AMICO: Adaptive Matched Identifier for Clusters

• AMICO is an adaptive matched-filter galaxy cluster finder that models the observed galaxy distribution as a cluster signal plus field-galaxy background to optimize detection in photometric surveys.
• It employs a cluster template combining a Navarro–Frenk–White profile and a Schechter luminosity function, using amplitude measurements as robust mass proxies.
• The method provides probabilistic galaxy memberships with iterative deblending, enabling precise cosmological analyses and halo-structure studies across multiple survey implementations.

AMICO, the Adaptive Matched Identifier of Clustered Objects, is a galaxy-cluster finder for photometric surveys that models the observed galaxy distribution as the superposition of a cluster signal and a field-galaxy background, then applies an optimal linear matched filter to maximize cluster detection signal-to-noise. In its standard formulation it works in sky position, magnitude, and photometric-redshift space, returns an amplitude $A$, detection significance, cluster redshift and centre, and probabilistic galaxy memberships, and has been deployed on KiDS, COSMOS, and miniJPAS data sets for cluster cosmology and halo-structure studies (Bellagamba et al., 2017). It is also one of the two official cluster-finding algorithms in the Euclid mission pipeline (Maturi et al., 2023).

1. Matched-filter formulation and adaptive detection

AMICO starts from a generative model in which the data are written as a cluster template plus noise. One formulation used in the KiDS-1000 catalogue work is

$$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$

where $A$ is the cluster amplitude, $\tau$ is the cluster template, and $N$ is the field-galaxy term (Maturi et al., 18 Jul 2025). In the original AMICO presentation, the optimal filter is proportional to the ratio of the cluster model to the background model, $\Psi_c = M_c/N$, yielding an unbiased minimum-variance estimator for the amplitude (Bellagamba et al., 2017).

The cluster template is typically factorized into a radial profile and a luminosity function. In KiDS applications, the model cluster is built by combining a Navarro–Frenk–White projected radial density profile with a Schechter luminosity function, while galaxy photometric-redshift information enters through the individual $p_i(z)$ or equivalent photo-$z$ weights (Lesci et al., 2022). The method is not intrinsically tied to colour selection: in KiDS-DR3, AMICO uses galaxy angular positions, magnitudes, and photometric redshifts, but deliberately does not impose a red-sequence colour selection, reducing dependence on the presence of an old, red galaxy population (Romanello et al., 2023).

The “adaptive” component is operationally important. After identifying a significant peak in the amplitude map, AMICO computes galaxy membership probabilities, updates the field probability of each galaxy, and removes the imprint of the detected structure from the filtered map before searching for the next system. This iterative cleaning is the basis of its deblending behaviour. In the original validation on mocks, the method deblended close-by and aligned structures in more than $50\%$ of the cases for objects at radial distance equal to $0.5\times R_{200}$ or redshift distance equal to $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$0, where $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$1 is the typical photometric-redshift uncertainty (Bellagamba et al., 2017).

2. Detection observables, memberships, and richness proxies

The central AMICO detection statistic is the amplitude $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$2. In the KiDS weak-lensing formulation, for a trial centre $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$3 and redshift $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$4,

$$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$5

so $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$6 is an optimally weighted measure of galaxy overdensity consistent with the cluster model at $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$7 (Giocoli et al., 2021). Simulations show that $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$8 is a good mass proxy if the model is properly calibrated (Giocoli et al., 2021).

AMICO also computes a membership probability for each galaxy–cluster pair. In the KiDS-DR3 implementation,

$$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$9

where $A$0 is the field probability of galaxy $A$1 before accounting for detection $A$2 (Giocoli et al., 2021). These probabilities underpin the richness estimators and allow overlapping structures to share galaxies probabilistically rather than through hard assignments.

Two related richness definitions recur in the AMICO literature. The apparent richness $A$3 is the sum of membership probabilities over visible members. The intrinsic richness $A$4 is designed to be less sensitive to survey depth and is defined as a probability-weighted count of galaxies satisfying a magnitude cut and a fixed physical-radius cut. In the KiDS analyses,

$A$5

where $A$6 is the radius associated with $A$7 (Lesci et al., 2022). Because the threshold $A$8 is chosen to stay brighter than the survey limit over the calibrated range, $A$9 is approximately independent of depth and redshift in that regime (Lesci et al., 2022). In KiDS-1000 cosmology, $\tau$0 is the sole mass proxy used in the counts+lensing analysis (Lesci et al., 18 Jul 2025).

AMICO-derived catalogues also support alternative observables. In KiDS-DR3, the total $\tau$1-band luminosity $\tau$2 was used to calibrate a luminosity–mass scaling relation, while in miniJPAS a stellar-mass proxy $\tau$3 was introduced by summing stellar masses of high-probability members (Smit et al., 2021, Maturi et al., 2023). These are extensions of the same probabilistic-membership formalism rather than separate detection algorithms.

3. Survey implementations and catalogues

AMICO has been implemented across wide, deep, and narrow-band photometric surveys, with sample definitions tailored to the science case.

