthetic examples, but no error metrics are reported, so this concern is not resolved by the numerics.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces MdMvFIF, an extension of Fast Iterative Filtering for signals that vary simultaneously in space and time. The proposed algorithm alternately applies spatial FIF2-style filtering and temporal MvFIF-style filtering to extract spatial and temporal Intrinsic Mode Functions (IMFs), using FFT-based convolution and Fokker-Planck filters with adaptively computed support sizes. The method is demonstrated on two synthetic examples with known ground-truth components and on global daily air-temperature data. The authors claim that MdMvFIF is the first decomposition algorithm that treats time as a dimension separate from space, allowing independent frequency filtering in each domain.","tokens_in":8803,"tokens_out":3928,"duration_ms":39651,"significance":"If the algorithm is well-defined and its output is reliable, the paper addresses a real gap: prior multidimensional EMD-type methods treat time as an additional spatial dimension and therefore cannot independently filter frequency ranges in space and time. The conceptual separation of spatial and temporal IMFs is a useful contribution, and the synthetic examples suggest the method can recover known components. The paper also provides an online Matlab implementation, which is a positive step for reproducibility. However, the absence of a specified stopping criterion, the lack of convergence or error analysis, and the purely qualitative validation currently limit the significance of the claims.","major_comments":[{"comment":"The inner loops stop 'as soon as a prefixed threshold is reached' based on the relative change in f_k, but no threshold value, formula, or rule is given, and the supporting reference is incomplete ('[2, ?]'). As written, the output of Algorithm 1 is not well-defined: different thresholds will generally produce different IMF counts and waveforms. The authors must specify the stopping rule precisely, state the threshold used in all numerical experiments, and discuss sensitivity to that threshold.","section":"Section 2, Algorithm 1"},{"comment":"The outer while loop continues 'until there are no more oscillations left both in space and time', but the paper gives no operational definition of 'oscillations left' or of the detection procedure. Without a precise stopping condition for the outer loop, the total number of IMFs produced is ambiguous. Provide a concrete criterion (for example, a condition on the number of local extrema in each spatial slice and in each temporal series) and prove or at least verify experimentally that the outer loop terminates.","section":"Section 2, Algorithm 1"},{"comment":"No convergence or error analysis is provided for the alternating space-then-time inner loops. In particular, it is not shown that the iteration f_{k+1} = f_k - M(f_k) converges for the chosen filter supports (pΩ computed via Eq. (3) and L computed from θ̃(t) in Eq. (4)), nor that the result is independent of the space-then-time ordering. Because the central claim is that the algorithm extracts intrinsic components, the authors should either prove a convergence result under the stated assumptions on the Fokker-Planck filters or provide a numerical convergence study that demonstrates invariance of the extracted IMFs with respect to the stopping thresholds and the filtering order.","section":"Section 2 and Section 1.1"},{"comment":"The validation against ground truth is only visual; the paper reports no quantitative error metrics between the extracted and true spatial or temporal IMFs. This is load-bearing because the abstract and introduction claim that MdMvFIF is 'capable of extracting IMFs'. Add quantitative errors (for example, relative L2 errors, correlation coefficients, or instantaneous-frequency errors for each recovered IMF) and, where possible, compare with FIF2, Serial-EMD, or FA-MVEMD on the same synthetic examples.","section":"Section 3, Figures 5 and 10"}],"minor_comments":[{"comment":"The pseudocode uses inconsistent variable names: 'IMFss' and 'IMFst' should be unified into a single output structure, and the initialization 'IMFs = tu' appears to be a typographical artifact that should be replaced with the empty-set notation.","section":"Algorithm 1"},{"comment":"The sentence describing f(v, t̃) as 'a vector in a R^{n+1} space' is misleading: the angle θ̃(t) is computed between spatial fields, i.e., vectors whose length is the number of spatial grid points, not vectors in R^{n+1}. Reword this passage to avoid confusion.","section":"Section 2, Eq. (4)"},{"comment":"The incomplete citation '[2, ?]' for the stopping criterion should be corrected to the appropriate reference (likely [2] or [3]).","section":"Section 2"},{"comment":"Figures 5 and 10 display differences between ground truth and recovered components, but no numerical scale or acceptable error level is discussed in the text; a sentence describing the magnitude of the residual errors would be helpful.","section":"Section 3"},{"comment":"The statement that IF is 'the only based on iteration, and therefore not requiring any a priori assumption on the signal' overstates the case, since the stopping criterion, the filter support rule, and the choice of filter all involve assumptions; please soften or qualify this claim.","section":"Section 1"}],"recommendation":"major_revision","confidential_remarks":"The core idea is publishable, but the manuscript currently leaves the algorithm under-specified and the validation under-quantified. The missing stopping criterion is the most serious issue because it makes the reported experiments difficult to reproduce. The authors should be encouraged to add a convergence analysis or at least a thorough numerical sensitivity study, and to report the exact parameters used in the examples. Given the availability of code and the clarity of the intended contribution, major revision rather than rejection seems appropriate if the authors can address these points."