A resistor from output to non-inverting input is not enough. What you need is a second resistor from non-inverting input to ground or signal source.
The idea with the feeback resistor is to superimpose a small voltage to the non-inverting input, which has the same polarity as the signal which caused the comparator to toggle. And this just at the moment when it toggles.
It's as if you help an old man to climb a staircase: You give him positive feedback, means you push him up the staircase, when he wants to climb up.
For the same reason feedback resistor providing a hysteresis must always be connected from output to non-inverting input.

Now there are two ways to proceed:

1. You apply the reference voltage to the inverting input. The actual signal you apply to the non-inverting input. But not directly, but via a resistance of a few kiloOhms. Then you connect a high ohmic resistor in the MOhm range from output to non-inverting input.
This methode needs a low impedance source. Also, it can show some instability, especially with fast comparators.
It can help to filter the reference voltage at inverting input, which means a simple capacitor to ground, if reference voltage is provided by a resistive voltage divider from Vcc to ground.

2. Another way is to connect the reference voltage to the non-inverting input. For instance via a resistive voltage divider from Vcc to ground. Then you connect the feedback resistor from output to non-inverting input. Here again the voltage divider should contain resistors in the kiloOhm range, while the feedback resistor should be in the MOhm range.
The actual signal is applied to inverting input.
It can help to add a RC-low pass filter to inverting input.

Kai