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Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case
(Scientific Research, 2012) Sun, Qingquan; Wu, Peng; Wu, Yeqing; Guo, Mengcheng; Lu, Jiang
Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research.
However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative
matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning
point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a
three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior
knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is
achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that
our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.
JCES Continues to Bring Disciplines Together
(University of Alabama Division of Community Affairs, 2011) Simon, Cassandra E.
For Higher Ed, the Crucible Moment Has Arrived
(University of Alabama Division of Community Affairs, 2011) Simon, Cassandra E.
Exploring the tectonostratigraphy of the Pakistan Himalaya with new detrital zircon geochronology and neodymium isotope data from the Kaghan Valley
(Elsevier, 2023) Schiffer, W. Joel; Robinson, Delores M.; Faisal, Shah; Stowell, Harold H.
In the central Himalaya, the Greater and Lesser Himalayan tectonostratigraphic zones can be distinguished from each other by combining detrital zircon U-Pb ages and whole-rock Nd isotopic data. In
the Hazara-Kashmir syntaxis of northern Pakistan, rock units in the Kaghan valley have been variously
assigned to the Tethyan, Greater, and Lesser Himalayan zones. To determine which tectonostratigraphic
zones are represented, we sampled across the Batal thrust in the northern Kaghan valley because this
structure is identified in some research as the Main Central thrust. Samples from the footwall yield
Paleo- to Mesoproterozoic maximum depositional ages (~1.8–1.1 Ga) and an average eNd(0) value of
14.3. Samples from the hanging wall yield Neoproterozoic maximum depositional ages (~1000–
600 Ma) and eNd(0) values of 17.3. The contrasting detrital zircon ages show that the Batal thrust in
the Kaghan valley is a major structural division. However, these data lack the characteristic detrital zircon
age spectra and eNd(0) values of Greater and Lesser Himalayan rocks north and south of the Main Central
thrust in the central Himalaya, respectively. Therefore, either the Batal thrust is not the Main Central
thrust, or the Main Central thrust in the Kaghan valley cuts a different structural level and carries rock
units not seen outside the Hazara-Kashmir syntaxis.
Structural Architecture of the Pakistan Fold-Thrust Belt, Western Himalaya: Insights from a Balanced Cross Section, Detrital Zircon Geochronology, and Low-Temperature Thermochronology
(2026-08-13) Schiffer, W. Joel; Robinson, Delores M.; Faisal, Shah; Bhattacharya, Gourab
In the Pakistan fold-thrust belt, the tectonostratigraphic and structural relationships are not easily correlated across the western Himalayan syntaxis. To determine these relationships, estimate minimum crustal shortening across the thrust belt, and provide a kinematic interpretation, we present the first balanced cross section based on field work from the Main Mantle thrust to the Salt Range thrust. Our interpretation indicates that Paleoproterozoic rocks in the footwall of the Main Mantle thrust are duplexed, creating a folded thrust contact with Neoproterozoic rocks in the hanging wall. The Tanawal Formation has a maximum depositional age of ~700 Ma and is tectonostratigraphically similar to rocks in the Greater Himalayan klippen in the central Himalaya. Therefore, this folded thrust may be correlative to the Main Central thrust. Maximum depositional ages from Paleo- and Neoproterozoic units south of the Panjal-Khariabad thrust are ~1.1 Ga for the Hisartang and Dakhner formations and ~800 Ma for the Gandaf and Hazara formations, similar to Lesser Himalayan ages. We estimate minimum crustal shortening to be 433–503 km from the Main Mantle thrust to the Salt Range thrust, similar to estimates in the central Himalaya and NW India. Thermal modeling of zircon and apatite cooling ages suggests Neogene exhumation of the hinterland, with accelerated cooling at ~20 Ma from activity of the Panjal-Khairabad and Main Mantle thrusts.