Survey/application	Representative AMICO sample	Main characteristic
KiDS-DR3	7,988 detections with $\tau$4 in $\tau$5	Basis for counts, clustering, lensing, halo-bias, and splashback studies
KiDS-1000 / DR4	23,965 clusters over about $\tau$6 in $\tau$7	Cosmological catalogue with quality flags, SinFoniA selection function, and blinded completeness
miniJPAS	80, 30, and 11 systems with $\tau$8 and $\tau$9	Narrow-band application down to $N$0
COSMOS	1269 candidates with $N$1, 666 with $N$2, up to $N$3	Deep small-area catalogue with X-ray counterpart analysis

The KiDS-DR3 programme established AMICO as a multi-probe cluster-cosmology platform. The parent catalogue contains 7,988 detections with $N$4 over the photo-$N$5 range $N$6 (Lesci et al., 2022). Subsamples were then optimized for individual analyses: 6,962 clusters in $N$7 for stacked weak lensing (Giocoli et al., 2021), 4,934 clusters with $N$8 in two redshift bins for the redshift-space two-point correlation function (Lesci et al., 2022), and 5,162 clusters with $N$9 in three tomographic bins for angular clustering (Romanello et al., 2023).

The KiDS-1000 / DR4 catalogue introduced a larger, explicitly cosmology-oriented sample. Using AMICO over an effective area of about $\Psi_c = M_c/N$0, the catalogue contains 23,965 detections with $\Psi_c = M_c/N$1 in $\Psi_c = M_c/N$2, includes probabilistic membership assignments for galaxies with $\Psi_c = M_c/N$3, quality flags for border and artefact control, and purity/completeness estimates from the SinFoniA data-driven framework (Maturi et al., 18 Jul 2025). It was cross-matched to 321 eRASS1 “primary” X-ray systems and 235 ACT-DR5 SZ clusters, and its spectroscopic calibration with GAMA yielded a cluster redshift scatter of approximately $\Psi_c = M_c/N$4 after bias correction (Maturi et al., 18 Jul 2025).

Beyond KiDS, the miniJPAS implementation demonstrated AMICO in a 56-filter narrow-band setting, detecting systems down to $\Psi_c = M_c/N$5 and showing a gain of up to $\Psi_c = M_c/N$6 in detection signal-to-noise relative to a degraded broad-band-like photo-$\Psi_c = M_c/N$7 case, with cluster redshift uncertainty $\Psi_c = M_c/N$8 when refined with member galaxies (Maturi et al., 2023). In COSMOS, AMICO was pushed to $\Psi_c = M_c/N$9, $p_i(z)$0, and $p_i(z)$1, producing a catalogue explicitly aimed at calibrating optical mass proxies against X-ray masses in the group and high-redshift-cluster regime (Toni et al., 2023).

4. Cosmological and halo-structure applications

AMICO catalogues have been used in several complementary cosmological analyses. In KiDS-DR3, a joint counts plus stacked weak-lensing analysis of 3,652 clusters with $p_i(z)$2 over $p_i(z)$3 gave

$p_i(z)$4

with $p_i(z)$5 consistent within $p_i(z)$6 with WMAP and Planck (Lesci et al., 2020). A large-scale stacked weak-lensing analysis of 6,962 KiDS-DR3 clusters, exploiting the 2-halo term out to $p_i(z)$7, obtained $p_i(z)$8 in flat $p_i(z)$9CDM (Giocoli et al., 2021).

Clustering analyses produced consistent constraints from the same photometric catalogue. From the redshift-space two-point correlation function of 4,934 clusters with $z$0 in $z$1, the KiDS-DR3 3D clustering study obtained

$z$2

and found $z$3 for the normalization of the mass–richness relation when cosmology was fixed to Planck values (Lesci et al., 2022). In the tomographic 2D analysis of 5,162 clusters, the angular correlation function yielded

$z$4

while the angular power spectrum gave $z$5, $z$6, and $z$7, statistically consistent but noisier in $z$8 because of shot noise and mask-induced mode coupling (Romanello et al., 2023).

The AMICO samples have also supported direct halo-structure measurements. A stacked weak-lensing analysis of about 7,000 KiDS-DR3 clusters measured the halo bias–mass relation and found, for the full catalogue,

$z$9

with the observed bias–mass relation agreeing with $50\%$0CDM predictions within $50\%$1 and implying $50\%$2 when $50\%$3 and a simulation-based bias–mass prior were adopted (Ingoglia et al., 2022). A later KiDS-DR3 weak-lensing analysis of 6,962 clusters measured the splashback radius and found it close to $50\%$4, whereas theoretical models predict a larger value for low-accretion-rate halos, suggesting that optical selection may favor systems with higher central density on small scales than a purely mass-selected halo sample (Giocoli et al., 2024).