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper introduces MdMvFIF, an extension of Fast Iterative Filtering that decomposes spatiotemporal signals by alternating spatial filtering (FIF2) and temporal filtering (MvFIF). The genuinely new idea is treating time as a separate dimension rather than another spatial axis, which allows independent frequency filtering in space and time. That distinction from FA-MVEMD and Serial-EMD is fair, and the two synthetic examples with known ground truth suggest the decomposition recovers the components. The Earth temperature demo also looks plausible. Credit where due: the write-up is clear, and the authors link to code.\n\nThe soft spots are real but mostly addressable. The load-bearing one is the stopping criterion: the inner loops stop when a 'prefixed threshold' is reached, but no threshold value or operational definition of 'oscillations left' is supplied. The stress-test note is right that the output is therefore not well-defined as written; different thresholds could give different IMFs. The outer loop condition is similarly vague. There are also no quantitative error metrics, only difference plots, so the synthetic results are visually encouraging but not numerically pinned down. The paper does not compare against FA-MVEMD or Serial-EMD, which would have made the claimed advantage concrete. The pseudocode has typos (IMFss vs IMFst), and reference [2, ?] is incomplete. None of this kills the central idea—the method appears to work on the examples, and the missing pieces are standard referee demands rather than fundamental flaws.\n\nFor a methods paper, I'd want the stopping rule specified, some consistency statement, quantitative comparisons, and clean pseudocode. If that is added, I'd cite it. As it stands, I would not cite the current version, but I would send it to a serious referee rather than desk reject—it is a useful tool for applied communities, not a paradigm shift. Reading group: maybe.","headline":"A plausible spatiotemporal extension of fast iterative filtering with a real novelty—separate space and time filtering—but underspecified stopping criteria make the current version not fully reproducible.","tokens_in":9315,"tokens_out":3174,"would_cite":false,"duration_ms":30130,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["65T50","94A12"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper introduces MdMvFIF, an algorithm that decomposes non-stationary signals varying over both space and time into separate spatial and temporal Intrinsic Mode Functions, allowing independent frequency filtering in each domain.","keywords":["signal decomposition","intrinsic mode functions","iterative filtering","multivariate signals","multidimensional signals","non-stationary signals","fast iterative filtering","empirical mode decomposition"],"falsifier":"Run MdMvFIF on a synthetic signal with a known non-separable coupling, such as $f(v,t)=\\sin(2\\pi (v + ct))$ for a known speed $c$, and check whether the spatial IMF and temporal IMF together reproduce the signal without cross-contamination and without depending on the stopping threshold.","tokens_in":8447,"feed_emoji":"📡","tokens_out":6466,"duration_ms":161810,"temperature":0.7,"pith_summary":"The paper introduces the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) algorithm, which decomposes signals that vary simultaneously across space and time into Intrinsic Mode Functions (IMFs), simple oscillatory components. Unlike earlier extensions of empirical mode decomposition that treat time as an extra spatial dimension, MdMvFIF keeps time separate, so it can filter different frequency ranges in space and in time independently. The algorithm alternates between extracting a spatial IMF and a temporal IMF, with filter sizes chosen adaptively from the signal's own extrema and rotation behaviour. The paper demonstrates the method on synthetic signals and on a year of global air-temperature measurements.","feed_headline":"Signals in space and time get separate frequency filters","feed_subtitle":"MdMvFIF adaptively decomposes non-stationary data into spatial and temporal IMFs without a pre-chosen basis.","key_machinery":"The method's engine is the alternating inner-loop iteration $f_{k+1}=f_k - M(f_k)$, where the moving average $M$ is a convolution with a compactly supported, nonnegative, even Fokker-Planck filter. In space, the filter support $\\hat{\\Omega}$ is set to the minimum over all time steps of the adaptive support sizes used by FIF2; in time, the filter half-length $L$ is twice the average distance between successive extrema of the rotation angle $\\tilde{\\theta}(t)$ between consecutive multivariate signal vectors. All convolutions are evaluated in the frequency domain using the FFT, making each inner step cheap. The alternate extraction of space then time IMFs is the mechanism that keeps the two domains decoupled.","core_discovery":"The central claim is that a non-stationary signal $f(v,t)$ defined on space $v \\in \\mathbb{R}^n$ and time $t$ can be decomposed into separate spatial and temporal IMFs by alternating iterations: first filter in space with a multidimensional Fokker-Planck window whose support is the minimum over time of the adaptive FIF2 filter supports, then filter in time with a window whose length is set from the rotation angles of the multivariate vectors $f(\\cdot,t)$. The