  In this paper, we found 2939 S-type stars from LAMOST Data Release 10 using
two machine-learning methods, and 2306 of them were reported for the first
time. The main purpose of this work is to study how to divide S-type stars into
intrinsic and extrinsic stars with photometric data and LAMOST spectra. Using
infrared photometric data, we adopted two methods to distinguish S-type stars,
i.e., XGBoost algorithm and color-color diagrams. We trained XGBoost model with
15 input features consisting of colors and absolute magnitudes of Two Micron
All Sky Survey (2MASS), AllWISE, AKARI, and IRAS, and found that the model
trained by input features with 2MASS, AKARI, and IRAS data has the highest
accuracy of 95.52%. Furthermore, using this XGBoost model, we found four
color-color diagrams with six infrared color criteria to divide S-type stars,
which has an accuracy of about 90%. Applying the two methods to the 2939 S-type
stars, 381 (XGBoost)/336 (color-color diagrams) intrinsic and 495 (XGBoost)/82
(color-color diagrams) extrinsic stars were classified, respectively. Using
these photometrically classified intrinsic and extrinsic stars, we retrained
XGBoost model with their blue and red medium-resolution spectra, and the 2939
stars were divided into 855 intrinsic and 2056 extrinsic stars from spectra
with an accuracy of 94.82%. In addition, we also found four spectral regions of
Zr I (6451.6A), Ne II (6539.6A), H{\alpha} (6564.5A), and Fe I (6609.1A) and C
I (6611.4A) are the most important features, which can reach an accuracy of
92.1% when using them to classify S-type stars.