The KiDS-1000 counts+lensing analysis substantially tightened the AMICO cosmology constraints. Using about 8,000 clusters over $50\%$5 up to $50\%$6, and explicitly accounting for impurities, projection, halo orientation, miscentring, truncation, correlated matter, multiplicative shear bias, baryons, geometric distortions, halo mass function uncertainties, and super-sample covariance, it obtained

$50\%$7

The same analysis reported an average mass precision of $50\%$8 and an intrinsic scatter of the $50\%$9 relation of $0.5\times R_{200}$0, explicitly concluding that $0.5\times R_{200}$1 is an excellent mass proxy (Lesci et al., 18 Jul 2025).

5. Selection effects, systematics, and common misconceptions

A recurring misconception is that AMICO is a red-sequence finder. In the KiDS implementations it is explicitly not: the detector uses galaxy positions, magnitudes, and photometric redshifts, but does not require a red-sequence colour selection, precisely to reduce sensitivity to the presence of old, red galaxies and to avoid bias against blue or high-redshift systems (Lesci et al., 2022). This design choice is central to its use in Euclid-like photometric surveys.

Systematics are treated at several levels. In clustering, photometric-redshift errors are modeled directly in redshift space through a Gaussian damping term in the power spectrum, with KiDS-DR3 mocks yielding $0.5\times R_{200}$2 for the cluster photo-$0.5\times R_{200}$3 scatter parameter (Lesci et al., 2022). In the original KiDS-DR3 counts+lensing cosmology analysis, the likelihood included purity and completeness corrections from realistic mocks, richness measurement scatter of about $0.5\times R_{200}$4, a marginalised cluster redshift bias, halo mass-function uncertainty parameters, and super-sample covariance (Lesci et al., 2020).

The KiDS-1000 catalogue added several catalogue-level controls. The filter/noise model was estimated globally over the full survey rather than tile by tile, border effects between neighboring tiles were mitigated algorithmically, and each detection carries tile-edge and artefact flags (Maturi et al., 18 Jul 2025). Purity and completeness were estimated with the SinFoniA data-driven approach rather than with fully synthetic simulations, and a blinding scheme was applied to the selection function to support cosmological analyses (Maturi et al., 18 Jul 2025). The same work also notes a practical limitation: above $0.5\times R_{200}$5, the $0.5\times R_{200}$6 threshold approaches the survey limit, so $0.5\times R_{200}$7 becomes increasingly redshift-dependent and noisy (Maturi et al., 18 Jul 2025).

Downstream inference from AMICO catalogues can also be sensitive to methodological choices in the lensing estimator. A KiDS-DR3 study using 6,925 AMICO clusters showed that replacing the conventional weighted mean of ellipticities by $0.5\times R_{200}$8 regression changes the recovered excess surface density by a few percent and leads to a $0.5\times R_{200}$9 difference in $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$00, while preserving a tightly constrained luminosity–mass slope of $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$01 (Smit et al., 2021). This indicates that precision use of AMICO samples depends not only on cluster finding and selection-function calibration, but also on robust estimators in the subsequent weak-lensing analysis.

6. Extensions, astrophysical uses, and outlook

AMICO outputs are not limited to cosmological counts. In KiDS-DR3 they have been used to study central-galaxy selection, red and blue member fractions, and comparisons to Illustris-TNG. In that programme, the AMICO catalogue over $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$02 and up to $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$03 showed good agreement with Illustris-TNG at $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$04, while at higher redshift the simulations produced a lower fraction of blue galaxies than observed, and blue central galaxies were found to have lower stellar mass than red central galaxies at fixed cluster mass (Radovich et al., 2020).

Deep and narrow-band implementations have extended the method into regimes not accessible in the original wide-field KiDS work. In miniJPAS, AMICO detected 80, 30, and 11 systems above $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$05, $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$06, and $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$07, respectively, down to $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$08, and introduced a stellar-mass-based proxy $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$09 made possible by the 56-filter photometry (Maturi et al., 2023). In COSMOS, the combination of depth, redshift reach, and X-ray information yielded 1,269 candidates with $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$10, 666 with $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$11, and 622 systems with X-ray flux estimates, enabling the calibration of optical mass proxies up to $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$12 and below $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$13 (Toni et al., 2023). A notable result of that calibration is that redder bands, especially $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$14 and $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$15, showed more stable mass–proxy behaviour with redshift than the $$D(\vec{x}, z, \vec{m}) = A \,\tau(\vec{x}, z, \vec{m}) + N(z, \vec{m}),$$16 band (Toni et al., 2023).

The KiDS-1000 catalogue paper frames AMICO as a large, homogeneous, well-characterized cluster sample for cosmology, while the KiDS-1000 counts+lensing analysis demonstrates that the same matched-filter and probabilistic-membership formalism scales to a data set with markedly improved statistics and tighter cosmological constraints (Maturi et al., 18 Jul 2025, Lesci et al., 18 Jul 2025). Within the published applications, AMICO has therefore become both a detection algorithm and a calibrated observational infrastructure: it delivers the catalogue, the membership probabilities, the richness and amplitude observables, and the selection-function machinery needed to connect photometric cluster samples to halo mass, large-scale bias, and cosmological inference.