alternating procedure is continued until no oscillations remain in either domain. Because the space and time filters are computed independently, the method can remove high-frequency content in time while keeping low-frequency structure in space, or the reverse, which earlier multidimensional EMD-based algorithms cannot do.","pith_inferences":["The paper does not state it, but if the alternating iteration reliably converges, the same space-time separation could be applied to higher-dimensional data such as volumetric climate output or 4D microscopy, where filtering each axis independently would be valuable.","A natural testable extension, not explored in the paper, is to apply MdMvFIF to signals with known separable components and measure the cross-talk between the extracted spatial and temporal IMFs.","The rotation-angle rule for setting the temporal filter length could be transferred to other adaptive decomposition methods that currently rely on one-dimensional extrema statistics."],"forward_implications":["The algorithm can filter different frequency ranges in space and time independently, which earlier multidimensional EMD variants cannot do.","Signals with non-stationary behaviour in both domains can be decomposed without a priori assumptions about the number of components or a chosen basis.","The method applies to data of any spatial dimension, and its FFT-based convolutions keep each iteration efficient for large tensors.","The demonstrated application to Earth's air temperature shows the method producing interpretable spatial and temporal IMFs from a real 3D dataset."],"supporting_citations":[{"why":"Introduces the Empirical Mode Decomposition and the concept of Intrinsic Mode Functions that this work extends.","marker":"[1]"},{"why":"Defines Iterative Filtering, the moving-average subtraction loop that forms the inner iteration of the new algorithm.","marker":"[2]"},{"why":"Refines the adaptive filter-length selection for local iterative filtering, referenced for the stopping criterion.","marker":"[3]"},{"why":"Presents the Multivariate FIF whose rotation-angle rule is adapted here to set the temporal filter length.","marker":"[5]"},{"why":"Provides the multidimensional FIF (FIF2) and the Fokker-Planck filter family used for the spatial filtering step.","marker":"[6]"},{"why":"A prior serialization-based multidimensional EMD that treats time as an extra spatial dimension, the limitation the new method addresses.","marker":"[10]"},{"why":"A prior fast adaptive multidimensional multivariate EMD with the same space-time limitation, used as a comparison point.","marker":"[11]"},{"why":"Motivates the need for independent space-time frequency filtering in thermography applications.","marker":"[12]"}],"fun_headline_variants":["New algorithm separates space and time in signals","MdMvFIF: adaptive decomposition for space-time signals","Splitting signals into spatial and temporal parts adaptively","Fast filtering for non-stationary multidimensional signals"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The alternating space-then-time iteration is assumed to converge to a stable decomposition for any input, but no convergence proof, error bound, or explicit stopping threshold is given.","fun_headline_variants_meta":{"raw":{"variants":["New algorithm separates space and time in signals","MdMvFIF: adaptive decomposition for space-time signals","Splitting signals into spatial and temporal parts adaptively","Fast filtering for non-stationary multidimensional signals"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000534,"raw_usage":{"total_tokens":2600,"prompt_tokens":1010,"completion_tokens":1590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":626,"completion_tokens_details":{"reasoning_tokens":1527}},"tokens_in":626,"tokens_out":1590,"duration_ms":10086,"temperature":1.0,"reasoning_tokens":1527,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:13:13.768932+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run MdMvFIF on a synthetic signal with a known non-separable coupling, such as $f(v,t)=\\sin(2\\pi (v + ct))$ for a known speed $c$, and check whether the spatial IMF and temporal IMF together reproduce the signal without cross-contamination and without depending on the stopping threshold.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the Empirical Mode Decomposition and the concept of Intrinsic Mode Functions that this work extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Iterative Filtering, the moving-average subtraction loop that forms the inner iteration of the new algorithm."},{"cited_title":"Cicone, J","cited_arxiv_id":null,"evidence_quote":"Refines the adaptive filter-length selection for local iterative filtering, referenced for the stopping criterion."},{"cited_title":"Cicone and E","cited_arxiv_id":null,"evidence_quote":"Presents the Multivariate FIF whose rotation-angle rule is adapted here to set the temporal filter length."},{"cited_title":"Cicone and H","cited_arxiv_id":null,"evidence_quote":"Provides the multidimensional FIF (FIF2) and the Fokker-Planck filter family used for the spatial filtering step."},{"cited_title":"Zhang, F","cited_arxiv_id":null,"evidence_quote":"A prior serialization-based multidimensional EMD that treats time as an extra spatial dimension, the limitation the new method addresses."},{"cited_title":"Thirumalaisamy, P","cited_arxiv_id":null,"evidence_quote":"A prior fast adaptive multidimensional multivariate EMD with the same space-time limitation, used as a comparison point."},{"cited_title":"Tshiangomba, G","cited_arxiv_id":null,"evidence_quote":"Motivates the need for independent space-time frequency filtering in thermography applications."}],"review_version":1}