  We describe the construction of a highly reliable sample of approximately
7,000 optically faint periodic variable stars with light curves obtained by the
asteroid survey LINEAR across 10,000 sq.deg of northern sky. Majority of these
variables have not been cataloged yet. The sample flux limit is several
magnitudes fainter than for most other wide-angle surveys; the photometric
errors range from ~0.03 mag at $r=15$ to ~0.20 mag at r=18. Light curves
include on average 250 data points, collected over about a decade. Using
SDSS-based photometric recalibration of the LINEAR data for about 25 million
objects, we selected ~200,000 most probable candidate variables and visually
confirmed and classified approximately 7,000 periodic variables using phased
light curves. The reliability and uniformity of visual classification across
eight human classifiers was calibrated and tested using a SDSS Stripe 82 region
variable star catalog, and verified using an unsupervised machine learning
approach. The resulting sample of periodic LINEAR variables is dominated by
3,900 RR Lyrae stars and 2,700 eclipsing binary stars of all subtypes, and
includes small fractions of relatively rare populations such as asymptotic
giant branch stars and SX Phoenicis stars. We discuss the distribution of these
mostly uncataloged variables in various diagrams constructed with
optical-to-infrared SDSS, 2MASS and WISE photometry, and with LINEAR light
curve features. An interesting side result is a robust and precise quantitative
description of a strong correlation between the light-curve period and
color/spectral type for close and contact eclipsing binary stars. These large
samples of robustly classified variable stars will enable detailed statistical
studies of the Galactic structure and physics of binary and other stars, and we
make them publicly available.
